Descriptive Archaeoastronomy and Ancient Indian Chronology [1st ed.] 9789811569029, 9789811569036

Table of contents :
Front Matter ....Pages i-xv
Introduction (Amitabha Ghosh)....Pages 1-10
Rudiments of Positional Astronomy and Archaeoastronomy (Amitabha Ghosh)....Pages 11-41
Astronomy in Ancient India (Amitabha Ghosh)....Pages 43-60
Descriptive Archaeoastronomical Approaches (Amitabha Ghosh)....Pages 61-86
Archaeoastronomical Study of Ancient Indian Chronology: Dating Mahābhārata (Amitabha Ghosh)....Pages 87-107
Chronology of Vedic and Vedānga Periods (Amitabha Ghosh)....Pages 109-137
Archeaological, Geological and Genealogical Indications of Ancient Chronology (Amitabha Ghosh)....Pages 139-159
Back Matter ....Pages 161-198

Citation preview

Amitabha Ghosh

Descriptive Archaeoastronomy and Ancient Indian Chronology

Descriptive Archaeoastronomy and Ancient Indian Chronology

Amitabha Ghosh

Descriptive Archaeoastronomy and Ancient Indian Chronology

123

Amitabha Ghosh Indian Institute of Engineering Science and Technology Howrah, West Bengal, India

ISBN 978-981-15-6902-9 ISBN 978-981-15-6903-6 https://doi.org/10.1007/978-981-15-6903-6

(eBook)

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

To Arunabha Siddhartha Debolina & Mili So that they do not forget their roots

Preface

Though the term ‘archaeoastronomy’ is of relatively recent origin, the technique has been employed in estimating the antiquity of an ancient astronomical reference since quite some time. The author of this volume has taken the liberty of dividing the subject archaeoastronomy into two classes—physical archaeoastronomy and descriptive archaeoastronomy. In physical archaeoastronomy, ancient structures are studied for possible stellar alignments. However, the scope of this technique is somewhat limited as very few ancient structures of adequate antiquity are available for application. The only exceptions are the major pyramids of Egypt and some ancient megalithic structures. In all these cases, however, only the astronomical alignments are related to the rise and setting of the sun on the solstitial and equinoctial days. In some cases, the rising and setting of moon are also studied. The types of studies are conducted mainly to understand the cultural aspects of the ancient civilizations. Since the sunrise positions on the solstitial and equinoctial days do not change due to the precessional motion of the earth, no information regarding the antiquity can be extracted from these studies. India’s case is very unique as it possesses a vast corpus of very ancient literature rich with a large number of astronomical references. In many cases, the stellar alignments can help in determining the antiquity of a particular description. Of course, often only an approximate idea about the antiquity can be gained because of the inherent inaccuracies involved in the ancient naked-eye astronomical observations. Only in some cases, somewhat accurate dating is feasible using the analysis of some spectacular astronomical events like total solar eclipse described in the ancient texts. It is hoped that the database of ancient astronomical references can be expanded in the future. With this expanded database, appropriate computer programmes can be developed that can help more precise dating employing a 'temporal triangulation' technique type approach. This book is written for general readers only and, so, a chapter on positional astronomy presents the basic ideas and terminologies of positional astronomy. The phenomenon of the precessional motion of the spinning earth has been explained in detail. The effects of this precessional motion on the stellar alignments and other

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astronomical matters have been explained. The applications of these effects for dating old astronomical observations have also been elaborated. Since one has to refer to the ancient observational references, it is essential for one to be familiar with the system of positional astronomy followed by the ancient observers. In this respect, India offers a very rich heritage as astronomy was developed in ancient India to a reasonable degree of sophistication. Thousands of years of observation led the ancient astronomers of India to develop a luni-solar calendar based upon the twenty-seven nakshatras as the markers in the sky. The twelve zodiacal sign-based astronomy was started towards the beginning of the common era. Apart from the precession of the equinox, the exaltation of a planet against a particular nakshatra can also help in dating ancient observation. An application of this technique has also been presented. Various astronomical references in the scriptures have been studied and an approximate chronology has been developed. However, to create enough confidence in the approximate chronology of the protohistoric period of India, the astronomical dating has been corroborated by other approaches. As has been declared by many scholars, the sheet anchor of ancient Indian history is the Mahābhārata war. Because of this, a very large number of scholars have attempted to arrive at the date of this epochal event. The results have been presented. Once the Mahābhārata date is decided, the recorded genealogical trees of the ancient kings help one to guess the antiquity of the various periods ruled by these kings. This way a tentative chronological order can be established. Major geological happenings also provide some clue to the ancient India’s history, and a very large number of scholars from eminent research organizations are working along this direction. Although a very direct archaeological corroboration of the events described in the ancient texts is still not possible, many eminent archaeologists appear to have found indirect evidences. A major problem in Indian archaeology is the extensive settlements above the ancient sites. But with the advent of more advanced technologies in this area, it is hoped that in the near future more conclusive evidence of many major events of Indian civilization will be found out. As mentioned, this book is meant for general readers only so as to make them interested in the subject. It is hoped that this volume will also make many to be aware of the current level of the understanding of ancient India’s civilization. Professor Asok Mallik has critically examined the manuscript and his suggestions have made remarkable improvement. He deserves most sincere thanks from the author. The author is grateful to his wife Meena for her constant supportive actions. Sincere thanks are also due to his son and daughter-in-law, Arunabha and Debolina. Sourav Kundu has done an excellent job of typing the manuscript. Author’s former student Deepayan has helped him by developing the computer programme for solving some nonlinear equations related to the change in relative positions of the stars with the passage of time. The author would also like to record his thanks to Mr. Ashok Bhatnagar, former Director, Positional Astronomy Centre, for providing the websites for studying eclipses. This book would have not been possible without

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the interest taken by Ms Swati Meherishi of Springer. The author is grateful to her. Many friends and colleagues of the author provided him constant encouragement to work in this field and all of them are being thankfully acknowledged. Finally, the author takes this opportunity to thank the Indian National Science Academy, New Delhi, for providing the financial help to meet the cost of preparation of the manuscript. A book of this nature is bound to have mistakes and omissions of various types. The author will remain grateful if these are pointed out by the readers. There will be sincere efforts to make the corrections and to take care of the suggestions received to prepare an improved version in its next edition. Shibpur, Howrah, India Deepavali 2018

Amitabha Ghosh

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Importance of Chronology in History . . . . . . . . . . . . . . 1.3 Problems with Establishing Ancient Indian Chronology 1.4 Application of Astronomical Technique . . . . . . . . . . . . 1.5 Influence of Astronomy on Society . . . . . . . . . . . . . . . 1.6 Structure of Ancient Indian Chronology and Its Self Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Rudiments of Positional Astronomy and Archaeoastronomy 2.1 Introduction to Positional Astronomy . . . . . . . . . . . . . . . . 2.1.1 A Few Basic Points . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Celestial Coordinates . . . . . . . . . . . . . . . . . . . . . . 2.2 Variation in Astronomical Parameters . . . . . . . . . . . . . . . 2.2.1 Periodic Variations . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Secular Changes . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Eclipse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Physical and Descriptive Archaeoastronomy . . . . . . . . . . . 2.4.1 Physical Archaeoastronomy . . . . . . . . . . . . . . . . . 2.4.2 Basics of Descriptive Archaeoastronomy . . . . . . . . 3 Astronomy in Ancient India . . . . . . . . . . . . . . . . . . 3.1 Importance of Understanding the Ancient Indian Astronomical System . . . . . . . . . . . . . . . . . . . . 3.2 Rediscovery of Ancient Indian Astronomy . . . . . 3.3 Major Features of Astronomy in Ancient India . . 3.3.1 Presiddhāntic Astronomy . . . . . . . . . . . . 3.3.2 Siddhāntic Astronomy . . . . . . . . . . . . . .

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4 Descriptive Archaeoastronomical Approaches . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Effects of the Precession of the Equinoxes on Observational Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Changing Relation of Seasons with Lunar Month . . 4.2.2 Simultaneous Transit of Important Stars . . . . . . . . . 4.2.3 Heliacal Rising of Stars and Constellations . . . . . . . 4.3 Exaltation of Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Ancient Eclipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Advance of Perihelion of Earth’s Orbit . . . . . . . . . . . . . . . 4.6 Saptarshi Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Archaeoastronomical Study of Ancient Indian Chronology: Dating Mahābhārata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introductory Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Ancient India’s Geographic Boundaries as Implied in Ancient Texts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Structural Framework for Ancient Indian Chronology . . . . . . . 5.4 Genealogy of Puranic Dynasties . . . . . . . . . . . . . . . . . . . . . . 5.5 Date of Mahābhārata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Types of Astronomical References . . . . . . . . . . . . . . . 5.5.2 Dating Mahābhārata War . . . . . . . . . . . . . . . . . . . . . . 5.5.3 Consistency of Mahābhārata Date with Other Sources . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Chronology of Vedic and Vedānga Periods . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Hints to High Antiquity of Vedas . . . . . . . . . . . . . . . . . . . 6.3 Astronomical References in Vedic and Other Ancient Texts 6.3.1 Heliacal Rising of Ashvins at Winter Solstice . . . . . 6.3.2 Madhu Vidyā and Heliacal Rising of Ashvin . . . . . . 6.3.3 Orion’s Head Near Vernal Equinox . . . . . . . . . . . . . 6.3.4 Heliacal Rising of Maghā (a Leonis) on Summer Solstice Day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.5 Dogs of Yama and the Direction to Pitriloka . . . . . . 6.3.6 Prajāpati-Rohini Legend . . . . . . . . . . . . . . . . . . . . . 6.3.7 Solar Eclipse Recorded in Rigveda and Tāndya Brāhmana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Astronomical References in Brāhmanas . . . . . . . . . . . . . . . 6.4.1 Krittikā Never Swerves from the East . . . . . . . . . . . 6.4.2 Solar Eclipse and Heliacal Rising Described in Brāhmanas . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6.5 Vedānga Jyotisha . . . . . . . . 6.6 Dating Through Astrological 6.7 The Emerging Picture . . . . . References . . . . . . . . . . . . . . . . .

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7 Archeaological, Geological and Genealogical Indications of Ancient Chronology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Consistency of Astronomical Dating . . . . . . . . . . . . . . . . . 7.2 Lost River Sarasvati . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Changing Sea Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Genealogical Sources for Investigating Ancient Indian Chronology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Archaeological Discoveries and Ancient Indian Chronology References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Appendix A: Spherical Trigonometry and Astronomy . . . . . . . . . . . . . . . 163 Appendix B: Positions of Nakshatras and Zodiacal Signs . . . . . . . . . . . . 179 Appendix C: Genealogical Lists of Puranic Kings . . . . . . . . . . . . . . . . . . 181 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

About the Author

Amitabha Ghosh received his Bachelor’s, Master’s and Doctoral degrees in Mechanical Engineering from Calcutta University in 1962, 1964 and 1969, respectively. After serving as a Lecturer in Mechanical Engineering at his alma mater, Bengal Engineering College, Shibpur (now an Institute of National Importance—Indian Institute of Engineering Science and Technology, Shibpur) from 1965 to 1970, Prof. Ghosh joined Indian Institute of Technology Kanpur as an Assistant Professor in January 1971. He served at the Institute as a Professor of Mechanical Engineering from 1975 until his retirement in 2006. From 1977 to 1978, Professor Ghosh visited the RWTH Aachen as a Senior Fellow of the Alexander von Humboldt Foundation, and subsequently visited the RWTH Aachen in the same capacity several times between then and 2012. He served as Director of the Indian Institute of Technology Kharagpur from 1997 to 2002. His primary areas of research are manufacturing science, robotics, kinematics and mechanism theory and dynamics of mechanical systems. Prof. Ghosh has received many academic awards including a number of Calcutta University Gold Medals, the D.Sc. (h.c.), Distinguished Teacher award from IIT Kanpur and the Award for Excellence in Research by the National Academy of Engineering.

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Chapter 1

Introduction

1.1 Preamble The dawn of civilization in ancient India is still shrouded in mystery and controversy. Whether civilization flourished in the soil of Indian subcontinent or was brought from outside by the invaders is still not conclusively established and the subject is still hotly debated. It was not customary in ancient India to record history in the conventional way. Since it is generally accepted by scholars and historians that literature reflects the characteristics of contemporary society and depends in many situations on the actual events, quite often historians use such literature in establishing history. Unfortunately, when it comes to the history of ancient India the western scholars refuse to accept the vast literature available from ancient India to have any relation with the real happenings of ancient India and consider such literature not to reflect real events and treat all such literature to be purely figments of imagination. However, many ancient texts refere to historical events. In fact quite a few Pur¯anas viz V¯ayu Pur¯ana and Brahm¯anda Pur¯ana state very clearly that they record history. In the concluding chapter of V¯ayu Pur¯ana it states.

When translated it means “The learned Br¯ahmana who hears or tells or teaches the old history will enjoy happiness for eternity in the abodes of Mahendra.”

Pur¯ana word itself implies history (Daftari 1942). Most Indian scholars and historians also do not dare to oppose the stand taken by conventional scholars and ignore the huge amount of ancient literature while establishing the ancient history of India. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 A. Ghosh, Descriptive Archaeoastronomy and Ancient Indian Chronology, https://doi.org/10.1007/978-981-15-6903-6_1

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1 Introduction

Of course, the primary reason behind such an attitude is because of extensive use of allegory in the descriptions of ancient events in such literatures. Even though, the events described in these scriptures and epics may not be taken to reflect real events, there is no reason why the description of contemporaneous stellar alignments in the sky should be considered totally imaginary and devoid of any relation with the reality. As will be shown later in this volume, the characteristics of the celestial sphere change with the seasons. Besides, this season-sky correlation also slowly varies with time very slowly due to the precession of the equinox. It takes about 26,000 years to complete a cycle and, therefore, this phenomenon can function as a time keeper covering the whole of late Pleistocene and the Holocene periods. Thus, almost the whole history of the modern man after civilization began is taken care of by this phenomenon. Of course, there are two other techniques which are used for dating of ancient events besides using the precession of the equinox. One of these is to study the descriptions of ancient total or annular solar eclipses. A total or annular solar eclipse at a particular location at a particular day of the year and at a particular time of the day is an extremely rare phenomenon. Apart from that these types of events are very spectacular in nature and cannot go unnoticed. Study and analysis of such descriptions can help in establishing the antiquity of the event. A third technique that is used occasionally for establishing antiquity is the exaltation of the planet Mars. Since this phenomenon plays a very important role in astrology, there are enough references of exaltation of Mars in the past. But this phenomenon plays a relatively less significant role in establishing ancient chronology. It has been noticed that the major structures in the ancient times used to be constructed keeping a strict alignment with the cardinal directions. Apart from that many features of such important major structures used to have unique relationship with contemporary stellar alignments. Such alignments are lost due to the precession of the equinox. Studying the accumulated error in the alignments it is possible to estimate the time elapsed after the original construction. Such techniques of physical archaeoastronomy have been applied to the study of major pyramids of Egypt and some other major structures in other ancient civilizations. The results have been found to be quite useful and indicative. Unfortunately, in ancient India there was no tradition of constructing major structures in memory of kings, queens and other important personalities. Megasthenis wrote in his memoir on ancient India of the third century BCE that in ancient India it was believed that a person was remembered after his/her death because of the good work done. Only after Buddha’s time (seventh century BCE) major structures were started; but these were also not enough in number. Besides, the post Buddha period comes within the purview of recorded history of India. Thus, India lacks huge structures created in ancient times; and, consequently, the technique of physical archaeoastronomy is not of much assistance in establishing the ancient chronology. But India possesses a unique wealth—a huge body of ancient scriptures and literatures rich in astronomical description. Over and above that, positional astronomy in ancient India was very well developed and matured. Therefore, the descriptions of ancient star alignments and their arrangements in the celestial sphere are quite significant. Above all, astronomical observation and its recording played a very significant

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role in the daily house hold activities. Many texts, viz. Mah¯abh¯arata, contain a large amount of descriptions of various astronomical phenomena many of which can be very useful for application of descriptive archaeoastronomy. Of course, in most situations exact dates cannot be established but reasonably good idea about the epoch for a particular astronomical reference can be formed. Application of archaeoastronomical technique requires a number of precautions. The descriptions of a phenomenon that is being analyzed should be as unambiguous as possible for a correct interpretation and casting it in modern scientific language. The descriptions should be also reasonably accurate and well specified. Good results can be obtained if the described phenomenon is reasonably rare. Establishing antiquity through analyses of reasonably frequent phenomenon is difficult and not very reliable. The names of various stars given in ancient descriptions need to be matched carefully with those used in the present times. Since positional astronomy reached a high level of maturity, many times the descriptions are highly scientific. The last text of ancient Indian astronomy that has been preserved is Ved¯anga Jyotisha which gives various algorithms for different astronomical calculations. This has been dated around 1400 BCE. This dating has been done by analyzing the astronomical characteristics contained in the text itself. The ancient chronology that has emerged through the application of descriptive archaeoastronomical technique matches well with that obtained through other procedures. This provides the technique and data enough credibility and the results can be accepted as reasonably correct. It is important to have some minimum idea of positional astronomy for understanding the techniques used in descriptive archaeoastronomy. Therefore, a simple introduction to the subject has been given in this volume so that the reader can follow the procedure without requiring to refer to other books. Apart from this it is necessary to have some basic idea about the astronomy followed in ancient times for applying the techniques of archaeoastronomy to ancient descriptions. It is important to know the terminologies used in the past and the system developed for the description of the stellar arrangements. The section on ancient Indian astronomy is very useful to the readers who are not already familiar with the subject and this volume becomes self explanatory. Establishing ancient Indian chronology by employing the technique of descriptive archaeoastronomy is not a new subject. Even in the nineteenth century various scholars and astronomers have worked in this field. Very notable work on this subject was done by Prof. Prabodh Chandra Sengupta in the 3rd and 4th decades of the twentieth century as an eminent Professor of Astronomy in Calcutta University. His book ‘Ancient Indian Chronology’ was published by Calcutta University Press in 1947. This is a valuable asset to the researchers in this field. However, this book is not very easy to follow by common readers as it was written for the professionals in the area. Calcutta University had excellent programmes on ancient astronomy. Its deterioration is a matter of great concern as such subjects have been abandoned since long.

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1 Introduction

With the advent of computer science many planetarium softwares have been developed. Using these it has become much easier to analyze astronomical data. Earlier analysis of ancient astronomical data was a laborious task and only highly competent astronomers could handle the task. Since now it has become much easier, many enthusiastic scholars can make significant contributions in the field and enrich the understanding of ancient India. One of the primary objectives of this book is to encourage common readers with familiarity with ancient scriptures and some interest in basic astronomy to contribute and enrich this field. If this book helps to create enough awareness and interest among common readers the author will find his endeavour a success.

1.2 Importance of Chronology in History History of a country unravels the story of her progress with time. It encompasses all areas of activities involving politics and governance, development of infrastructure, growth of economic status and, of course, progress in education leading to expansion of the knowledge domain. Since all these are intimately related with the passage of time the temporal interrelation of various aspects are inseparable components of a nation’s history. It is well known that in most situations culture and customs followed by a society are dynamic entities and change with time. Indian civilization is considered to be the oldest living and continuing civilization in the world. The Indian society has undergone many transformations although certain basic features of the Indian civilization have remained unaltered. Knowing the history of one’s own country is essential for preserving one’s dignity and self confidence. It is observed that all societies show a keen interest in establishing the antiquity of their beginnings and the progress along the path of civilization. Generally one feels happy to be a part of a society whose civilization is old and possesses a rich ancient history. Even if one does not agree to the suggestion that history teaches a society to avoid earlier mistakes in the future activities, it is generally accepted that being aware of a rich historical past can be useful in providing impetus to future growth of civilization. In the case of India the importance of establishing the correct history of her past is more important as it is still shrouded in mystery and is full of controversies. It is very important to figure out how this great and ancient civilization started in Indian subcontinent. The richness of Sanskrit language has tempted the scholars of the whole world to investigate the past history of this language. Chronology forms a very important component of history and without a correct chronological component history is never complete. It is for this reason a major task of the archaeologists is to establish the date of their new findings. A very large number of scientific methods have been developed for this purpose and with the progress of science and technology newer methods are being invented. Recording of history needs the dates and the historians attempt to estimate the dates by establishing these events, relationships with certain cardinal events for which the dates are already

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established. Such events are usually termed as ‘sheet anchors’; for example the western scholars consider the visit of Alexander as a sheet anchor in Indian history. Using this the period of Gautam Buddha has been estimated and, according to most western historians, the history of India begins with the birth of Buddha! Nothing can be more ridiculous! It is very well known that civilization in India must have a hoary past as indicated in many contemporary literatures. Max Mueller attempted to date the most ancient text of the world ‘Rigveda’. He gave some adhoc decisions based on a number of unsound assumptions and at a later time he himself withdrew his suggestion that Rigveda is 3200 years old. This again he related to a proposed hypothesis suggesting that there was an invasion by a western race termed as ‘Aryan’ and it was taken for granted that India’s civilization was brought by these invading ‘Aryans’. However, the scenario got completely transformed after the discovery of the Indus Valley cities which were estimated to be more than 4000 years old. Subsequently a huge amount of investigation has shown that many settlements in the north and north-west part of this subcontinent are more than 9000 years old. An erroneous dating of Rigveda by Max Mueller has introduced enormous aberration in the history of India resulting in a large number of controversies and mystery. It very clearly indicates how important it is to establish a correct chronological order. Without correct estimates of the antiquity of various phases of the past history of India it will not be possible to form a correct picture of the progress of civilization.

1.3 Problems with Establishing Ancient Indian Chronology Indian subcontinent lies in the tropical region and, therefore, is a very suitable place for sustaining all forms of life. Because of its temperate climate, abundance of water, plant and animal life it is expected that it is a very suitable location for civilization to flourish. However, at the same time the tropical climate does not permit preservation of ancient objects and all evidences of ancient structures decay with time unless these are made out of stone or similar durable materials. According to the writings of Megasthenis Indian people did not have the custom of erecting large structures in memory of kings; the philosophy was that a person should be remembered by his/her good work done during his/her life time. Thus, evidences of ancient creations are not in abundance in the country. Although language and literature in ancient India were extremely well developed there was no tradition of recording history in the conventional format. Whatever information the ancient people wanted to preserve these were in allegorical form couched in complex language. Perhaps, the objective had been to make the knowledge inaccessible to the general public. There is a huge amount of ancient literature. It is quite indicative of the existence of a very well developed civilization from very ancient times but explicit proofs of that is not available. This leads to a situation where conflicting conjectures and interpretations can be arrived at depending on the personal bias of the historian/scholar involved.

6

1 Introduction

India was ruled for many centuries by the people from the Islamic world and they had no interest in the ancient history of the country, nor were they interested in the ancient wisdom of India. Only after the British rule was established in India the western scholars started investigating the ancient past of this country. The richness of Sanskrit language and its similarity with the European and other languages drew their attention to investigate the possible origin of Sanskrit language and its relation to other languages. Since there was no archaeological evidence of any ancient civilization in Indian subcontinent it was surmised that some outside race (termed as Aryan) came from the west along with Sanskrit language and established the ancient Indian civilization. In the nineteenth century this theory became very popular and was known as the Aryan Invasion Theory. It was suggested by the famous Indologist Fredrich Max Mueller that these ‘Aryans’ came to India around 1500 BCE. They created the vedic literature and the basic foundation of what is known as Hindu religion, was laid. This theory explained a few things no doubt. It became easy to explain why the Indian subcontinent has two totally different language groups—north Indian languages derived from Sanskrit and the four languages of south India which do not appear to have any relation with Sanskrit and represent the language prevalent in India before the ‘Aryans’ came from the west. The AIT (Aryan Invasion Theory) became extremely popular with the western scholars, particularly the British rulers for a number of reasons, a detailed discussion of what is out of place here. And gradually the theory took the form of an established truth. On the contrary, no Indian tradition hints at such a situation. It was never imagined in India that Sanskrit is a language from outside and the ancient civilization of India was an import from outside. All ancient literatures give extensive details of happenings and events in ancient times but nowhere in this huge body of literary work there is any indication of Aryan Invasion! The date of Rigveda was fixed by Max Mueller to match his suggested date of Aryan Invasion and he suggested that the antiquity of Rigveda does not go beyond 1200 BCE. In the third decade of the twentieth century the Indus Valley civilization was discovered and the antiquity of Indian civilization was pushed back immediately by more than two millennia. But the theory of Aryan Invasion continued to rule the scene and, even today, it is a matter of serious debate if Indian civilization is indigenous or a foreign import. Thus, the true story of ancient India is still a debatable issue. The very large amount of ancient literature can be used to date the events described therein and some idea about the ancient Indian chronology can be formed. On the whole it has remained as a difficult task to establish ancient Indian chronology in the absence of conventional evidence of various major events described in the ancient literature available to us at present. One group of scholars, predominantly from the west, refuses to accept the major epics like R¯am¯ayana and Mah¯abh¯arata to have any relevance to reality and are considered as purely imaginary stories. Since the conventional archaeological techniques cannot help us in dating ancient scriptures, application of the technique of archaeoastronomy can be useful and can yield scientifically established information.

1.4 Application of Astronomical Technique

7

1.4 Application of Astronomical Technique It is mentioned in the previous section that no ancient structure or artifacts are available in India for applying conventional dating techniques. In case of India, however, something unique is available– the large volume of ancient scriptures and literatures. As astronomical observation has been an integral part of many ancient civilizations, ancient Indian literature is also full of astronomical references. It has been briefly hinted at the possibility of its use in the preamble. The star alignments have very specific relation with the seasons and this relationship changes very slowly with time as mentioned earlier. Since observation of such stellar arrangements for the onset of various seasons was an integral part of the ancient society, records of such observations are available in ancient texts. Examining the difference with the currently observed stellar patterns at different seasons, an idea about the antiquity of the recorded observations can be formed. It is not only the seasonal relationship which can be helpful for the dating technique there were other types of very interesting features of the ancient stellar alignments which are now different. This variation can be used to determine the epoch when the recorded observations were possible. Total and annular solar eclipses are also spectacular astronomical phenomena and such events rarely go unnoticed. Apart from being very interesting and rare, many rituals got associated with eclipse phenomena in Indian custom. A total or annular solar eclipse at a particular location is not a frequent phenomenon. So, studying the location, the date in a solar year and a particular time in a day, an eclipse can be dated. Since matching all conditions becomes a rare possibility, very ancient dating is possible. A number of planetarium softwares are available with which the dates of such ancient observations of total or annular solar eclipse can be derived. Since the phenomenon depends on the umbra of moon’s shadow falling at a particular spot on the earth’s surface the history of earth’s rotation must be accurately known for such dating. Sometimes error may occur due to certain uncertainties in the information about exact rotational history of the earth. Thus using the description of ancient eclipses may not always help in establishing the chronology. Astronomy in India was reasonably well developed even in the proto historic period. In the presiddhantic1 astronomy a very well developed ‘Nakshatra’ system used to be followed in which the groups of stars at locations occupied by the moon during a lunar month were identified and used as the markers in the sky. Thus, these 27 nakshatras along the ecliptic became a very well defined frame of reference for the planets, the sun and the moon. The positions of the sun along the ecliptic at different seasons were also recorded in ancient texts and such information can be used for astronomical dating as will be elaborated in the later chapters.

1 Siddhantas were authored from the onset of the common era and became matured from the time of

Aryabhata I (fifth century CE). The astronomical system before that is termed as ‘Presiddhantic’.

8

1 Introduction

Deriving the epochs from astronomical references may not provide very accurate results always but a reasonably good idea about the antiquity of ancient events, as described in ancient texts, can be achieved. In some cases very interesting star alignments are found in the ancient texts. As in many cases these are couched in allegory correct interpretation of such events is essential. Some very interesting cases exist in ancient Indian astronomical observations and scholars have used such descriptions to form some idea about the antiquity of the observations. Another phenomenon that is rare is the exaltation of the planet mars. Though this phenomenon has special significance in astrology, it represents very special astronomical configurations involving Mars, the sun and the earth. Such events occur at long periods of interval and description of the exaltation of planet mars against the backdrop of a particular nakshatra can help in establishing the date of occurrence of the event. In some isolated cases this phenomenon has been used for the dating of ancient observations. In Indian custom offering prayers facing the east at very early hours of dawn used to be a common practice, particularly among the sages and priests. This resulted in observing the stars which were visible just before the sunrise (called heliacal rising). Heliacal rising of some stars became identified with the seasons. This correlation of heliacal rising of some identified stars (or constellations) with the tropical seasons also undergoes change with the passage of time. This provides another technique for ancient dating. In case of ancient India this extensively practised observation form a rich source of material for application to establish ancient chronology. Since in ancient times the observation used to be done through naked eye astronomy the accuracy of positions etc. were limited. Therefore, a few other types of effects due to the variation of astronomical parameters cannot be of much help. The most dependable methods are based on the precession of the equinox (to be explained in the next chapter).

1.5 Influence of Astronomy on Society Since the dawn of civilization mankind has remained fascinated by the star filled sky and the apparent movement of the celestial objects. As the time progressed and the quality of observation improved many interesting correlations of the stellar alignments with the phenomena on the earth were established. The changing shape of the moon during a lunar cycle (called a lunar month) and the daily rising of the sun became two most important factors for calendrical purposes. Changing phase of the moon became one of the obvious markers for keeping track of the day; this has been followed by many tribal societies and is followed even at the present times. Man also observed some connection of the terrestrial phenomena with the sky. For example the strength of the ocean tide depends on the lunar phase, position of the sun among the constellations dictates the seasonal changes and the menstrual period of the women is linked with the lunar cycle. Thus, relating the rituals with astronomy was a very natural thing to happen. This led astronomy to be an influential subject and

1.5 Influence of Astronomy on Society

9

the tradition of linking the heaven with the daily life on the earth slowly developed. In many ancient civilizations where erecting huge monuments and structures used to be practised, using astronomical alignments for planning such structures was quite frequent. Major examples are the pyramids in Egypt and Central America. Even the prehistoric megalithic structures and arrangement were created with special astronomical alignments to identify the solstice and equinoctial days during a year. So, it is very natural that during the proto historic period astronomy played a major role in the daily affairs of the society. As a result in ancient India, where astronomy reached a well developed state, the literature is full of astronomical references.

1.6 Structure of Ancient Indian Chronology and Its Self Consistency Being the cradle of the most ancient continuous civilization of the world India’s correct chronology is essential for understanding the development of world civilization. At the same time scholars over the last two centuries have found the task extremely elusive and complex. As mentioned earlier the study of ancient India’s chronology has been further complicated by a number of false steps at the early stage of the subject. Correcting those mistakes and erasing the wrong impressions and removing the fixed motions in the people’s minds created by the long standing dogmas render the subject very challenging. Above all the subject of ancient India’s chronology is increasingly becoming more multidisciplinary in nature. In the 19th and early twentieth century the scholars had to depend primarily on the conventional procedures for studying history. Soon the subject of linguistics emerged and the technique of linguistics used to be employed for establishing the antiquity of a text and the descriptions therein. With this procedure there are significant chances of personal bias to influence the interpretations and opinions. An approach dependent on scientific principles can be more immune to such problems and may lead to dependable results. Since the beginning of the third decade of the twentieth century archaeological discoveries opened up new vistas for ancient India’s civilization, and, with the progress of time many new scientific methods are being developed for determination of antiquity of objects. Besides, new subjects like archaeoastronomy, paleoclimatology are emerging to enrich the facilities for the determination of age. Studies of the signature left by the past geological processes are also being employed for establishing ancient chronology. Modern techniques with the applications of satellite imagery are also helping the scholars in this endeavour. As indicated earlier the dependability of the derived chronology becomes significant if its consistency with other aspects of ancient India can be demonstrated. Thus, the ancient India’s chronology has to accommodate the Puranic genealogical order; archaeological data unearthed so far, the results of genetic study and the geological and climatological evidences. That is how the subject has become intensely multidisciplinary. As a result it is now beyond the capability of a historian to establish

10

1 Introduction Vedic and Puranic tradition

Astronomical pointers Mahabharata War

Gautama Chandragupta Buddhaa

Time line Puranic genealogical list of kings Sindhu – Sarasvati civilization

Mahapadma Nanda

Proto-historical period

0 CE

Historical period

Vedic Sarasvati and climate change

Fig. 1.1 The Composite nature of task of determining ancient Indian chronology

the chronology single handedly (as the earlier scholars used to do in the 19th and early twentieth century). Complexity of the task can be understood from a study of Fig. 1.1, that shows the structure of the task and the complexity of the exercise of establishing the consistency with other aspects is clearly visible.

Reference Daftari, K. L. – “The Astronomical Method and its Application to the Chronology of Ancient India”, Nagpur University, 1942.

Chapter 2

Rudiments of Positional Astronomy and Archaeoastronomy

2.1 Introduction to Positional Astronomy To understand the basic principles behind the techniques of archaeoastronomy, it is essential to have some idea about positional astronomy. Positional astronomy is a subject that is primarily involved with the positions of various celestial objects at different times of the day/night during a solar year. It also considers special events like eclipses. In the ancient times, observers of the sky had to depend on nakedeye observation using some simple devices. A good discussion on ancient Indian astronomy can be found in History of Science in India, vol. 1, part 2.

2.1.1 A Few Basic Points The stars are so far away that it is not possible for us to have any perception of their distances and all stars (and other celestial objects) appear to be attached to a sphere. This apparent sphere is called the celestial sphere. As the earth spins about its own axis once every day, the celestial sphere along with all objects on it appears to rotate in the opposite direction. The position of our solar system in the galaxy that is our island universe, the Milky Way galaxy, is indicated in Fig. 2.1. It is a vast system of about 1011 stars and our solar system lies in a relatively insignificant position approximately 30 × 1016 km from the centre. The whole system rotates about a central axis taking 25 × 107 years to make one complete rotation. The white patch running across the night sky (called the Milky Way) is a view of the galaxy seen from our solar system. It should be remembered that we can see the stars with naked eye which lie within 500 light years1 only and the number of stars 1 Light

year is a measure of distance used in astronomy. It represents a distance covered by light in one year. It is equal to 9.46 × 1012 km (or, 5.88 × 1012 miles). © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 A. Ghosh, Descriptive Archaeoastronomy and Ancient Indian Chronology, https://doi.org/10.1007/978-981-15-6903-6_2

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2 Rudiments of Positional Astronomy and Archaeoastronomy

Fig. 2.1 Milky Way galaxy

visible with naked eye is around 3000. Thus, all ancient astronomy involved these 3000 stars, the planets, the sun and the moon. Our solar system’s main constituents are the sun, the planets, the moons of the planets, the asteroid belt and the comets (Fig. 2.2). In the ancient times, of course, the solar system bodies known were the sun, the moon, the jupiter and venus. Gradually, saturn and mars were discovered and a little later the planet mercury became known. Due to its proximity to the sun viewing this small planet was difficult with naked-eye astronomy. It is clear from Fig. 2.2 that the planets are almost confined to a plane in which they orbit the sun. Beside revolving around the sun the planets also spin about their own axes which are again almost perpendicular to the plane of the planets’ orbits. In the case of the earth’s axis, it is inclined to the direction perpendicular to the orbital plane at an angle of 23.5°. The orbital plane of the earth is

ASTEROID BELT

Fig. 2.2 Solar system major components

2.1 Introduction to Positional Astronomy

(a) The sun-earth-moon alignment on a full moon night

13

(b) The sun-earth-moon alignment on a new moon night

Fig. 2.3 Full moon and new moon nights

called the plane of ecliptic and all the other planets and their moons are in planes with very small deviations from the plane of the ecliptic. The orbits are almost circular; only the planet mercury and mars have slightly ecliptic orbits. The position on an orbit that is nearest from the sun is called the ‘perihelion’ (‘helios’ stand for the sun) and the point that is farthest from the sun is called the ‘aphelion’. It is also well known that the tilt of the earth’s axis from the normal to the plane of the ecliptic causes the seasons. Figure 2.3 shows the relative positions of the sun, the earth and the moon on full moon and new moon days. Figure 2.3a shows the new moon against a fixed star A. When viewed from the earth in all directions along the ecliptic plane, the situation is shown in Fig. 2.4. During the period called sidereal lunar period (the time taken by the moon to return to the same position in the backdrop of the fixed stars) it takes 27 positions per night and these positions are marked by groups of stars which are called ‘nakshatras’ in ancient Indian astronomy. These nakshatras are the 27 markers in the sky. It is obvious that these markers are all in the plane of the ecliptic when expanded in all directions as can be inferred from the figure. A synodic lunar month is the period from one full moon to the next full moon. In ancient Indian system, the name of a lunar month used to be decided by the that of the ‘nakshatras’ against which the full moon was located. Figure 2.5 shows the nakshatras used for naming the months in ancient Indian system. In the very early stages, completion of a month used to be at the full moon.2 At a later time, this ‘purnim¯anta’ system was replaced by ‘am¯anta’ system in which a month used to start at a new moon and conclude at the next new moon; the name of the month, of course, used be according to the ‘nakshatra’ against which a particular full moon used to take place. This is an important point for understanding the ancient astronomical descriptions in India. 2 In

ancient times ‘moon’ used to be called ‘m¯as¯a’ and the full moon, i.e. ‘purna m¯as¯a’ used to indicate the completion of a month. The word ‘purnamasi’ has come from this and later ‘month’ used to be called ‘m¯as¯a’.

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2 Rudiments of Positional Astronomy and Archaeoastronomy

MILKY WAY GALAXY

Galactic centre

50,000 light years

Mid Plane of Milky Way galaxy

27,000 light years Sun

60.2º

Plane of the ecliptic

Plane of the ecliptic Galactic Centre

Jyestha Earth’s orbit Bishakha Purbasarha

Earth

Sun

Shrabana Ashvini Mrigashira Only a few of the 27 nakshatras’ directions are shown here

Fig. 2.4 27 nakshatras

It has been mentioned earlier that because of the great distances of the fixed stars a depth perception is not possible and the sky, when viewed from the earth, appears to be a star studded sphere, which is called the celestial sphere (Fig. 2.6). If the terrestrial equator is imagined to be expanded, the corresponding circle on the celestial sphere is called the celestial equator. The plane of the ecliptic intersects the celestial sphere along another circle that is called the ecliptic. Since the planets,

2.1 Introduction to Positional Astronomy

15

Fig. 2.5 Nakshatras for naming the months in ancient India

Fig. 2.6 Celestial sphere, the ecliptic and the celestial equator

the 27 nakshatras, the moon and the sun all lie more or less on the plane of the ecliptic, when viewed from the earth all these objects appear to be more or less along the ecliptic in the celestial sphere (the sun lies on the ecliptic exactly). The positions on the ecliptic that are nearest to either the north or the south pole are called the

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2 Rudiments of Positional Astronomy and Archaeoastronomy

Fig. 2.7 View of the sky from φ° N position on earth’s surface

(a) Actual motion of the earth round the sun

(b) Apparent motion of the sun when viewed from the earth

Fig. 2.8 Actual and apparent motions of the earth and the sun

‘solstice’3 positions. The ecliptic and the celestial equator intersect at two points which are called the equinoctial4 positions. When viewed from a position on the earth (say at latitude λ° N) the sky view is as shown in Figs. 2.7 and 2.8 needs to be studied to understand the apparent observed motion of the sun along the ecliptic as indicated in Fig. 2.7. It shows how the sun appears to move in the easterly direction. It should be carefully noted that when viewed from the north celestial pole the orbital motion of the earth (and also the moon) is in the counterclockwise sense as indicated in Fig. 2.8.

3 ‘Solstice’ 4 ‘Equinox’

means sun at stand still condition. means equal night and day.

2.1 Introduction to Positional Astronomy

17

Fig. 2.9 Synodic and sideral periods of the moon

When the sun (when viewed from the earth) takes the solstice position (SS) it is the longest day in the northern hemisphere. Similarly, the winter solstice position (WS) of the sun corresponds to the shortest day in the northern hemisphere. The two equinoctial positions, VE 5 and AE, of the sun correspond to the two days when the day and night are of equal duration. The four days in a solar year, when the sun takes SS, AE, WS or VE—positions, divide the year in four parts (which are not exactly equal, of course). From the position WS to SS, the sun apparently moves in the northernly direction a little bit with the passage of every day and this half of the year is called the period of ‘Uttar¯ayan’ in ancient Indian astronomy. Similarly, the other half of the year during which the sun position shifts towards the south is called ‘Dakhsin¯ayan’. It should be remembered that it is not possible to see the star against which the sun is lying on a particular day. It has to be inferred from a whole year’s observation. As on the full moon night, the moon’s position against a star can be directly seen after six months the sun will be against that star. In summary, the sun, moon along with the objects on the celestial sphere apparently revolve around the earth once every day. The sun and the moon appear to move in the easterly direction; the sun moves by approximately 1° every day whereas the moon moves by about 13° everyday. The terminologies ‘sideral’ and ‘synodic’ periods of the moon are explained in Fig. 2.9. The earth moves from position E to E from one full moon to the next full moon (which is the synodic period). On the other hand, the moon can be seen to be against the same star A somewhat earlier. If θ be the angle rotated by the earth during a synodic lunar month, the moon will have to rotate ‘θ ’ amount less to reach the same position against a star A as was the case when the month begun. The sideral period is 27.3217 days whereas the synodic period is 29.5306 days.

5 VE

and AE means vernal (or spring) equinox and autumn Equinox, respectively.

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2 Rudiments of Positional Astronomy and Archaeoastronomy

2.1.2 Celestial Coordinates For quantitative representation of the alignments of the celestial objects, it is essential to device means of quantitative description of the positions. On a plane surface, the position of a point is quantitatively described with the help of a rectangular coordinate system as indicated in Fig. 2.10. This is a very well-known procedure and is taught in the high schools. The sky appears as a sphere (which is termed as the celestial sphere). Thus, a concept of lines (representing shortest distance between two points) equivalent to straight lines on a plane surface has to be developed. Figure 2.11 shows a sphere, S, with O as its centre. To find out the path along with the distance between any two points A and B on the spherical surface, a plane P is imagined that passes through O and the two points A and B under consideration. This plane intersects the sphere along a circle, G, that is called great circle. The distance between A and B is shortest when measured along the segment of the great circle passing through A and B. Thus, great circles are equivalent to straight lines on a plain surface. In the case of describing positions of the celestial sphere, these great circles are employed. There are mainly three different systems followed as described below. (i)

Equatorial system: Fig. 2.11a shows the celestial sphere with N as the north celestial pole and E as the celestial equator. It should be noted that the celestial equator E is a great circle. The intersection point of E and the ecliptic is Υ corresponding to the vernal equinoctial point. To specify the position of a celestial object, S a great circle is drawn passing through N and S as shown in the figure. This great circle meets the equator E at A. The angle ∠Υ OA (= α) is called the Right Ascension (R.A.) and the angle ∠AOS (= δ) is the declination. Traditionally RA is specified with time and the range is from 0h 0m 0s to 24h 0m 0s . This corresponds with the earth’s daily rotation. The declination can be both positive (when S is in the northern hemisphere of the celestial dome) and negative (when S lies in the southern hemisphere) just like terrestrial latitude.

Fig. 2.10 a Coordinates of a point on a plane and b a great circle

2.1 Introduction to Positional Astronomy

(a) Equatorial coordinate system

19

(b) Ecliptic system

(c) Horizontal system Fig. 2.11 Different coordinate system used in positional astronomy

(ii) Ecliptic system: Fig. 2.11b shows the scheme which is analogues to the procedure for defining positions on the earth’s surface with the help of longitude and latitude. The ecliptic is one of the great circles and another great circle is drawn through P and S (the celestial object) P being the ecliptic pole where a line from the earth’s centre perpendicular to the ecliptic plane meets the celestial sphere. These intersect at point B. The angle ∠Υ OB (= λ) is the celestial longitude and the angle ∠BOS (= β) is called the celestial latitude. In this system also, β can be both positive and negative depending on the side of the ecliptic S lies in. When the R.A. and the declination of an object are given, the celestial longitude, λ, and celestial latitude, β, can be easily found out from the following relations sin β = sin δ cos φ − cos δ sin φ sin α and,

(2.1a)

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2 Rudiments of Positional Astronomy and Archaeoastronomy

cos λ =

cos δ cos α cos β

(2.1b)

where φ is the latitude of the observer’s location on the earth. The coordinates in the equatorial system, α and δ can be readily calculated in terms of λ and β from the following relations: sin δ = sin β cos φ + cos β sin φ sin λ

(2.2a)

and cos α =

cos β cos λ cos δ

(2.2b)

(iii) Horizontal system: The previous two systems are without any reference to the observer on the earth’s surface and are more abstract in nature. There is a third system that is directly related to the position of the observer and, therefore, quite convenient to use. The vertically top point (directly above the observer), Z, is called the zenith. The circle H defines the horizon (and the plane contained is the horizontal plane). A great circle is drawn passing through Z and the north celestial pole N. This great circle meets the horizon circle H at point P which is called the ‘north point’. The position of S is defined by two angles, ∠POC (= A, measured from east to west, i.e. in the CCW sense when viewed from the zenith Z) is called the ‘azimuth’, and, ∠COS (= a) called the ‘altitude’. This system is convenient for local observations with short duration. It is obvious that this system is not universal and varies from place to place on the earth. Since this system is dependent on the observer’s location, it is often desirable to transform the position coordinates to a system that is independent of the observer’s location. Thus, once the azimuth (A) and the altitude (a) are known the R.A. (α) and the declination (δ) can be determined from the following relations6 sin δ = sin α sin φ + cos a cos A cos φ

(2.3a)

and, sin H = −

sin A cos a cos δ

(2.3b)

with α = t – H, t being the local sideral time where φ is the latitude of the observer’s location.

6 Refer

to Appendix A for an introduction to spherical trigonometry and relation among various quantities.

2.2 Variation in Astronomical Parameters

21

2.2 Variation in Astronomical Parameters In the previous section, the basic parameters of the sun--earth--moon--planet system has been discussed. Almost all the parameters undergo variation with time. Some variations are secular and some are periodic. Brief descriptions of the important variations are presented below.

2.2.1 Periodic Variations Certain variations of the astronomical parameters are periodical in nature. For example, the tilt of the earth’s axis fluctuates between a minimum of 22.5° and a maximum of 24.5° and the period of this fluctuation in 41,000 years. However, the effects of the fluctuation cannot be observed with naked-eye astronomy and, therefore, cannot have any usefulness in archaeoastronomy. The earth’s orbit is slightly elliptical and the eccentricity of the ellipse representing the earth’s orbit fluctuates with time. The fluctuation has two main periods. The shorter period’s duration is 100,000 years whereas the cycle has a longer period of 413,000 years. The magnitude of the eccentricity varies between 0.005 and 0.0607. Though such variations have this effect on observational astronomy, it is not possible to expect any indication of an effect of varying eccentricity in the naked-eye observations of the ancient Indians.

2.2.2 Secular Changes There are mainly three parameters subjected to monotonic variations and produce some effects on astronomical observations. Advance of perihelion: One of the monotonically varying parameters is the advance of the perihelion position of the earth’s elliptic orbit (Fig. 2.12). The period of this advance is at the rate of 11.45 per year, i.e. about 113,000 years for one cycle. Since the orbital speed depends on the distance from the sun, the time taken to traverse the perihelion region is short and this effect in conjunction with the orientation of the earth’s axis controls the duration of the seasons. But this effect is also very subtle and is not of much use for the astronomical dating purpose. Slowing down of the earth’s spin: Another monotonically changing parameter is the rotational speed of the earth about its axis. It is now established that the earth is slowing down at a rate of 6 × 10−22 rad s−2 . This affects the number of the earth days in a solar year. Currently, a solar year’s duration is approximately 365.24 days. But as the earth had higher spinning rates in the past, the number of days was larger as can be seen from Fig. 2.13.

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2 Rudiments of Positional Astronomy and Archaeoastronomy

Fig. 2.12 Advance of the perihelion of the earth’s orbit

Fig. 2.13 Variation in the number of days per year

About 500 million years ago it was approximately 410 days every year. So, 5000 years ago the earth used to rotate at a faster rate and the day used to be of about 39 s lesser duration. For naked-eye astronomy, this effect is not noticeable but this variation in the rotational speed of the earth influences the dating of ancient total solar eclipses at a given place. Since the history of the variation in the spinning rate is not exactly known the determination of the dates and places (and the time) of ancient eclipses that involve certain amount of uncertainty, Fig. 2.14 shows how the relative orientation of the earth’s surface can decide from which locations a total solar eclipse can be seen. The orientation of the earth’s surface depends on the exact rotational history (since it is changing). Thus, unless the exact function Ω(t) is known (Ω is the angular speed of the earth’s spin rotation) determination of the orientation of the earth’s surface a

2.2 Variation in Astronomical Parameters

23

Fig. 2.14 Locations from where a total solar eclipse can be seen

very long time ago in the past may not be exact. This uncertainty becomes pronounced when one goes far back in the past and the accumulated error in the total angle rotated by the earth from its present position becomes larger. Precession of the equinox: This phenomenon is the most dependable one when dating of ancient astronomical observations is attempted. To understand the precession and its effect on positional astronomy, let the situation shown in Fig. 2.15 be considered. The earth spins about its axis once every day. As is often noticed the spin axis of a top rotating at a high speed makes a slow motion about a fixed axis (Fig. 2.16). This slow rotation of the axis of spin in called precession. Precession can be forward, i.e. when it is in the same sense as the spin or retrograde when it is in the opposite sense. Figure 2.16 shows retrograde precession. In the case of the spinning earth, the earth’s axis precesses slowly in the reverse direction (as indicated in Fig. 2.15) and it takes almost 25,771.5 years to complete one cycle. Fig. 2.15 Precession of the earth’s spin axis

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2 Rudiments of Positional Astronomy and Archaeoastronomy

Fig. 2.16 Precession of a spinning top

The effects of the precession of the earth’s spin axis can be understood by examining Fig. 2.17. Due to the gravitational attractions by the moon and the sun on the equatorial bulge of the earth, a moment acts on the spinning earth and its axis of spin precesses as indicated in Fig. 2.17.

Fig. 2.17 Effects of the precession of earth’s axis

2.2 Variation in Astronomical Parameters

25

Fig. 2.18 Wandering of the north celestial pole during the 25,800 yr. precession period

The precession is retrograde and takes about 25,771.5 years to complete one cycle. Two effects of this precessional motion are clearly visible---(a) The north celestial pole, decided by the intersection of the earth’s axis and the celestial sphere, changes with time and lie on a circle in the celestial sphere with an angular diameter of 47°. This implies that if a fixed star exists at the location of this intersection it will be the North Pole Star. But there may not be any star at the location and during those periods no North Pole Star exists. Figure 2.18 shows the wandering of the north celestial pole among the fixed stars during the 25,771.5 years period. It is seen from this figure that at present there is a Pole Star---the Polaris. In the past one has to go back to the third-millennium BCE to find a Pole Star that was called Thuban. Before that there was no Pole Star for a very very long time. There is another effect that influences positional astronomical observations. The celestial longitudes start at the north pole and goes to the south pole. Thus, when the pole positions change, the great circles which represent celestial longitudes also change as indicated in Fig. 2.19. Thus, at one time two stars S 1 and S 2 lying on the same longitude (i.e. on a north--south line) may not do so when the celestial poles shift to positions, N  and S  due to the precessional motion of the earth’s axis. (b) Another important effect of the precessional motion is the gradual shift (towards west) of the intersection points of the celestial equator and the ecliptic. Since the celestial equator is on a plane that is normal to the axis of the earth at all times, these intersection points (vernal equinox and the autumn equinox) slowly move along the ecliptic (it is a fixed circle in the celestial sphere) in a westwardly direction at the rate of 50.4 per year. This is why the phenomenon is termed as the ‘precession of the equinox’. Since the equinoctial points play very important

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2 Rudiments of Positional Astronomy and Archaeoastronomy

Fig. 2.19 Effect of the changing north celestial pole on the Right Ascension of a celestial object

roles in positional astronomy, this phenomenon is extremely useful in dating ancient astronomical references. Figure 2.20a shows how the vernal equinoctial position has changed in the fixed star background during the last few millennia. Figure 2.20b shows again the motion of the equinoctial positions due to the precessional rotation of the earth’s axis. The ecliptic is stationary with respect to the fixed stars. The celestial equator has the precessional motion that causes the vernal equinox (VE) to shift westwards at the rate of 50.4 per year. In the ecliptic system, the position of a star is given by its celestial longitude λ and the celestial latitude β. The origin of the system is the vernal equinox.7 Therefore, as the origin shifts westwards the s¯ayana longitude (measured from the VE point) of an object increases at the rate of 50.4 per year. The celestial latitude β does not change due to precession, of course. So if the difference in longitude of a star, observed at two different times be Δλ (expressed in arc seconds), the time difference t = (λ/50.4 ) years.

2.3 Eclipse Both lunar and solar eclipses are extraordinary celestial phenomena. A lunar eclipse takes place when the earth’s shadow falls on the moon making it dark as moon’s brightness comes from the sunlight falling on it. A solar eclipse takes place when the moon obstructs the sun coming between the earth and the sun. Figure 2.21 shows the relative positions of the sun, the earth and the moon at an instant. 7 In

the Indian system, the origin is a fixed point ‘Mesadi’ the first point of the sign Aries. The longitude in the Indian system is called ‘nir¯ayan¯a’. In the modern system, the longitude is ‘S¯ayana’.

2.3 Eclipse

27

Fig. 2.20 a Shift of the vernal equinoctial position during the last few millennia and b effect of precession on the celestial longitude λ

Moon’s orbit around the earth lies in a plane that is inclined to the plane of the ecliptic at an angle of 5°8 43 . The point where the moon’s orbit intersects the plane of the ecliptic while going below (in the figure shown), it is called the descending node and where it intersects while the moon comes above the ecliptic is called the ascending node. An eclipse occurs when the sun, the earth and the moon are aligned. When the moon is in conjunction (with the sun), it is not visible and the day is called a new moon day. Similarly, when the moon is in opposition, i.e. in a direction opposite to the sun, the earth observes a full moon night. Thus, a lunar eclipse can take place on a full moon night only whereas a solar eclipse is possible on new moon days.

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Fig. 2.21 Alignment of the sun, moon and the earth

However, on all new moon and full moon days eclipse does not occur as the moon’s orbit is slightly inclined to the plane of the ecliptic. An eclipse is possible only when on a new moon or full moon day the moon also lies on the plane of the ecliptic.8 Or, in other words, the moon has to be at either the ascending or the descending node on a full moon night for a lunar eclipse to occur. Same is the requirement on a new moon day for a solar eclipse to take place. The line joining the two nodes is called the line of nodes and this line of nodes also has a motion. This motion is a rotation of the line in a clockwise sense when viewed from above the plane of the ecliptic. The rate at which this line of nodes rotates is 19.4° per year. Figure 2.22 shows two consecutive position of the line of nodes. So it is clear that from the day when the line of nodes is aligned with the sun it takes another 346.62 days to become aligned next. This period is called the ‘eclipse year’. It can be shown that the eclipse pattern repeats after 18 years and 11 13 days and this cycle is called the ‘Saros cycle’. It should be noted that the pattern of the eclipses may repeat after 18 years and 11 13 days but the places on the earth from where these eclipses are visible not necessarily remain unchanged.

2.4 Physical and Descriptive Archaeoastronomy Although the use of astronomy in studying ancient structures and astronomical references has been practiced since the nineteenth century the term ‘archaeoastronomy’ is a recent coinage. The meaning of this term can be the study of astronomy of ancient times but it is used primarily for studying ancient structures or analysing 8 That

is why the plane is called the plane of ecliptic.

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29

Fig. 2.22 Two consecutive positions of the line of nodes

ancient astronomical references. With the progress of computer technology, many advanced planetarium softwares have been developed which can depict the sky at any time of any year as observed from any locations on the earth. This has made the analysis of ancient astronomical description much easier and convenient. Archaeologists date ancient objects using a number of scientific techniques among which the use of Carbon-14 isotope is the oldest and most common. In the past, most of the archaeologically excavated sites have been dated using such scientific techniques. But problem arises in the absence of objects and physical structures. Besides, carbon isotope dating technique requires some organic objects. In such cases, scholars have adopted various methodologies based upon astronomical principles for determining the antiquity of a structure. In many cases, the archaeologists study ancient structures and investigate their possible relationships with astronomical alignments. This often throws some light on the social and ritualistic practises by the ancient people. Nevertheless, nowadays the term ‘archaeoastronomy’ refers to either study of ancient structures for any possible relationship with the stellar alignments or estimating the antiquity of an ancient astronomical description. The subject ‘archaeoastronomy’ can be, thus, divided into two branches. One, in which ancient structures are studied for any astronomical relationship, may be termed as ‘physical archaeoastronomy’, and the other which analyses ancient astronomical references only may be termed as ‘descriptive archaeoastronomy’. In case of ancient India, physical archaeoastronomy is not very relevant due to the absence of major structures from ancient periods like the pyramids in Egypt. However, India possesses something very

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unique not found in other ancient civilizations—a vast collection of rich ancient literature and scriptures with many astronomical references. So, descriptive archaeoastronomy is particularly useful in establishing the chronology of ancient India. But before presenting the techniques of descriptive archaeoastronomy, some discussion on the physical archaeoastronomy may be desirable for the sake of completeness.

2.4.1 Physical Archaeoastronomy As mentioned above physical archaeoastronomy requires the presence of ancient structures. It is found that even in the prehistoric times man used astronomy for various purposes---particularly to determine the onset of various seasons. That was very important once the civilization started depending on agriculture. International Astronomical Union (IAU) and UNESCO have jointly undertaken programmes to undertake wide-ranging survey of astronomical heritage. Astronomical heritage means material evidence of astronomy and its social and cultural use in the ancient times. A major part of the programme is related to physical objects, both movables and immovables. Immovables consist of ancient structures, ancient town plan, rock paintings, etc. The movable objects can be in the form of drawings, maps, etc. Prehistoric period: Evidence is in abundance that during the prehistoric period man used astronomical observations for some purposes. Old mammoth bones with notches matching the lunar cycle have been discovered in ancient cave shelters in Europe and Africa. Even before agriculture was discovered, ‘hunter gatherers’ man needed some knowledge about the seasons and their relationship with the flora and fauna. At a later stage, a number of megalithic sites with special stone arrangements with specific astronomical relationships have been discovered. In the prehistoric period, the two primary celestial objects which were observed by the ancient people are the sun and the moon. Continued observation led the observers to notice a few things. The path followed by the sun changed over a period as indicated in Fig. 2.23. If an observer is located at φ° N latitude, then φ  = 90° − φ is the colatitude and the sun’s path at sunrise is inclined to the horizontal at an angle φ  as shown. The path of the sun during the summer solstice (SS) day will be the northernmost one and that on the Winter Solstice (WS) day will be the southernmost one. On the equinoctial days, the sun rises exactly on the east and sets exactly at the western point in the horizon. During one half year, the sun gradually moves from the summer solstice path towards the south and after reaching the winter solstice position, it reverses its gait towards the north. In ancient times, this particular phenomenon was noticed by the observers and they also noticed the relation between various seasons with the summer and winter solstice and the equinoctial days. Many ancient megalithic arrangements have been discovered where alignments indicate these important dates. Figure 2.24 shows the rising and setting azimuths of the sun. Figure 2.25 shows the celestial equator and the ecliptic for a complete solar

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31

Fig. 2.23 Sun’s path in a day during a year

Fig. 2.24 Rising and setting sun compass rose at a particular latitude. The angle Λ depends on the latitude λ

Fig. 2.25 Sun’s path along the ecliptic and the celestial equator

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cycle. The sun has been shown on a day after the vernal equinox when its declination is δ. It is seen from the figure that on the summer solstice day the sun’s declination is equal to ε, the tilt of the earth’s axis. On the winter solstice day, the declination is –ε. The following relation gives the declination in terms of the number of days elapsed after the summer solstice: sin δ = sin ε cos 0.986n

(2.4)

where n is the number of days since summer solstice and (0.986n) is expressed in degrees. According to (A9) the azimuth for the rising point of the sun is given by the following relation AU = cos−1



sin δ cos ϕ



where AU is the azimuth of the rising point of the sun, δ is the declination of the sun and ϕ is the latitude of the observers’ position on the earth. Using this relation AU at certain places on the SS, WS and the equinoctial days can be calculated as shown in Table 2.1. As can be observed that at the latitude 66.5° N the azimuth is zero implying that the sun rises in the north point and returns to the same position for setting (in fact it neither rises nor sets, it just touches the horizon at the north point). However, on the equinoctial days, the sun rises exactly in the east and sets exactly in the west. It is emphasized again that the sunrise or sunset positions on the cardinal days do not get affected by the precession of the equinox. Only the change in the inclination of the earth’s axis can influence the positions. The inclination of the axis is the declination of the sun on the solstice days. Only near the Arctic Circle the effect on the sunrise point azimuth on the solstice days is significant. Table 2.1 Sunrise point azimuth; at the current epoch δ = 23.5° on the SS day and –23.5° on the WS day. It is 0° on the equinoctial days Sl. Place

Φ (in degree) AU (SS)

1

Singapore

1.352° N

2

New Delhi

28.614° N

3

London

51.507° N

4

Fairbank

64.85° N

5

Lapland

66.5° N

6

Hammerfest 70.663° N

AU (WS)

AU (Eq)

66.493°

113.507°

90°

62.985°

117.015°

90°

50.160°

129.84°

90°

20.232°

159.768°

90°

0

180°

90°

Imaginary (Sun is always Imaginary, no sunrise 90° above horizon)

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Fig. 2.26 Major and minor standstills of the moon

In the case of the moon, the motion characteristics is a bit more complicated. The sun lies exactly on the ecliptic but the plane of the moon’s orbit is inclined to the plane of the ecliptic at an angle (i) of 5°9 . So in the case of moon—rise on the solstice days its azimuth can be a little bit more or less than that of the sun. So moon has a major standstill and a minor standstill. Figure 2.26 shows the major and minor standstill of the moon. It is easy to figure out that the declinations of the sun at the solstice positions are ± ε; but for the moon it ranges between ε ± i at the northern standstill position and between –ε ± i at the southern standstill position. Unlike the stellar alignments the azimuths of the sun and the moon are not affected by the precession of the equinox. Many of the prehistoric megalithic sites show stone alignments to determine the cardinal days during a year. In some sites, the evidence exists that observation of the rising and setting moons was also made. The distribution of ancient megalithic monuments in Europe is shown in Fig. 2.27. As an example the megalithic monument Stonehenge is being briefly discussed below. Among the large number of ancient megalithic monuments discovered the most famous one is at the Salisbury Plain in the Wiltshire district of England. It is famously named as Stonehenge.9 Figure 2.28a shows the arrangements and alignments of Stonehenge. The stones used were quite massive reaching a height of 7 m in many cases. Figure 2.28b is a view of this megalithic monument. Extensive study and analysis have established a number of astronomical associations with the alignments of the stones. The alignment with the sun at summer solstice is reasonably visible. But many other astronomical alignments are somewhat speculative and debatable. 9 The

word ‘henge’ means a prehistoric monument consisting of a circle of menhirs or wooden pillars.

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Fig. 2.27 Distribution of megalithic monuments in Europe

Fig. 2.28 a Stonehenge plan, b a view of Stonehenge and c sunrise above the Heel stone

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35

When Stonehenge (Latitude 51.1789° N) was built about 4500 years ago the earth’s axis tilt was near 24° instead of 23.5°. So the azimuth of the summer solstice was   sin 24◦ = 50.5◦ cos−1 cos 51.1789◦ instead of current value of 49.552°. Thus, in those days, the sun used to rise almost 1° north of the current sunrise position. A major effort has gone in studying the alignments with reference to the directions of the rising and setting sun on the cardinal days (SS, AE, WS, VE) and sometimes, also of the moon at its rising and setting positions. A large number of temples in Egypt have been found to be aligned keeping the astronomical objects in mind. Ancient burials have also been studied by archaeologists to find out statistically relevant issues in their alignments. Generally, in majority of such cases, the objective had been to investigate the sociocultural customs practiced by the ancient people of the region under study. Protohistoric and historic period: Once civilization progressed, astronomical knowledge of the people got enriched and associating the activities on the ground with the heavenly bodies became more and more popular. Among the major ancient structures, the pyramids of Egypt have a very special place not only because of their enormous size but also because of their very interesting association with astronomy. The pyramids of Giza will be taken up for a brief discussion. Association with the heaven is very clear when one studies the locations and relative sizes of the three pyramids along with the constellation Orion. Orion played a very major role in the Egyptian civilization. Figure 2.29a shows the interesting match of the three major pyramids with the three stars in Orion’s belt. Among the interesting studies on the alignments of these pyramids, that conducted by Kate Spence, a Ph.D. researcher at Cambridge University, is worth mentioning here. The accurate dating of the pyramids can be done by studying and analysing the precession of the two stars Kochab (in Ursa Minor) and Mizar (in Ursa Major). At a certain date when the line joining these two stars was vertical, this line passed through the exact location of the celestial north pole. There was no star to mark the spot exactly in those days. Thus, the simultaneous transit of these two stars (Fig. 2.29b) could be used to find the true north. Quoting from her article (Nature, v 408, p 320, 16 November 2000) the following statements are reproduced here. ‘The ancient Egyptian Pyramids of Giza have never been accurately dated…. Modeling the precession of these stars yields a date to the start of construction of the Great Pyramid that is accurate to ± 5 years, thereby providing an anchor for the Old Kingdom chronologies’. Figure 2.29b shows the two aforementioned stars in simultaneous transit in 2467 BCE. At present, the situation is shown in the sky map in Fig. 2.29c. Robert Bauvel published a similar theory in his book ‘The Orion Mystery’ published in 1994 and also in some other articles published in 1993. Of course the principle of using the precession of the equinoxes to date the great pyramid

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a

b

c

Fig. 2.29 a Association of the Giza pyramids with Orion, b simultaneous transit of Kochab and Mizan in 2467 BCE, c situation at present

2.4 Physical and Descriptive Archaeoastronomy

37

Fig. 2.30 Misalignments of the pyramids and chronology

was first employed by astronomer Piazzi Smyth in 1865. He used the Pole Star Alpha Draconis. Another astronomer from University of California Irvine, Virginia Trimble used the Pole Star and Delta Orionis in 1964 to date the great pyramid to 2600 BCE. Such interest in the alignment of the great pyramid is quite justified as its north-south alignment is extremely accurate and correct within 3 of the true north--south. Kate Spence further studied the construction of the later pyramids and noticed the expected error in alignment as the same principle of using the simultaneous transit of Kochab and Mizar was employed. Due to the precession of the equinoxes this line did not pass through the north celestial pole. The errors in the alignments can be then used to establish a chronology as indicated in Fig. 2.30. Apart from the alignment along the north--south direction, the visibility of certain important stars through the shafts in the pyramids has also been employed for dating purpose. Figure 2.31 shows schematically the stellar alignments of the three shafts of Khufu pyramid. Though originally these were thought to be for ventilation purpose, later it has been established to be not so. These were designed as pathways to the main destinations of the Pharaoh after death. Since the northern shaft is aligned with the location of Thuban (the Pole Star during the period 3000 BCE to 2500 BCE), the pyramid’s construction date can be guessed from this alignment also.

2.4.2 Basics of Descriptive Archaeoastronomy Unlike physical archaeoastronomy, descriptive archaeoastronomy does not require any physical structure to study antiquity. Descriptive archaeoastronomy is a subject where an ancient description of stellar alignments in the sky is studied and, in many cases, indicates the antiquity. There are primarily three types of descriptive archaeoastronomy as mentioned below.

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Lower southern shaft

Fig. 2.31 Stellar alignments of the shafts in Khufu pyramid

(i)

Analysis of stellar arrangements like the location of the north celestial pole, the occurrence of simultaneous transits of major stars, the location of the equinoctial points among the nakshatras along the ecliptic, etc. This also includes the study of the descriptions of heliacal rising of special stars/nakshatras. (ii) Study of the descriptions of ancient spectacular astronomical events like total or annular solar eclipses on specific and special days of the year. (iii) Analysis of the descriptions of exaltation of planet mars with a particular nakshatra in the background. The above topics are briefly described below. (i) The first group plays a major role in descriptive archaeoastronomy as such references are found in large numbers in ancient literature of India. Figure 2.18 shows the shift of position of the north celestial pole due to the precessional motion of the earth’s axis. It is seen that though at present we are fortunate to have a star at the location of the north celestial pole (the Polaris), during a major period in the past there was no star at this location that is visible in naked-eye astronomy. Only when one goes back to around 3000 BCE a North Pole Star was visible that is the star Thuban. Apart from this shifting of the north celestial pole in the background of the fixed stars, another visible effect can be observed. As shown in Fig. 2.19, the longitudes of stars slowly change. Therefore, at a certain epoch, two major stars can lie on the same meridian or, longitude, although their present locations may not be so. This phenomenon has been used in establishing the antiquity of such observations. It has been shown earlier that the locations of the equinoctial points gradually shift along the ecliptic. Figure 2.20b shows the shift of the vernal equinoctial point

2.4 Physical and Descriptive Archaeoastronomy

39

over a long period. In ancient Indian nakshatra-based astronomy, the markers along the ecliptic are shown in Fig. 2.32. It should be carefully noted that this view is from the south celestial pole as the orbital rotation of the earth is in the clockwise sense. As the equinoctial positions shift along the ecliptic, the nakshatras where the sun lies on the equinoctial days can be recorded. Similarly, the nakshatras on which the sun lies on the solstice days can also be determined. In approximately 700 years, the position shifts by 10°. This has been shown in Fig. 2.33. The sun’s position in a nakshatra gets revealed by the full moon position among the nakshatras. Accordingly, the relation of the seasons with the month names changes as the month name used to be linked with a particular nakshatra at the corresponding full moon location. Observing the eastern sky in very early morning used to be a well practiced custom, particularly by the sages. Thus, the heliacal rising of some prominent stars used to be noticed and their association with the seasons used to be good indication to identify the onset of seasons. Heliacal rising of a star (or nakshatra) also gets influenced by the precession of the equinoxes and can be an indicator of the antiquity of a particular description recorded in an ancient text. (ii) References to solar eclipses, particularly the total and annular ones, are found in ancient texts. Since the motions of the earth and the moon around the sun are known quite accurately, it is mathematically possible to find out the dates and times of past eclipses. It may appear at a first glance that eclipses are not that rare as celestial events and any meaningful result in determining the antiquity may

Fig. 2.32 The twenty-seven nakshatras along the plane of the ecliptic

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2 Rudiments of Positional Astronomy and Archaeoastronomy

Fig. 2.33 Shift of the summer solstice position among the nakshatras from 1998 CE to 2600 CE

not be possible. But a total solar eclipse at a particular location on a particular day in a tropical year occurring at a particular time of the day is very rare. Thus, if all the above conditions are satisfied it is possible to pinpoint the event. Apart from this, a special type of combination of two consecutive eclipses (one solar and one lunar) can indicate a situation that can be used for dating the event. As mentioned earlier, it is necessary to determine the positions of the earth and the moon in relation to the sun to identify an eclipse. But the spot on the earth’s surface from where the total solar (or annular) eclipse is visible depends on the angular orientation of the earth at that particular instant of time to determine that the exact knowledge of the earth’s rotational history is necessary. Higher the antiquity of the event longer is the time period involved, and more uncertainties in the knowledge of the earth’s angular orientation get introduced. So, sometimes this may lead to error in the analysis and the result. (iii) Exaltation of mars is a very important phenomenon for the astrologers. This excessive apparent brightness of a planet is because of its proximity to the earth. Figure 2.34 shows the orbits of the planet mars and the earth. The orbit of the earth is very nearly circular the eccentricity being of the order of 0.017. On the other hand, the eccentricity of the orbit of mars is much larger about

2.4 Physical and Descriptive Archaeoastronomy

41

Fig. 2.34 Exaltation of planet mars

0.093. To make the distance between the earth and mars minimum, mars must be at its perihelion and the earth at its orbit’s aphelion, with the planet mars in opposition. When all these conditions are satisfied, this smallest distance between mars and the earth is 55.35 × 106 km, whereas the farthest distance in opposition is equal to 100.23 × 106 km. When mars is nearest to the earth its brightness is almost 3 times the brightness of the brightest star Sirius! On the other hand, the brightness of mars when it is farthest (in opposition, of course) is only 0.6 times that of Sirius. This phenomenon of excessive brightness of a planet is called ‘exaltation’. Since the planets are also not far from the ecliptic the exalted planet can be observed against a particular nakshatra and recorded. As the orbital speeds of the earth and planet mars are different, the configuration leading to the brightest opposition for mars repeats after 15 and 17 years alternately. But for exaltation, the mars should be at brightest opposition and at its perihelion position. The perihelion of mars advances at the rate of 0.43355° per century. Thus, the exaltation position of mars against the  also changes. A description of mars exaltation at a longitude λ must be nakshatras λ0 −λ × 100 years old if the longitude where current exaltations are observed be 0.43355 λ0 . Some descriptions of exaltation of mars are found in old astrological references.

Chapter 3

Astronomy in Ancient India

3.1 Importance of Understanding the Ancient Indian Astronomical System To apply the principles of descriptive archaeoastronomy for investigating the chronology of ancient India before the historical period, it is imperative that one understands the astronomical system followed by ancient Indian astronomers. It is needless to mention that astronomy in ancient India was based on naked-eye observation occasionally supported by simple instruments. Astronomy in ancient India developed to a sophisticated level (to the extent possible, of course) as the sages of ancient India were keen observers of the sky generation after generation. Since the astronomical alignments took important places in the daily rituals and sacrifices and the development of a luni-solar calendar became a necessity, astronomy had to develop to a reasonable degree of sophistication. The large number of astronomical references, which are found in the vast body of ancient Indian literature, can be understood and analysed if and only if one understands the ancient astronomy developed in India. It should be remembered that the astronomical science prevalent in ancient India was different from the system followed now. As the application of astronomical principles for establishing chronology requires correct interpretation of the ancient references, it is also important to be familiar with ancient names of stars and constellations (nakshatras).

3.2 Rediscovery of Ancient Indian Astronomy Since Indian subcontinent was the cradle for one of the most ancient civilizations, it was very natural that astronomy flourished as a well-established branch of science. But as it happened with other branches of scholarly activities, astronomical knowledge remained confined to a small group of people representing the academic world © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 A. Ghosh, Descriptive Archaeoastronomy and Ancient Indian Chronology, https://doi.org/10.1007/978-981-15-6903-6_3

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3 Astronomy in Ancient India

and Sanskrit studies. Subsequently, India experienced a series of invasions from outside and finally a major part of the subcontinent came to be ruled by foreign rulers from western Asia. Since for about 800 years the Islamic rulers did not bother either to preserve or to practice the ancient knowledge, most of that became lost. As a result, the ancient Indian astronomy was also forgotten till India came under the influence of European rulers from the eighteenth century. European scholars got the first hint of the astronomical knowledge in ancient India in 1687 from the fragment of a manuscript brought by L. A. Loubere from Thailand, then called Siam. The manuscript contained the rules (and data tables) for calculating the positions of the sun and the moon. The origin of these rules and procedures were lost in the darkness of India’s antiquity. The celebrated astronomer Cassini could explain the meanings after studying the manuscript and he came to the conclusion that the procedures for calculation yielded correct results if 3 and 40 were subtracted from the calculated positions for the sun and the moon, respectively. This implied that the reference meridian that was used for preparing the tables was 18° west of Siam and it passed over Varanasi, India. In 1750, Father du Champ sent more elaborate tables from a town in Karnataka to de l’Isle. But the real progress in rediscovering the astronomical knowledge of ancient India started after Le Gentile returned from India after observing a transit of venus from Pondicherry in 1769. He was also amazed to see the accurate and rapid calculations by the Pundits. Since that time a considerable interest was generated among the European scholars and the matter started receiving serious attention from the scholars in Europe. Being highly impressed by the astronomical knowledge of ancient Indian scholars, J. S. Bailly published his book ‘Traite & de l’ Astronomie Indienne et Oriental’ in 1787. According to his analysis, ancient Indian astronomy suggested a hoary antiquity and the tables were prepared in the third-millennium BCE. He also believed that the origin of astronomy was indigenous to the subcontinent. Subsequently, many scholars like Laplace, Playfair, Bently and others studied the astronomical knowledge that got developed in ancient India. Many controversies arose and heated debates took place. From the later period of the nineteenth century, a considerable progress has been made by both European and Indian scholars like F. Max Muller, J. Burgess, W. Brennand, Jacobi, S. B. Dixit, B. G. Tilak, K. Mukherjee and many others. In the first half of the twentieth century, the research by R. Shyamshastry, P. C. Sengupta and G. R. Kay is noteworthy. During the subsequent period, the volume of research on ancient Indian astronomy by both Indian and Western scholars has been enormous.

3.3 Major Features of Astronomy in Ancient India Ancient Indian civilization was highly developed as evidenced by the remains of the vast Indus--Sarasvati Valley Civilization. Agriculture was the main activity, and it is inconceivable that astronomy did not develop as the seasons are closely linked with the astronomical alignments. The scholars have discovered a large number of megalith sites. But such establishments are not very important for the subject matter

3.3 Major Features of Astronomy in Ancient India

45

of this volume. Thus, the astronomical references implied in the prehistoric era may not be very useful and will be omitted in the presentation here. The main interest lies in the protohistoric period of India. It is suspected that a large number of texts on the subject astronomy existed in the ancient era. Unfortunately, most of those are lost forever. The only astronomical text that has survived is the ‘Ved¯anga Jyotisha’. Luckily, as a part of vedic texts, this purely astronomical text survived. This book consists of shlokas which are nothing but algorithms for astronomical calculations. In total there are 49 verses in the two recensions of Ved¯anga Jyotisha. Till the later part of the nineteenth century, the meanings of all the verses could not be deciphered. Only now all the verses are understood. Astronomy in ancient India can be divided into two major classes. From the thirdcentury BCE, India started having contact with Greece and other nations outside the subcontinent. So, the basic structure of Indian astronomy had outside influence although the astronomical concepts and the major parameters were India’s own. The astronomers used to term their astronomical texts as ‘Siddh¯antas’ (Siddh¯anta means final decision). The system of 12 Zodiacal signs was started during this period in place of the previous nakshatra-based system. The scholars working in this area feel that ancient Indian astronomy can be classified under two major headings---(i) presiddh¯antic astronomy and (ii) siddh¯antic astronomy. The Presiddh¯antic astronomy is covered by the protohistoric period in India that is the period of primary concern so far as this volume is concerned.

3.3.1 Presiddh¯antic Astronomy This subject primarily concerns with the motion of the sun and the moon, the two most prominent objects in the sky. The other objects whose motions were also noticed and recorded are the five planets---mercury, venus, mars, jupiter and saturn. In the very early period, only Jupiter and Venus were referred to; the other three planets are found in later Pur¯anic texts. Presiddh¯antic astronomy covers the vedic and the Pur¯anic periods. The astronomers of ancient India observed the daily change of shape and the position among the fixed stars for the moon. It was found that the moon returns to the same position after a little more than 27 days. The positions taken by the moon on each day were marked by a group of stars which were termed as ‘Nakshatra’. These 27 nakshatras were the 27 position markers in the sky along the ecliptic. Figure 3.1 shows the 27 nakshatras used in the pre-siddh¯antic astronomy when viewed from the south celestial pole as the earths appears to orbit in the clockwise sense. Since the 360° of the whole ecliptic was equally divided among the 27 nakshatras each nakshatra occupied 13.333° of the ecliptic. Table 3.1 shows the principle stars for each nakshatra. Appendix B also shows the locations of the nakshatras along the ecliptic. The nakshatra-based system was already developed in Rigvedic era as evident from the various astronomical references in the vedic texts.

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3 Astronomy in Ancient India

Fig. 3.1 Twenty-seven nakshatras

Table 3.1 Principal stars of the nakshatras 1. Ashvinee α Arietis

2. Bharanee 41 Arietis

3. krittik¯a  Tauri

4. Rohinee α Tauri

5. Mrigasheersha λ Orionis

6. Ardr¯a γ Geminorium

7.Punarvasu β Geminorium

8. Pushy¯a δ Cancri

9. Ashlesh¯a ζ Hydree

10. Magh¯a α Leonis

11. Poorva Ph¯alguni θ Leonis

12.Uttar Ph¯alguni β Leonis

13. Hasta δ Curri

14. Chitr¯a α Verginis

15. Sw¯atee α Bootes

16. Vishakh¯a Libra

17. Anur¯adh¯a β Scorpi

18. Jyesth¯a α Scorpi

19. Mool¯a λ Scorpi

20. Poorv¯ash¯adh¯a  Sagattari

21. Uttar¯ash¯adh¯a π Sagattari

22. Shravan¯a α Aquilli

23. Shravisth¯a α Delphini

24. Shatabhishaj λ Aquarii

25. Poorva Bh¯adrapada α Pegasi

26.Uttara Bh¯adrapada γ Pegasi 27. Revati ζ Pesium

In the pre-siddh¯antic astronomy of the earliest periods (Rigvedic era) only two planets were recognized---the jupiter and venus. Interestingly, venus was named ‘Ven¯a’ in Rigveda meaning ‘daughter of sun’. Most probably this planet’s proximity to the sun (as it never goes beyond an angular distance from the sun and is always seen either as a morning star or an evening star) led to this name. But what is more interesting is that the similarity with the name ‘Venus’ used in Hellenistic astronomy in the first millenniums BCE! There is no known ancient contact between India and Greece before Alexander.

3.3 Major Features of Astronomy in Ancient India

47

Fig. 3.2 Naming of the months in pre-siddh¯antic astronomy (this view is from the south celestial pole)

It was also known in pre-siddh¯antic astronomical period that there is only one sun and it supplies all the light and energy. It was also recognized that the moon’s luminosity was because of reflected sunlight. Rigvedic sages recognized that there is a link between the moon’s phases and the ocean tide; they understood that the tides are caused by the moon. In pre-siddh¯antic astronomy, it was also understood that the earth is round like a sphere and it floats freely in space. In the Br¯ahmana texts, it was mentioned that the sun neither sets nor rises! This statement is just one stage behind the understanding that the apparent daily motion of the heaven is due to the daily rotation of the earth about its axis.1 Time reckoning: The time reckoning in pre-siddh¯antic astronomy depended both on the motions of the moon and the sun that led to the development of a ‘luni-solar’ calendar for a tropical year. The change of the moon’s shape was clearly noticeable and the period from one full moon to the next full moon was called a lunar month. In the Rigvedic period, the moon used to be called by the terms ‘m¯as¯a’. Thus, a full moon was termed as ‘purnam¯as¯a’ indicating the completion of a month. Gradually, this led the word ‘m¯as¯a’ to be used for the word ‘month’. In the early era of pre-siddh¯antic astronomy, the month used to be from a full moon to the next full moon. The name of the month used to be according to the nakshatra in which the full moon used to take place. Figure 3.2 shows the twelve nakshatras which led to the names of the twelve months in a year. Whenever the moon is in opposition, there will be a full moon and the name of the preceding lunar month is according to the nakshatra against which the full moon is observed. Thus, for the case shown in the figure, the name of the month is ‘Baisakhi’. 1A

clear statement to this effect was first proposed by Aryabhata I in the fifth-century CE.

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3 Astronomy in Ancient India

¯ ardh’, ‘Shr¯avan’, ‘Bh¯adra’, The other names follow accordingly as ‘Jaistha’, ‘As¯ ¯ ‘Ashwin’, ‘K¯artik’, ‘Agrah¯ayan’ (same as Mrigashir¯a), ‘Poush’, ‘M¯agh’, ‘Ph¯algun’ and ‘Chaitra’.2 As mentioned earlier, during the later period this ‘purnim¯anta’ system was changed to ‘am¯anta’ system. In this, the month reckoning was from new moon to the next new moon and the name used to be according to the nakshatra against which the full moon took place in the middle of the month. Appendix B gives the total list of ‘nakshatra’ and their current celestial longitudes. One civil day, i.e. ‘s¯avana’ day used to be measured from sunrise to the next ¯ sunrise. Of course much later in the siddh¯antic astronomy Aryabhatta I started an ‘ardhar¯atrik¯a’ system in which a civil day used to be measured from midnight to the next midnight (as is done at present). In pre-siddh¯antic astronomy, 29 21 civil days used to be taken as a lunar month. Thus, one lunar year was equal to 29 21 × 12 (= 354) days. Hence, it fell short from one solar year by about 11 days. This was noticed by the ancient astronomers; it was also recognized by them that the seasons used to depend on the solar year and this led to the development of a luni-solar calendar. A lunar month was divided into two parts--the bright half from new moon to the full moon was called the ‘shukla paksha’ and the other half had the name ‘krishna paksha’. A lunar month was also divided into 30 units and these units were called ‘tithi’. Thus, ‘tithi’ represented a lunar day. This concept of ‘tithi’ played the predominant role in daily activities and the rituals and sacrifices. Even today in India, many of the rituals are based upon this ‘tithi’ system. In ancient India, the ‘new moon’ and the ‘full moon’ days played such important roles that a finer terminology was developed. The full moon day (rather night) was called ‘R¯ak¯a’ and the day before that was called ‘Anumati’. On the other hand, the ‘new moon’ day (or night) was called ‘Kuhu’ and the day before was called ‘Sinib¯ali’. The luni-solar System: In the European astronomical system, the year is ‘solar year’. This implies the period the sun takes to make one complete cycle along the ecliptic. In Islamic astronomy, the calendar was and continues to be purely Lunar. However, in India, the ancient astronomers noticed that the sun takes a little more than 365 civil days to complete a solar year. It was also observed by them that the occurrence of the different seasons (including the monsoon) was linked with the sun. Thus, in a lunar system, the seasons gradually shift in their correspondence with the ¯ ardh’ may be the onset of the rainy season but after months. Thus, in some year, ‘As¯ some centuries it may be totally a different season. To avoid this, the pre-siddh¯antic astronomers of ancient India developed a ‘luni-solar’ system. As 12 months of 30 days each result in 360 days, it was considered to be the nominal period of a solar year. Taittiriya Samhit¯a states that 5 extra days over this 360-day period will complete the correspondence with the seasons. It was stated that 4 days were too short and 6 days more make it too long!

2 Though

the same names are used even today the duration of the month is no longer decided based on a purely lunar system.

3.3 Major Features of Astronomy in Ancient India

49

Another method to match the lunar and solar years used to be adopted by ancient Indian astronomers. As a lunar year consisted of 354 days and a tropical solar year was 365 (or, 366) days long, in every year there was a shortfall of 11 days (or, 12 days). Thus, after every 3 years (approximately), an extra intercalary month used to be added to bring the lunar calendar at par with the solar year to keep the relationship with the seasons intact. To take care of this mismatch between the solar and lunar years, the pre-siddh¯antic astronomers of ancient India devised another clever system. An idea of a ‘Yuga’ comprising of 5 solar years was conceived. In a ‘Yuga’, there will be 60 days more than the period covered by 5 lunar years. These extra days can be introduced as one intercalation month after 2 21 years. It is obvious that with this also an exact matching is not possible and corrections had to be introduced at regular intervals. The names of the years in a Yuga were also specified in the following order---(i) ‘Samvatsara’, (ii) ‘Parivatsara’, (iii) ‘Id¯avatsara’, (iv) ‘Anuvatsara’ and (v) ‘Idvatsara’. In the presiddh¯antic period, the solar months were difficult to identify and the ‘lunar month’ names were to be depended upon by the astronomers. It is needless to mention that the gradual shift of the sun to the north during a period of six months followed by a southward shift during the next six months was noticed by the ancient astronomers in India. The whole solar year was, thus, divided into two halves called the ‘ayanas’. The six month period from the winter solstice to the summer solstice was called the ‘uttar¯ayana’ period and the following six months was ‘dakshin¯ayana’ period. Some scholars also mention that a system of two ayanas---‘devayana’, from spring equinox to autumn equinox followed by ‘pitriy¯ana’ for the next six months existed in ancient India. The concept of ‘pitriy¯ana’ and ‘dev¯ayana’ was also intimately linked to the Hindu faith that after death people follow a ‘pitriy¯ana’ route towards the south. Seasons: In pre-siddh¯antic astronomy, a solar year was divided into six seasons. However, in the very early Rigvedic era to begin with three, then five and finally six seasons were mentioned. Each season was considered to have two months. Table 3.2 shows the names of the months as found in vedic texts. It is not very clear why the month names are different from the nakshatra-based names which existed from the pre-siddh¯antic astronomy period. Perhaps these names originated much earlier before the nakshatra-based system was set up. The sacrificial year used Table 3.2 Seasons and months in pre-siddh¯antic Astronomy

Season

Month

Vasanta

Madhu and M¯adhava

Grisma

Sukra and Shuchi

Vars¯a

Nabhas and Nabhasya

Sh¯arad

Ish¯a and Urj¯a

Hemanta

Sahas and Sahasya

Sisira

T¯apas and Tapasy¯a

50 Table 3.3 Division of a day

3 Astronomy in Ancient India Type of division Names of the parts Two divisions

‘purv¯ahna’ and ‘apar¯ahna’

Three divisions

‘purv¯ahna’, ‘madhy¯ahna’ and ‘apar¯ahna’

Four divisions

‘purv¯ahna’, ‘madhy¯ahna’, ‘apar¯ahna’ and ‘s¯ay¯ahna’

Five divisions

‘pr¯atah’, ‘sangava’, ‘madhy¯ahna’, ‘apar¯ahna’ and ‘s¯ay¯ahna’

to commence with the beginning of spring equinoctial day. The month ‘M¯adhava’ used to start from the spring equinoctial day. As mentioned earlier the pre-siddh¯antic astronomy was based upon 27 nakshatras. Dividing the ecliptic into 12 ‘r¯ashis’ was not in vogue. The similarity of the names of the Indian ‘r¯ashis’ with the names of the signs as used in Europe is considered to be due to the influence of Hellenistic astronomy on siddh¯antic astronomy that started towards the later part of the first-millennium BCE. But very interestingly Rigveda mentions the constellations ‘Mesa’ (i.e. ‘Aries’) and Vrisabha (i.e. ‘Bull’). Of course in later vedic texts these two names are not found. Thus, very early Rigvedic period is really shrouded in mystery and its connection with the west needs to be investigated. The fire alters in the vedic age had very close relationship with astronomy, but a detailed discussion of the topic can be avoided here. Different types of division of a day are found in vedic literature. One ‘s¯avan’ (or, civil) day was from sunrise to sunset; it had different types of divisions as shown in Table 3.3. The day was also divided into 15 parts and each part was called a ‘muhurta’. Thus, there were 15 ‘muhurtas’ in the day and 15 ‘muhurtas’ in the night making a whole civil day consisting of 30 ‘muhurtas’. Each ‘muhurta’ was again subdivided into 15 ‘pratimuhurtas’with their individual names! Each ‘muhurta’ was equivalent to 48 min and each ‘pratimuhurta’ was equivalent to 3 min 12 s. Identification of time used to be through the use of 30 ‘muhurta’ and 15 ‘pratimuhurta’ names!! As will be discussed later in this section, in the Ved¯anga period, a more sophisticated system was developed. In the very early Rigvedic period, the names of only two planets are found (besides the sun, the moon, R¯ahu and Ketu, nothing but the nodal points of moon’s orbit)— jupiter and venus. Of course in the later pur¯anic texts, names of the five planets are mentioned. Again in the very early Rigvedic texts, there was no mention of a fixed Pole Star. In the later vedic literature, ‘Dhruva Tara’ is mentioned referring to the star Thuban. ‘Dhruva Tara’ represented permanency and its use was frequent in rituals like marriage. Then, again it disappeared from the astronomical texts except for literary references to earlier vedic texts. This is a very important point for the dating of the vedic era as will be discussed later in this book. Yuga concept in Pre-Ved¯anga Jyotisha period: Ancient Indian astronomers were always conscious about matching the yearly system with the seasons which depended purely on the movement of the sun. In fact the ancient astronomers considered the

3.3 Major Features of Astronomy in Ancient India

51

seasons to be the creator of the year; it is clear from the sloka from Shatapatha Br¯ahmana shown below.

Its translation could be as follows3 : ‘The year is the fire and the seasons are the sling (for holding it); for, the year can stand by the help of the seasons. By the seasons only does (one) support the year’. It was also stated that ‘the six seasons constitute the year. They (men) stand in the year by standing in the seasons’ (Taittiria Samhita 7.5.1). Thus, the year was defined by a complete cycle of the sun which is equal to 365 14 days. But again Taittiriya Samhita (5.6.7) states ‘One should perform sacrifice for 6 days for six are the seasons of the year. One should perform sacrifice for 12 days for twelve are the months of the year. One should perform sacrifice for 13 days for thirteen are the months of the year. One should perform sacrifice for 15 days for fifteen are the nights of half the month’. TS (7.5.1) states that ‘He has got 360 stotriyas, for so many are the nights of one year’. The length of a normal year was taken to be 360 days is further stated in Satapatha Br¯ahmana (10.4.2)—‘The year is the Praj¯apati or the Fire. The Praj¯apati has got seven hundred and twenty days and nights taken together’. So every year there was a shortfall of 5 41 days and in four years this accumulated to 21 days. The vedic astronomers added 21 days as a thirteen month in the fourth year to make the fourth year as a ‘long year’ of 381 days. This way the consistency of the calendar with the seasons was restored. In Satapatha Br¯ahmana, the names of the 381 days are mentioned! Aswamedha yajna used to be performed in this ‘long year’. This restoration phenomenon is beautifully explained in Taittiriya Samhita (4.3.11) as follows:

The translation of the above shloka is ‘The eye of the Praj¯apati increased (grew); (while growing) it fell away. From it a horse came into being. A horse is called Aswa, because it grew Aswayat. That (the eye) the Gods set again in its place by the Aswamedha, itself. Therefore, he who sacrifice, makes the Praj¯apati complete’. K. 3 History

of Science in India, vol. I, pt. 2 ‘Astronomy’ by Amitabha Ghosh, published by The National Academy of Sciences, India, and the Ramakrishna Mission Institute of Culture, Kolkata, 2014.

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L. Daftari beautifully interpreted the whole shloka. The difference of 5 41 days grew as the years passed. Then ‘this eye was set in its place again by the Aswamedha’ means that the difference was filled up. Although in the later Ved¯anga Jyotisha period, the luni–solar calendar was created by a five year Yuga system, in the vedic period a Yuga was the four year period, the last year being a long year of 381 days. Thus, in V¯ayu Pur¯an this period was referred to as ‘chatur yuga’. So the statement ‘The king (R¯avana) ruled here for thirteen Chatur Yuges’ means that R¯avana ruled for thirteen times four year (with one long year) period. In today’s calendar, the period is equivalent to 52 years. Again vedas and Mah¯abh¯arata mention two types of Yugas---M¯anusha and Daiva; or, human and divine. So divine Yugas could be the astronomical Yuga and much longer than human Yugas as per the interpretation of K. L. Daftari. This can eliminate some inconsistencies. Astronomy during the Ved¯anga period: It is very unfortunate that no astronomical text of the vedic period has survived and is available now. However, as a matter of great luck, one purely astronomical text of the Vedanga period has survived that is ‘Ved¯anga Jyotisha’. Had it been kept as a purely astronomical text it would have also met the same fate as the other astronomical texts. But it was considered as a part of the great vedas and, so, it got preserved through the hundreds of generations of vedic seers for millennia. Ved¯anga Jyotisha is found in two recensions---‘Rik Jyotisha’ and ‘Yajur Jyotisha’, consisting of 36 and 43 verses, respectively. Out of the 43 verses of Yajur Jyotisha, 30 are common to Rik Jyotisha. So, all together there are 49 verses, which are nothing but algorithms for calculating dates, tithis, parvas and so on. The Rik Jyotisha was published by H. Jarvis in 1834 as an annexure to his book entitled ‘Indian Meteorology’. Later Weber published both the recensions in 1872. Since then a large number of European and Indian scholars like S. B. Dixit, B. G. Tilak, Lala Chhotolal and J. B. Modak have analyzed the verses and tried to decipher the complicated verses. From the verses 6, 7 and 8 of Yajur Jyotisha, it is known that during the period when Ved¯anga Jyotisha was composed the winter solstice was at the start of nakshatra Sravisth¯a and the summer solstice was at the middle of nakshatra Asles¯a. Comparing this with the current situation and using the known rate of precession of the equinox, the antiquity of Ved¯anga Jyotisha goes back to 1400 BCE. It is also mentioned in the Rik Jyotisha that the periods of daylight during the summer and winter solstice were 18 and 12 ‘ghatis’, respectively. From this, the latitude from where the observations were made can be computed. The location of the observations recorded in Ved¯anga Jyotisha is found out to be at 34°50 N latitude. This matches with the latitude of ‘Sapta-Sindhu’ region of north-west India where the vedic texts were supposed to have been composed. Basic features of Ved¯anga Jyotisha (VJ): Ved¯anga Jyotisha deals with primarily the ‘mean’ motions of the sun and the moon. The knowledge required to analyse the true motions was developed in the Siddh¯antic astronomy period. Differentiating two consecutive days just by observation is not at all easy, whereas it is not a difficult task to distinguish two consecutive nights by observing the moon’s phase. As a consequence of this, the ancient astronomers used the moon’s phases

3.3 Major Features of Astronomy in Ancient India

53

to distinguish one night from another during a lunar month. Beside this, they very ingeniously used the location of the full moon among the 27 nakshatras to determine the position of the lunar month in a tropical (solar) year. Thus, a primitive skeleton of a calendar was made possible. The basic scheme was based on ‘tithi’ and ‘nakshatra’. A tithi referred to a ‘phase’ of the moon whereas a nakshatra identified the location of the moon (and sun also) in the background of the fixed stars. As the tropical solar year has no direct relation with the phases of the moon the astronomers of vedic period had to observe the sideral positions of the sun and the moon along the ecliptic for thousands of years to identify a time cycle that was in harmony with both the solar and the lunar cycles. What was achieved was quite inaccurate by today’s standards but it helped the ancient Indian society in conducting the rituals and sacrifices. The 5-year Yuga system that was set up in the pre-siddh¯antic astronomy is described below: According to Ved¯anga Jyotisha, the solar year was considered to have 366 days but the lunar year, consisting of 12 lunar months of 30 tithis each, had 354 days. As a result a lunar year falls short by approximately 12 days every year. This generates 60 extra days in a 5 year ‘Yuga’ period. These extra 60 days are incorporated into the Yuga period as two intercalary months of 30 days each. As mentioned earlier the first intercalary month is introduced at the end of two and half years and the second one at the end of the cycle. Figure 3.3 shows the 5-year Yuga scheme schematically. Fig. 3.3 A 5-year Yuga period

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3 Astronomy in Ancient India

In Ved¯anga Jyotisha (VJ) period, the ‘purnim¯anta’ system was already replaced by the ‘am¯anta’ system as mentioned earlier. In the am¯anta system, a month used to start on ‘shukla pratip¯ada’, i.e. the day after the new moon. Of course the name of a particular month used to be according to the nakshatra where the fullmoon took place (at the middle of particular month). A ‘Yuga’ began with the first day of a month, i.e. on a ‘shukla pratip¯ada’ day. It used to end also on the last day of a month, i.e. ‘am¯avasy¯a’. During Ved¯anga Jyotisha period, the beginning of a ‘Yuga’ used to also coincide with the winter solstice day (i.e. the day ‘Uttar¯ayan’ started and ‘Dakshin¯ayan’ ended). The winter solstice used to be at the beginning of nakshatra Sravistha. From this, a particular day’s month, tithi, etc., could be calculated using the rate of movement of the sun and the moon along the ecliptic. Most of the verses of ‘Ved¯anga Jyotisha’ are the algorithms for these calculations presented in a very condensed and cryptic form. Terminologies and Calculation Procedures in Ved¯anga Jyotisha: A brief description of the calculation procedure in Ved¯anga Jyotisha may be in order here. The various terms used in this text are being summarized here to start with: (i)

(ii) (iii) (iv) (v) (vi)

(vii)

Solar year—In VJ, one tropical solar (s¯amp¯atik soura) year is the time taken by the sun to go from one vernal equinox to the next vernal equinox.4 The sidereal solar year is the time taken by the sun to come back to the same location in the background of the fixed stars. The two periods are slightly different because of the precessional motion of the earth’s axis. Actually, the sidereal year is about 20 min longer than the tropical year. Of course this finer distinction was not perceived in VJ period. A solar year was considered to consist of 366 days. Civil day—A civil day (s¯avana) day was the period from one sunrise to the next sunrise (24 h). Lunar month—The period from one full moon to the next full moon which is a little more than 29 21 days. Solar month—The solar year is divided into 12 equal solar months each being of 30 21 days duration. Tithi (or lunar day)—A lunar month is divided into 30 equal periods, called ‘tithis’. It is a little shorter than a civil day and is of 23 h 37 min duration. ‘Paksha’ and ‘Parva’—The period of 15 ‘tithis’ from new moon to full moon (and also from full moon to new moon) is termed as a ‘paksha’; the first paksha in a month is ‘sukla paksha’ and the second half is ‘krisna paksha’. The angular distance traversed by the sun along the ecliptic during a paksha is called a ‘parva’. Bh-amsa—For the purpose of calculating the sun and moon’s positions and also the ‘tithi’, ‘parva’, etc., the year is divided into ‘tithis’, ‘nakshatras’ and ‘Bh-amsa’. ‘Bh-amsa’ is a finer subdivision and 1 nakshatra is equivalent to 124 ‘Bh-amsa’ (nakshatra part).

4 Identifying an equinoctial day is much easier than detecting a solstice. During summer and winter

solstices, the sun appears almost stationary for almost 11 days. Thus, observationally it is easier to detect an equinoctial day.

3.3 Major Features of Astronomy in Ancient India

55

Fig. 3.4 Spatial and temporal divisions of year

The temporal and spatial divisions used by the astronomers of Ved¯anga Jyotisha period is diagrammatically shown in Fig. 3.4. The details of this division procedure are presented below. In 1 year, the sun traverses through 27 nakshatras covering 360° of the ecliptic. Again 1 year consists of (30 × 12 + 12 =) 372 tithis. So, the sun takes (372/27 =) 124/9 tithis to cross one nakshatra. Again 1 nakshatra = 124 Bh-amsa. So, in 1 tithi the sun travels through 9 Bh° (Bh-amsa). For the spatial division, it is noted that 1 nakshatra covers 13.33° of the ecliptic. So, 1 Bh° (13.33/124 =) 0.1075° of ecliptic. Again one parva consists 15 tithis and, so, in 1 year there are (372/15 =) 24.8 parvas. Thus, in 1 parva the sun travels through (15 × 9=) 135 Bh°. For crossing 1 nakshatra, the sun takes 124/135 parva. Time measurement in Ved¯anga Jyotisha was also quite developed. Yajur recension of Ved¯anga Jyotisha states the ‘A vessel which holds 50 ‘palas’ of water is the measure called “¯adhaka"’. It should be understood that the time was the time required to empty the vessel through a hole. The following time units were specified as follows: 50 ‘palas’ ≡ 1 ‘¯adhaka’ 4 ‘¯adhaka’ ≡ 1 ‘drona’ ≡ 200 ‘palas’ ≡ 64 ‘kudava’ Another time unit ‘n¯adika’ is also used 1 ‘n¯adika’ ≡ 61 ‘kudava’ ≡ 10 +

1 20

‘kal¯as’ ≡ ½ ‘muhurta’

Thus, one whole civil day has 30 ‘muhurtas’ ≡ 60 ‘n¯adik¯as’ ≡ 603 ‘kal¯as’. There are some other finer time units in Ved¯anga Jyotisha. The equivalence with the presently used units is as follows: 1 day = 24 h 1 ‘muhurta’ ≡ 48 min 1 ‘n¯adik¯a’ ≡ 24 min 1 ‘kal¯a’ ≡ 2.4 min 1 ‘k¯astha’ ≡ 1.1 s Two other very fine time units are found in VJ – 1 ‘m¯atr¯a’ ≡ 0.11 s and 1 ‘truti’ ≡ 0.00003 s. The use of such fine time units is not understood.

56

3 Astronomy in Ancient India

The method of studying the sun’s motion has been discussed above. Computation of the moon’s position among the nakshatras and its phases (i.e. ‘tithis’) used to be done in a manner that is briefly discussed here. The parameters of the 5 years Yuga system are illustrated below: (i) (ii) (iii) (iv) (v) (vi)

The number of civil (s¯avana) days in a solar year = 366 A solar year has 2 ayanas, 6 ritus and 12 months In a 5-year Yuga, there are 1830 s¯avanadays and (1830 + 5 =) sidereal days5 The number of synodic months in a Yuga is 62 The number of lunations in a Yuga is (62 + 5 =) 67 The number of moon’s rising in a Yuga is (1835 − 67 =) 1768

The term ‘lunation’ means the period taken by the moon to return to the same place from where it started. It is slightly different from one fullmoon to the next fullmoon. The moon moves through 27 nakshatras 67 times in a Yuga and, therefore, the moon traverses through (27 × 67 =) 1809 nakshatras in one Yuga. Since one civil day has 603 kal¯as in 1 Yuga, there are (1830 × 603 ≈) 1,103,490 kal¯as. Thus, the moon traverses through 1 nakshatra taking a time equal to 1830 × 603 = 610 kala ≡ 1 day + 7 kalas 27 × 67 Using the above the moon’s position can be determined. A detailed discussion of the calculations is omitted here and the reader can refer to appropriate texts (See Footnote 3). Though Ved¯anga Jyotisha is a purely astronomical text of Ved¯anga period dating back to about 1400 BCE there are other texts of Ved¯anga era which also contain a reasonably good amount of astronomical references. The epic text Mah¯abh¯arata and Par¯asara Samhit¯a are the two such examples. As will be shown later, Mah¯abh¯arata war has been dated to a period between 1900 BCE and 1500 BCE. Par¯asara belonged to the era from 1300 BCE to 1100 BCE. In Mah¯abh¯arata one finds the names of all the five planets of the pretelescopic era of astronomy; but no mention of the twelve zodiacal signs (R¯ashi) or the seven days of the week is found in Mah¯abh¯arata. The mention of the 5-year ‘Yuga’ system is found in Mah¯abh¯arata and this establishes its link with the pre-siddh¯antic astronomy. Though all the five planets and even some of their retrograde motions are mentioned in Mah¯abh¯arata; the absence of any influence of Hellenistic astronomy is clearly established. Par¯asara Samhit¯a is available only in fragmented form and in quotations by authors of the later siddh¯antic astronomy. Although Par¯asara Samhit¯a refers to all the planets but the seasons were described in reference with the nakshatras. No mention of the 12 ‘R¯ashis’ (zodiacal constellations) is found. The astronomy of Par¯asara Samhit¯a was not matured enough like the later siddh¯antic astronomy but was definitely more matured as it states the cycle of Venus to be 591 days (the modern value being 5 One sidereal day means 1 rotation of the earth with reference to the fixed stars. It is slightly shorter

than one ‘s¯avana’, or, civil day.

3.3 Major Features of Astronomy in Ancient India

57

584 days) establishing the accuracy level of observation. Even the sidereal periods of planets jupiter and saturn were observed and recorded as 12 and 28 years, respectively, very near to the correct values!! Par¯asara presents discussion on comets in great details classifying them into eleven groups. Total number of comets described was 101. Subsequently, there was another name that appears in the history of astronomy— Garga. But since quite a few Gargas are found in the history, the pre-siddh¯antic Garga is referred to as Vriddha Garga. Apart from recounting the whole work of Par¯asara, Garga also discussed comets in great details. As per his text, the period over which all the listed comets appeared was 1300 years. Strangely Garga Samhit¯a states that 1000 years elapsed between the appearances of two comets ‘Samvartaka’ and ‘Dhuma’! After Garga nothing much is found related to astronomy till the firstcentury CE.

3.3.2 Siddh¯antic Astronomy After Ved¯anga Jyotisha there is a misty period till the early centuries of the Common Era. Since the third-century BCE, a considerable amount of interaction with the western world started taking place and an amalgamation of the original Indian astronomical principles with Hellenistic astronomy led to the zodiacal sign-based siddh¯antic astronomy. The siddh¯antic astronomy developed methods for determining the true positions of the sun, moon and the planets. The most noted among the siddh¯antic astronomers included Aryabhatta I, Brahmagupta, Bhaskaracharya, Barahamihira and many others. Aryabhatta was the first to announce that the earth rotates about its own axis once every day. He was subjected to heavy criticism for this view. Although siddh¯antic astronomy was far more advanced and accurate compared to pre-siddh¯antic astronomy, the siddh¯antic astronomy period is mostly covered by recorded history and astronomical dating does not play any major role in establishing chronology. Therefore, any discussion on siddh¯antic astronomy is not being presented in this volume. However, a brief account of the very basic and essential elements may not be out of place. Post-Ved¯anga Jyotisha astronomy in ancient India can be divided into primarily three periods as mentioned below: (i) Early Siddh¯anta period—100 BCE to 400 CE (ii) Siddh¯anta period---400 CE to 1100 CE (iii) Late Siddh¯anta & Medieval period---1100 CE to 1800 CE The basic features of siddh¯antic astronomy are presented below for capturing a glimpse. Siddh¯antic astronomy is a vast subject with contributions from a very large number of astronomers working for over one and half millennia. The whole knowledge base of this science can be grouped under four schools:

58

(i) (ii) (iii) (iv)

3 Astronomy in Ancient India

Bramha paksha ¯ Arya paksha Ardhar¯atik¯a paksha, and Saura paksha

Although the basic tenants of the science in all these four schools (or, ‘paksha’) were not very different the units of time and arrangements of the Mah¯ayuga systems had some variations. In Ved¯anga Jyotisha, a Yuga was comprised of 5 years primarily to achieve integer number of lunar months and solar years in this period. However, in siddh¯antic astronomy, a Yuga implied a much longer period of time. This was done with the primary aim to express the planetary revolutions with integer numbers. So, unlike the usual understanding (that came into existence at a much later period) the early siddh¯antic astronomers in all probability did not consider the ‘Yugas’ and ‘Mah¯ayugas’ to be real temporal eras with any physical existence. Of course, at a later period the ‘Kalpas’, ‘Manus’, ‘Manvantaras’ became linked with the life cycles of the world. ¯ A major problem has been created by Aryabhata I by announcing the onset of the current ‘Kaliyuga’ on the midnight of the 17 February 3102 and 18 February 3102 ¯ BCE. It is still not known on what basis Aryabhata I made this assertion. Siddh¯antas had different sections; the primary ones were ‘madhyam¯adhik¯ara’ and ‘spast¯adhik¯ara’, dealing with the mean motions6 of the sun, moon and the planets, and the true positions, respectively. The siddh¯anta astronomers were aware of the ‘precession of the equinoxes’ called ‘ayanachalana’. The specification of the longitude in Indian ancient astronomy was a little different from that in western astronomy. In the western system the longitude is always measured from the vernal equinoctial point and, therefore, varies with time since the VE shifts with time due to the precession. As mentioned earlier this longitude is called ‘s¯ayana’ longitude. Conversely, in the Indian system the longitude is always measured from a fixed point on the ecliptic, the starting point of ‘Aries’ or sign ‘Mesha’. This point is referred to as ‘Mesh¯adi’ and such longitudes are called ‘nir¯ayana’ longitude. Thus, Indian astronomers reckon the first point of Aries which coincided with the vernal equinox in the year 285 CE. In ancient Indian astronomy, the prime meridian was the great circle passing through the poles and Ujjayani. To determine the mean position, a straightforward approach was followed. Starting from the epoch7 the number of days is calculated to the desired day. This was called ‘ahargana’. Then, multiplying the ‘ahargana’ by the mean motion the mean position of the object could be determined. If n be the mean motion (degrees/civil days) and λ-0 be the longitude of the object at the epoch (the starting date of the era from which the ‘ahargana’ is counted), then the mean longitude is given by  λ=R

 nA + λ0 360◦

6 Due to various reasons, the motions of the sun, moon and planets are not uniform in the background

of the fixed stars. So, as a first step, the mean position of a body was determined and then corrections were imposed to get the true position. 7 The first day of a particular era.

3.3 Major Features of Astronomy in Ancient India

59

Fig. 3.5 Computation of ‘ahargana’

where A is the ‘ahargana’ and R denotes the residue. It should be remembered that since all planets, the sun and the moon go along the ecliptic, latitude remains unchanged (more or less). The procedure is quite straightforward but siddh¯antic astronomy was based on a luni-solar system. Thus, since the motions of the sun and the moon are mixed up, determination of ahargana is a little involved. Steps of the computation of ahargana are diagrammatically represented in Fig. 3.5. For the computation process, a ratio and proportion approach used to be followed and the data for the mean motion of the sun and the moon (for computing ahargana only the data for the sun and the moon are necessary) are given in Table 3.4. The daily mean motions of various objects according to different systems of siddh¯antic astronomy are shown in Table 3.5. The data given in this table along with the positions at the epoch completes the information required to determine the mean positions of the planets, the sun and the moon. These are given in Table 3.6. After the determination of the mean position, the true position is found out by employing some corrections. The reader can refer to a standard book to get more information on the subject.

60

3 Astronomy in Ancient India

Table 3.4 Standard data for ‘ahargana’ computation Number in a Mah¯ayuga

According to ¯ Aryabhattiya

Surya Siddh¯anta

Siddh¯anta Siromani

1

Rev. of the sun

4,320,000

4,320,000

4,320,000

2

Rev. of the moon

57,753,336

57,753,336

57,753,336

3

Rev. of the earth

1,582,237,500

1,582,237,828

1,582,236,450

4

Civil days

1,577,917,500

1,577,917,828

1,577,916,450

5

Solar months (M s )

51,840,000

51,840,000

51,840,000

6

Lunar months (M l )

53,433,336

53,433,336

53,433,300

7

Intercalary months (M i )

1,593,336

1,593,336

1,593,300

8

Solar days (Ds )

1,555,200,000

1,555,200,000

1,555,200,000

9

Lunar days (Dl ) (tithis)

1,603,000,080

1,603,000,080

1,602,999,000

10

Omitted lunar days (Do ) (tithis)

25,082,580

25,082,252

25,082,550

Table 3.5 Daily mean motions Object

Daily mean motion, n Aryabhattiyam

Surya Siddhanta

Modern Value

Sun

0°59 08 .170294

0°59 08 .10097

0°59 08 .2

Moon

13°10 34 .87759

13°10 34 .5202

13°10 34 .9

Mercury Perigee

4°05 32 .3152

4°05 32 .2042

4°05 32 .4

Venus Perigree

1°36 07 .7381

1°36 07 .4337

1°36 07 .7

Mars

0°31 26 .4636

0°31 26 .2810

0°31 26 .5

Jupiter

0°04 59 .1502

0°04 59 .0848

0°04 59 .1

Saturn

0°02 00 .3782

0°02 00 .2253

0°02 00 .5

Table 3.6 Starting positions at the kali epoch Object

λ0 Aryabhatta

Surya Siddhanta

Siddhanta Siromani

Sun

00 s 00°00 00

00 s 00°00 00

00 s 00°00 00

00 s

00°00 00

00 s

00°00 00

00 s 00°00 00

Mercury Perigee

11 s

21°21 36

00 s

00°00 00

11 s 27°24 29

Venus Perigree

11 s 27°07 12

00 s 00°00 00

11 s 28°42 14

00 s

00°00 00

00 s

00°00 00

11 s 29°03 50

Jupiter

11 s

27°07 12

00 s

00°00 00

11 s 29°27 36

Saturn

00 s 00°00 00

00 s 00°00 00

11 s 28°46 34

Moon

Mars

Chapter 4

Descriptive Archaeoastronomical Approaches

4.1 Introduction A brief description of the basic principles involved in descriptive archaeoastronomy was given in Sect. 2.4.2. In this chapter the principles are going to be elaborated that can help better the understanding of their application for dating purpose. As mentioned earlier, in descriptive archaeoastronomy only the descriptions of past stellar and planetary alignments are used. It was also mentioned briefly that there are a few phenomena which can have use for the determination of the date (or a period) of the observation under consideration. For a reliable result the phenomenon should be a relatively infrequent one like total or annular solar eclipse at a particular time of the day. Another phenomenon that can serve very useful purpose for dating of ancient observations is the precession of the equinox. In fact this approach is not only most dependable but the phenomenon of the precession is manifested in various ways which is noticeable with naked eye astronomy. A somewhat less popular approach is the observation of exaltation of planet mars at a given nakshatra. These approaches are presented below. Precession of the equinox playing the most important role will be taken up first.

4.2 Effects of the Precession of the Equinoxes on Observational Astronomy In Sect. 2.2.2 the secular changes in the astronomical parameters were discussed. As discussed the most important of the various effects is the precession of the equinoxes. The precessional motion of the earth’s axis of daily rotation causes two simultaneous effects presented below:

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 A. Ghosh, Descriptive Archaeoastronomy and Ancient Indian Chronology, https://doi.org/10.1007/978-981-15-6903-6_4

61

62

4 Descriptive Archaeoastronomical Approaches

Fig. 4.1 Variation of α and δ with time due to precession

(i) The equinoctial points shift slowly westwards at the rate of about 50.4 of arc per year. This amounts to a 1° shift of the equinoctial points (towards west) along the ecliptic every 72 years. (ii) The celestial pole describes a circle with 47° diameter with the ecliptic pole as the centre. It takes about 25,800 years to complete one cycle. Figures 2.18 and 2.20 show the effects of this precessional motion of the celestial pole and the equinoctial points. Another secondary effect of the shift of the celestial pole’s position in the background of the fixed stars is that the meridians and latitudes of the heavenly bodies also change with time. This phenomenon is shown in Fig. 2.19. Equation (A20) of the Appendix A depicts the mathematical form of this phenomenon. Figure 4.1 shows the nature of variation of α and δ with time due to the precessional motion of the earth’s axis. As the meridians change two stars at different R.A.’s can be found to lie on the same meridian at some era due to this effect. Further, as the celestial pole position shifts, the circumpolar 1 character of the stars near the pole also undergoes alteration. Therefore a constellation near the north pole may be circumpolar in some era but may lose this character at some other period. Figure 4.2 shows the north pole region at two different eras as seen from the latitude of New Delhi. Whereas in Fig. 4.2a the constellation “Saptarshi Mandal” (or, ‘Great Bear’) is found to be circumpolar in 2000 BCE, at present this constellation is no longer circumpolar as evident from Fig. 4.2b. Such references from the past can sometime establish the antiquity of the observations recorded in texts.

1 The

word’circumpolar’ means that a star (or a constellation) never seen to go below the horizon when seen from a place during whole day or night.

4.2 Effects of the Precession of the Equinoxes on Observational Astronomy

63

Fig. 4.2 a Saptarshi Mandal in 2000 BCE, b Saptarshi Mandal in 2000 CE

4.2.1 Changing Relation of Seasons with Lunar Month The methodology that was followed in ancient India for naming the lunar months has been described in earlier chapters. The name of a month was linked with the nakshatra against which the full moon of the month was observed. Figure 4.3 shows two (almost) diametrically opposite positions for the earth, E and E  . As shown in the figure the earth’s axis is tilted exactly towards the sun in position E and away from the sun in position E  . Thus, it is clear that at position E it is the summer solstice day and at position E  the day in the northern hemisphere is of the shortest duration implying at E  the earth experiences the winter solstice. Now, the month name when summer solstice occurs depends on the nakshatra, N, against which the full moon is observed. Similarly, the name of the month when winter solstice occurs is given by the nakshatra, N  , against which full moon is observed as the moon M  is in opposition. It should be noted that the full moon is not necessarily be expected to take place on the summer or the winter solstice days. But these days fall in the months N and N  . Had there been no precessional motion of the earth’s axis the relationship between the month name and seasons would have remained the same all along. But the precessional motion causes the earth’s axis to change orientation in the frame of reference of the fixed stars. Figure 4.4 shows the summer solstice at two different era. In 2018 the full moon is seen to be against nakshatra N in the month of the summer solstice (when the earth’s axis tilts directly towards the sun as indicated in the figure). But the orientation of the tilted axis is not fixed; it slowly precesses in a sense opposite to the direction in which the earth goes round the sun and the moon goes round the earth. The rate of the precession causes a 1° rotation in 72 years. Thus, around 100 BCE the orientation of the tilted axis (when seen from the north ecliptic pole) will make approximately 30° with the position in 2018 as shown in

64

Fig. 4.3 Relation of month with season

Fig. 4.4 Summer solstice at two different era

4 Descriptive Archaeoastronomical Approaches

4.2 Effects of the Precession of the Equinoxes on Observational Astronomy

65

Fig. 4.4. Thus, the summer solstice will be in a month when full moon is seen against a nakshatra N  . Hence, the peak summer month name becomes different. Since the solstice and equinoctial days decide the seasons the month names for various seasons also change. Not only the full moon position in the ecliptic (identified by the circle through the 27 nakshatras) the position of the sun in the ecliptic on specific cardinal days also undergo variation. In 2018 the sun lies at nakshatra n on the summer solstice day, but in 100 BCE the summer solstice position of the sun was at n . Of course the nakshatra at which the sun lies at a particular time cannot be directly observed for obvious reasons, and, it has to be ascertained from the moon’s position on the corresponding full moon day as already mentioned in a previous section. A similar situation also arises in the case of the equinoctial points. Because of the precession, the equinoctial points shift westwards along the ecliptic at the rate of 1° per 72 years. These imaginary points on the ecliptic play very important roles in positional astronomy. Figure 4.5a, b show the vernal equinoctial points’s shift westwards along the ecliptic. Any star (or group of stars) at the equinoctial points lies on the celestial equator also. As explained in Sect. 2.4.1 and Fig. 2.23 the celestial equator cuts the eastern horizon exactly in the east. Therefore, any heavenly object at the location of an equinoctial point rises exactly on the east (like all other stars lying on the celestial equator on that day). It is already described in Sect. 2.4.1 that the sun also

Fig. 4.5 a Position of the vernal equinoctial point at time t 1 (2000 CE), b position of the vernal equinoctial point at time t 2 (1900 CE)

66

4 Descriptive Archaeoastronomical Approaches

rises exactly on the east and sets exactly at the western point of the horizon on the equinoctial days. Thus, rising and setting of important stars and nakshatras provide indication of the period when the observation was recorded. Figure 4.6 shows the situation on the summer solstice day and the winter solstice day during the past six thousand years. Similarly, Fig. 4.7 shows the situation on the equinoctial days during the past 6000 years. These figures show the relationship of these cardinal days in a year with the nakshatra reference system. The configuration of the sun and the earth indicates the direction when the moon is in opposition and a particular nakshatra is in the background.

Fig. 4.6 Situations on the summer solstice and on the winter solstice days during the past 6000 years when viewed from the south celestial point

Fig. 4.7 Situations on the spring (vernal) and autumn equinoctial days during the past 6000 years when viewed from the south celestial pole

4.2 Effects of the Precession of the Equinoxes on Observational Astronomy

67

4.2.2 Simultaneous Transit of Important Stars Transit of a star is defined as the crossing of a star of the prime meridian great circle. For a given observer the prime meridian is defined by the great circle passing through the north celestial pole and the zenith point. Simultaneous transit of two stars can be used for finding the true north or true south directions. In case of circumpolar stars (around the north celestial pole) the exactly vertical line joining two stars—one at its highest position the other being at the lowest—has been used in the ancient times for finding the true north in the absence of any visible pole star. Figure 4.8 explains the phenomenon. As mentioned the prime meridian is defined by the great circle passing through the north celestial pole and the zenith point of the observer. This is shown as the line L. If two visible stars A and B cross this line simultaneously then a line joining them passes through the north pole. Furthermore when this line AB takes the vertical position the direction identified by the line points to the true northerly direction. This method was used in ancient times for orienting major pyramids when no stars were available at the position of north celestial pole. But with the passage of time this simultaneous crossing of the prime meridian also gets affected as explained in Fig. 2.19. Figure 4.9 shows the northern region of the sky. The north celestial pole describes a circle with the pole of the ecliptic as the centre. At a time when the north pole is at point N the line joining the stars A and B passes through the pole, and when AB is vertical it can be used to get the true north direction. But if the north celestial pole changes its position to, say, N  the line AB no longer passes through the pole. So, the time when AB can be used for detecting true north is reasonably well identified. Fig. 4.8 Simultaneous crossing the prime meridian (prime great circle) by two stars

68

4 Descriptive Archaeoastronomical Approaches

Fig. 4.9 Change of simultaneous transit

4.2.3 Heliacal Rising of Stars and Constellations The term heliacal rising was briefly explained in Sect. 2.4.2. More details about this particular type of observation is given in Appendix A. In this section it will be discussed how observation of heliacal rising of important stars and constellations can be used for dating of such ancient observations. The science behind the occurrence of the phenomenon for a particular star originated from the time of Ptolemy about 2000 years ago. The key parameter that takes a decisive role in a particular case is the ‘arcus visionis’. It is the minimum distance between the horizon and the sun (below the horizon line) and the star and the horizon when the star is last to be visible (above the horizon line). Figure 4.10 explains this term ‘arcus visionis’. If it is assumed that a star is visible as soon as it is just above the horizon line then ‘arcus visionis’ (hv ) is given by the depth of the sun below the horizon. However, in general a star is visible only when it is above the horizon line by some minimum distance due to a number of reasons like refraction phenomenon, atmospheric pollution etc. In such cases the ‘arcus visionis’

Fig. 4.10 ‘Arcusvisionis’ for heliacal rising

4.2 Effects of the Precession of the Equinoxes on Observational Astronomy

69

Fig. 4.11 The configuration for heliacal rising

is given by the sum of the depth of the sun below horizon hH and the minimum distance of the star above horizon hs . Thus, hv = hH + hs . It is obvious that the value of ‘arcus visionis’ depends on the brightness of the star in consideration as has been explained in Appendix A. When calculating the date of heliacal rising a variation in hv by 1° can affect the result by a couple of days. The heliacal rising depends on the location of the observer also. Figure 4.11 shows a situation when a star X is rising heliacally, the sun being at H. the declination of the sun is δ and as a special case the star X is also on the same latitude circle (i.e. the same declination) as the sun. N T U S V is the horizontal circle, U and V being the rising and the setting points of the sun (and the star X), respectively. If a great circle is drawn joining the zenith and the sun, H, it will intersect the horizon circle at point T at right angles. Since the angular distance HU is small the region of the celestial sphere in the immediate vicinity of the rising point can be approximately represented by a plane triangle HTU as shown in Fig. 4.12. Since the great circle ZTH intersects the horizon at right angles HTU is a right angled triangle, ∠HU T being the co-latitude ϕ  of the observer’s location. The heliacally rising star is at X (as a special case). Thus according to the condition specified for heliacal rising the ‘arcus visionis’ hv = H T + Y X where Y is the intersection point of the line drawn from the star X normal to the horizon line. From the figure

70

4 Descriptive Archaeoastronomical Approaches

Fig. 4.12 The region of heliacal rising

HU ≈

HT sin ϕ 

and U X ≈

XY sin ϕ 

so, h v = (HU + U X ) sin ϕ  ≈ H X sin ϕ  Hence the necessary difference in longitude λ of the sun and the heliacally rising star (on the same latitude circle of the sun as a special case) X, is given by λ ≈ sinh vϕ  . This shows that heliacal rising of a star also depends on the observer’s position. At lower latitudes of the observer’s location the longitude difference necessary for heliacally rising of a star will be smaller. Here, a different star satisfies the condition for heliacal rising. If the star be at a different latitude circle then the condition for heliacal rising is shown in Fig. 4.13.

Fig. 4.13 Heliacal rising when the star’s declination is different from that of the sun

4.2 Effects of the Precession of the Equinoxes on Observational Astronomy Table 4.1 Heliacal rising of Agastya in 2014

Observer location

Latitude 06

71

Date of helical rising

Srinagar

34°

Jaipur

26° 19

September, 24 August, 24

19

August, 20

Varanasi

25°

Bengaluru

13° 0

July, 27

Kanyakumari

8° 04

July, 18

The declination of the star under consideration has a declination δ less than that of the sun. If the latitude circle of the star is not too far away from the latitude circle of the sun, i.e. when δ is not large λ ≈ Q X = Q D + D X hv + DX = sin ϕ  hv + δ cot ϕ  = sin ϕ  When the declination of the star is more than that of the sun λ =

hv − δ + ϕ  sin ϕ 

All the above relations are, of course, approximate in nature and valid for small values of hv and λ. Now, it should be remembered that the location of the sun on the ecliptic relative to the equinoctial and solstitial positions decides the season. Therefore, heliacal rising of a star indicates the seasons. Again due to the precessional motion of the earth’s axis the location of the cardinal positions (equinoctial and solstitial) in the background of the fixed stars (including the nakshatras) changes with time. Hence the heliacal rising of a star (or, a constellation) at a particular season can identify the era. To show how the latitude of the observer can affect the heliacal rising the example of heliacal rising of star Agastya in the year 2014 has been shown for different latitudes is taken and shown in Table 4.1.

4.3 Exaltation of Planets Although exaltations of planets are primarily associated with astrology such descriptions in ancient texts can sometimes be helpful to establish the antiquity of the observation. In Sect. 2.4.2 the topic has already been introduced and explained. Here a few more details are going to be added. As mentioned in Sect. 2.4.2 the exaltation phenomenon is most pronounced (and, therefore, easily identifiable with naked eye

72

4 Descriptive Archaeoastronomical Approaches

observation) in the case of the planet mars. This is so as the eccentricity of mars’s orbit around the sun possesses a substantial degree of ellipticity. It has been explained already that the brightest opposition for mars takes place when mars in opposition is also at its perihelion position. Or in other words, the perihelion of mars’s orbit is identified by the exaltation. But the perihelion point of the mars’s orbit undergoes slow change. It moves by 1° in approximately 225 years. The s¯ayana longitude of mars’s perihelion can be expressed as follows: λ ≈ 336◦ 03 37 + 1598 T − 0.62 T 2 − 0.011 T 3 where T is measured in centuries starting from 2000 CE. Hence the nir¯ayana longitude of the perihelion of mars’s orbit can be expressed as λ0 ≈ 312◦ 12 12 + 1598 T − 0.62 T 2 − 0.011 T 3 as the equinoctial point shifts. The necessary correction is called ‘ayan¯amsha’. Now, A = 23◦ 51 25 + 5029 T + 1.1 T 2 + 0.0001 T 3 and λ − A = λ0 . So, the nir¯ayana longitude of mars’s perihelion position can be found out from the position of the exalted mars in ancient texts.

4.4 Ancient Eclipses Solar and lunar eclipses are extraordinary celestial phenomena. Out of the two types of eclipses, solar eclipses are more spectacular events, particularly if it is a total one. It is unconceivable that such events were not closely observed by the ancient people. Thus, records of such spectacular celestial phenomena are found in ancient texts. Besides, eclipses used to instill fear in the minds of the ancient people from all walks of life and, as a result, used to make deep impressions in the minds of all. Since the real scientific reason behind these natural phenomena were unknown in most cases eclipses were generally considered something evil. Certain types of solar eclipses, total and annular, at a particular location on a particular day of the year are very rare,2 and, can be used for investigating ancient chronology. Earlier, dating ancient eclipses was a complex and tideous exercise requiring special knowledge. After the progress in computer science and technology such exercise has become relatively easier. Another feature associated with eclipses is the temporal proximity between two consecutive eclipses, (one lunar and the other solar). An eclipse taking place on one of 2 From

a given location on the earth a total solar eclipse can be seen once in every 360 years.

4.4 Ancient Eclipses

73

the four cardinal days in a year is also a rare event, and can be used for chronological study. References to such eclipses are also found in ancient literature. A brief account of the phenomenon of eclipse is being presented so that it will be easier to follow the discussions on using ancient references to eclipses for establishing chronology. Though both lunar and solar eclipses are described, solar eclipses are more important as total eclipses are comparatively rare and are described in more details. During total solar eclipse the solar disc becomes completely invisible whereas during lunar eclipse the eclipsed moon is still visible as a reddish disc. As mentioned earlier solar eclipses, particularly near total, total and annular are relevant for analysing the ancient references. In this section a brief account of solar eclipse is being presented. It is well known that when the moon comes in between the sun and the earth obscuring the solar disc either partially or completely a solar eclipse occurs. Hence for a solar eclipse can take place only on the new moon days as the moon is then in conjunction. However an eclipse does not take place on all new moon days. Figure 4.14 shows the sun, earth and the moon. The orbital plane of the moon is slightly tilted with the plane of the ecliptic by approximately 5.15° as shown in Fig. 4.14. Therefore, in all conjunctions the sun, moon and the earth do not lie in one straight line which is necessary for an eclipse to occur. This can happen only when the moon lies on the plane of the ecliptic when in conjunction. Since the orbit of the moon intersects the ecliptic plane, the intersecting point, called a node—ascending or descending, depending on the configuration, must be between the earth and the sun. If the moon happens to be at this node at the moment a solar eclipse takes place. In the figure points A and D are the ascending and descending nodes, respectively, and

Fig. 4.14 The orbits of the earth and the moon

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4 Descriptive Archaeoastronomical Approaches

Fig. 4.15 a Moon at the desending node, b Moon at the ascending node

the line joining them is the nodal line. When line AD is aligned with the line joining the earth and the sun the configuration is suitable for a solar eclipse to take place. (Of course the moon has to be in conjunction for a solar eclipse or in opposition for a lunar eclipse). Figure 4.15 shows the two situations when a solar eclipse is possible. In one case the moon is at the descending node whereas in Fig. 4.15b it is at the ascending node. This happens as the nodal line AD also slowly rotates in a retrograde direction at the rate of about 20° per year as indicated. The configuration for a solar eclipse is shown in Fig. 4.16. The shadow of the moon shown in the form of a darker cone is called the umbra. From any point within the cone the sun will be totally invisible. So from the locations on the earth surface where umbra hits a total solar eclipse is observed. The shadow of the moon, shown in lighter shade, is called the penumbra. From any point on the earth’s surface where penumbra falls a partial solar eclipse is observed. From other points on the earth outside the range of penumbra no eclipse is observed. Figure 4.17 shows the situation when an annular solar eclipse is observed. Since the moon’s orbit around the earth is elliptic the distance of the moon from the earth varies. At apogee the moon is at a greater distance from the earth as compared

Fig. 4.16 Sun-moon-earth position during solar eclipse

4.4 Ancient Eclipses

75

Fig. 4.17 Situation for annular solar eclipse

to when it is at perigee. Thus at apogee the moon’s apparent size is less and the earth’s surface is beyond the inflexion point of the umbra as shown in the figure. In such a situation an annular eclipse is visible from the area. Table 4.2 gives some important data relevant to solar eclipse phenomenon. It is seen that the diameter of the sun’s disc can be larger than that of the moon and if a central solar eclipse occurs it will be annular. In fact in reality frequency of annular eclipse is more than that of a total solar eclipse. Figure 4.18 shows the configuration is more details. R and r are the solar and lunar radii, respectively, whereas D and d are the distance of the sun and the moon, respectively, from the earth’s centre as shown. P represents the point of inflexion of the umbra. The distance of P from the moon’s centre is s. Now from the figure one can write R r = s s+ D−d Table 4.2 Data relevant to solar eclipse Sl No.

Parameter

Value

1

Mean solar diameter

1.392 × 106 km

2

Mean lunar diameter

3.475 × 103 km

3

Mean distance of the sun from the earth

149.6 × 106 km

4

Distance of earth at perihelion

152.1 × 106 km

5

Distance of earth at aphelion

147.1 × 106 km

6

Distance of the moon from earth at apogee

405.7 × 103 km

7

Distance of moon at perigee

363.1 × 103 km

8

Mean distance of moon from earth

384.4 × 103 km

9

Mean angular diameter of solar disc

0.533°

10

Maximum angular diameter of sun

0.542°

11

Minimum angular diameter of sun

0.524°

12

Mean angular diameter of moon

0.518°

13

Maximum angular diameter of moon

0.548°

14

Minimum angular diameter of moon

0.491°

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4 Descriptive Archaeoastronomical Approaches

Fig. 4.18 Configuration of sun-earth-moon during solar eclipse

or, s =

Dr D (D − d)r ≈ ≈ R −r R 400.5

(4.4.1)

as D  d and R  r. Since the values of D and d varies with time the value of s lies in the range as shown below: 367,300 km ≤ s ≤ 379,800 km Now the value of d lies between 363,100 km and 405,700 km. Therefore, the earth’s surface can be on either side of point P depending on the relative distances. The condition necessary for a solar eclipse to take place is explained in Fig. 4.19.

Fig. 4.19 Configuration near solar eclipse

4.4 Ancient Eclipses

77

Fig. 4.20 Geocentric configuration for solar eclipse

Angle between the ES and EM lines is β, i is the inclination angle of the moon’s orbital plane and the ecliptic and α is the angle between the moon-earth line and the nodal line. When β > 0.95° the moon’s centre will be more than about 6370 km from the plane of the ecliptic. This is so as 0.95 ×

π × 384, 400 ≈ 6370 km 180

In this case no central3 eclipse can take place. Considering the spherical triangle SMN (Fig. 4.19) sin α =

sin β sin i

The above relation yields that when α ≤ 10.5° and β ≤ 0.95° a central eclipse is possible. For a partial eclipse to be possible β ≤ 1.45° (= 0.95° + 0.5°) and α ≤ 16°. The sideral period of moon’s orbital motion around the earth is 27.322 days. But to come back to the nodal point the moon takes 27.212 days as the line of nodes rotate in a retrograde sense as already mentioned. This period of rotation of the nodal line is 18.62 years. A kinematically equivalent geocentric picture of earth-sun-moon is shown in Fig. 4.20. At the instant shown the moon is at the descending node of the nodal line. Next time when the sun will be aligned with the nodal line is indicated by S  . If ∠S E S  = ψ 3 Total

or annular.

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4 Descriptive Archaeoastronomical Approaches

and, if the time taken to reach position S be T, then T =

ψ 360◦ − ψ = φ˙ ψ˙

when φ˙ is the speed of rotation of the sun and ψ˙ is the speed of rotation of the nodal line. Now φ˙ = 360°/yr and ψ˙ = 20°/yr. 360◦ − ψ ψ = ◦ 360◦ /1 20 /1 or, 360◦ − ψ = 18ψ

So,

or, ψ =

360◦ = 18.947◦ and T = 341.05 days 19

This period of 341.05 days is called the eclipse year. However, to find out the possibility of an eclipse the procedure involved has two steps. At first it is determined if the earth enters the penumbra of the moon’s shadow when in conjunction at a location sufficiently near to one of the nodes. Once a possibility is found to exist a detailed analysis is carried out for more accurate characteristics of the eclipse. Here, only the first step is being discussed. Figure 4.21 shows the situation when the moon is in conjunction near a node N. S and M are the sun and the moon, respectively, having the same longitude. The part of the celestial sphere near the node is shown in the left. As the area covered is small the spherical triangle SMN can be approximately represented by a plan triangle SMN. SM = β, the latitude of the moon and i is the inclination of moon’s orbit with the ecliptic and, its value is near 5.15°. After an interval of time from the conjunction the moon moves to M and at the same time the sun moves to S  . The rates of their motion are θ˙ rad/unit time and ϕ˙ rad/unit time, respectively. The angular separation of the moon and the sun is S  M  = η. The minimum value of η has to be found out to check if it falls below the required amount so that an eclipse occurs. Now for an

Fig. 4.21 Determination of the possibility of solar eclipse

4.4 Ancient Eclipses

79

approximate analysis the plane diagram will considered. From the figure S M = β, S  M  = η, S1 = γ (say SS  = β tan γ , S  M = β sec γ , ∠S M M  = M M  = qβ tan γ where q =

θ˙ ϕ˙

π − (i + γ ) 2

Considering S  MM   π − (i + γ ) η2 = β 2 sec2 γ + q 2 β 2 tan2 γ − 2qβ 2 tan γ sec γ × cos    2 = β 2 tan2 γ q 2 − 2q cos i + 1 − 2q tan γ sin i + 1 The minimum value of η can be found out by the standard method of equating dη/dy to zero. Differenting both sides with respect to γ and putting dη =0 dy one obtains either sec2 γ = 0, or, tan γ =

q sin i q 2 − 2q cos i + 1

(4.4.2)

Using this value of, the minimum value of η is given by 

(q cos i − 1)  ηmin = β  2 q − 2q cos i + 1

1/2 (4.4.3)

If ηmin is less than 1.45° an eclipse is possible. A detailed analysis is needed to further investigate the eclipse. A total or annular solar eclipse is visible only from the points where the umbra hits the earth’s surface. Since the moon and the earth are moving and the earth is rotating, the umbra describes a narrow strip of restricted length as shown in Fig. 4.22. When trying to investigate very ancient eclipse the uncertainty exists as the angular motion Ω of the earth is not exactly known. Before the various planetarium softwares were developed the researchers used the concept of cycles of eclipse to check if an eclipse occurred on an ancient date. To investigate the occurrence of solar eclipses in the ancient past the eclipse-cycles of 456, 391 and 763 tropical years were used. The following cycles have also been employed by the scholars in the past: (a) 18 Julian years and 10 21 days (b) 57 Julian years and 324 34 days (c) 307 Julian years and 173 14 days

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4 Descriptive Archaeoastronomical Approaches

Fig. 4.22 The path of umbra shadow

(d) 365 Julian years and 132 34 days (e) 1768 Julian years and 338 days. When converted to civil days the above cycles become respectively, of (a) 6585, (b) 21,144, (c) 12,305, (d) 133,449 and (e) 646,100 days. For quick assessment the above cycles can be used as the first step. Julian day on 1st January, 1900 CE is to be taken as 2,415,021. Catalogues of the past and future solar and lunar eclipses are also available online. The following two are useful: (a) Espena K Fred and Meeus Jean, Five Millennium Catalogue of Solar Eclipses (2000 BCE to 3000 CE)—Revised, NASA/TP-214174. Goddard Space Flight Centre, Greenbelt, Maryland (2009) (b) ibid, Five Millennium Catalogue of Lunar Eclipses (2000 BCE to 3000 CE) NAST/TP-2009-214173, Goddard Space Flight Centre, Green belt, Maryland (2009).

4.5 Advance of Perihelion of Earth’s Orbit This is a phenomenon that can be used to identify the era of certain astronomy related observation. Although the earth’s orbit around the sun is almost circular but, nevertheless, the orbit possesses an eccentricity of 0.017. Figure 4.23 shows the earth’s elliptic orbit with exaggerated degree of ellipticity. At some instant of time the earth is at E at a distance of r from the sun. According to Kepler’s 2nd law the earth describes equal area in equal times during its orbital motion and the instantaneous speed v depends on the distance r from the sun. Thus if r a and r p be the aphelion and the perihelion distances, respectively, and the speed of the earth at these positions be va and vp then vara = vprp

4.5 Advance of Perihelion of Earth’s Orbit

81

Fig. 4.23 Perihelion of earth’s orbit around the sun

 Since rp ra , vp va implying that the speed of the earth is more near perihelion compared to that near the aphelion.4 Now when the tilt of the earth’s spin axis is examined, at position B the tilt is towards the sun implying summer solstice at this position. Similarly position C indicates the winter solstice day. Thus the part of the orbit from B to C represents the half year from summer solstice to winter solstice and from C to B is covered by the earth in the other half year from winter solstice to summer solstice. Now it can be easily seen that since the half year from B to C contains the perihelion of the orbit, the earth covers this part is less time than the other half. This means that the number of days from the summer solstice day to the winter solstice day will be less than the number of days in the other half year. This is due to two reasons—(i) the total length of the path from B to C is less than that from C to B and, (ii) at the same time, the average speed with which the earth covers this path from B to C is more than the average speed of the earth from position C to B. So the total number of days in a year—365.25—will be unequally divided between the two halves of a year. The kinematics of the situation is complex as the earth’s spin axis precesses at the rate of 50.4 /yr in the retrograde direction (i.e. opposite to the orbital motion) and the major axis of the earth’s orbit also slowly rotates relative to the fixed stars at the rate of 11.57 /yr in the forward direction (Fig. 4.24). In the year 1246CE the winter solstice day coincided with the perihelion position. Currently the perihelion is about 2 weeks after the winter solstice day. In the year 6430 CE the perihelion will coincide with the vernal equinoctial day. At the present rate the perihelion and the aphelion days shift by 1 day every 58 years. Thus, the relative rotational motion of the orbital major axis and the earth’s spin axis is about (11.57 + 50.4 =) 61.97 per year.

4 The

speeds of the earth at the perihelion and aphelion positions are 30.3 km/s and 29.3 km/s, respectively.

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4 Descriptive Archaeoastronomical Approaches

Fig. 4.24 Change in relative position between the perihelion position and the tilt axis

The situation is depicted in Fig. 4.25 when the perihelion and the winter solstice coincide. The view is taken from a direction normal to the plane of ecliptic. Due to precessional motion of the earth’s tilt axis the north pole describe a circle with a centre that is called the ecliptic pole. Now to find out the duration of the period from winter solstice to summer solstice at a certain epoch Fig. 4.26 shows the scheme. The orbital ellipse has one focus at S where the sun is located. WS and SS are the winter solstice and the summer solstice positions, respectively, and WS, S and SS lie on one line as the amount of precessional

Fig. 4.25 View of the earth-sun system from a direction normal to the plane of the ecliptic

4.5 Advance of Perihelion of Earth’s Orbit

83

Fig. 4.26 Duration of the period from winter solstice to summer solstice

motion of the earth’s axis during this half year period is only around 25 of arc. If the angle ∠P S A = θ , where P and A are the perihelion and the winter solstice positions then time taken by the earth to traverse the path from A to P, t 1 can be found out using the following relations: t1 = 2.898 × 109 (E − 0.017 sin E) sec Where, E = cos−1



(0.017 + cos θ) (1 + 0.017 cos θ)

(4.5.1)

(4.5.2)

Again time of travel from P to B, where B is the summer solstice position, is given by   t2 = 2.898 × 109 E  − 0.017 sin E  sec where, E  = cos−1



(0.017 − cos θ ) (1 − 0.017 cos θ )

(4.5.3)

(4.5.4)

Thus, the total period of this ‘notional’ half year    t AB = 2.898 × 109 (E − 0.017 sin E) + E  − 0.017 sin E 

(4.5.4)



(0.017 + cos θ ) where E = cos and (1 + 0.017 cos θ )

 −1 (0.017 − cos θ ) E = cos (1 − 0.017 cos θ ) −1

The total year t AB + t BA (time of travel from A to A) is fixed and equal to 365.25 days. So if the number of days in the two parts are given the angle θ can be estimated. The epoch (or the year of observation) is given by  1246 +

 θ CE 61.97

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4 Descriptive Archaeoastronomical Approaches

where θ is expressed in arc second. It should be noted that when A is A (i.e. on the other side of P) then one has to keep in mind to subtract the period and the epoch is given by  1246 −

 θ CE 61.97

As mentioned above in the year 1246 CE the winter solstice and the perihelion coincided. So, again it takes (360° × 3600/61.97 =) 20,913 years to have a similar coincidence. It is clear that in the year (1246 + 20,913/4 =) 6474 CE the relative separation between the winter solstice and the earth’s tilt axis will be equivalent to quarter of a year. Thus the perihelion will be coincident with the vernal equinox.

4.6 Saptarshi Cycle In a significant number of ancient texts a statement on the “movement of Saptarshi along the Nakshatras” is found; but till today it has remained a mystery what the statement exactly means. This statement (in different forms) is found is Brihatsamhit¯a, Vishnu Pur¯ana, Matsya Pur¯ana, Vayu Pur¯ana and Bh¯agvat Pur¯ana. The earliest reference to this “motion” of the Saptarshi is found in Vishnu Pur¯ana and the relevant ‘shlok¯a’ is given below:

When translated it reads as “take those stars of Saptarshi (seven sages) which are seen first after the rise. The nakshatra which is seen in the middle of it at equal distance at the night is said to be residence of Saptarshi for one hundred years of man’s life. Oh great brahmin, they were Magh¯a at the time of Parikshit (Vishnu Pur¯ana, 4.4. 105– 106)”. This statement has remained inexplicable and a mystery as there is no direct astronomical truth in this. Many have treated this as pure nonsense. But many feel that this is linked with the precession of the equinox and ancient Indian astronomers used this for chronological purpose. Since there are 27 nakshatras, according to the statement, 2700 years are required to complete a cycle. This 2700 year long cycle is referred to as the ‘Saptarshi Cycle’ and has been used in India for the determination of chronology. Since the proper motion of stars are very small for a period of 8000 years the stars’ relative positions among themselves can be considered unchanged. So Saptarshi cannot have any movement along the ecliptic where the 27 nakshatras are situated.

4.6 Saptarshi Cycle

85

Hence apparently the Saptarshi mandal (i.e. the Big Dipper) has been used as a pointer for the purpose of reckoning time. But that also faces difficulty for acceptance. Due to the precession of the equinox the celestial pole position changes as discussed earlier in this chapter. And, therefore, an imaginary line connecting the pole and the first two stars of Saptarshi meets a point on the ecliptic which changes with time. But calculation shows that this interpretation also encounters difficulties as the motion of this imaginary line does not match with the proposed rate of 100 years per nakshatra. The problem has been studied by many researchers but that conducted by Sule, Ankit et al. (Daftari 1942; Sule 2007) is most noteworthy. The authors have paid attention to the earlier work by Filliozat (1962). He analyzed the situation that existed around 1000 BCE and the pointers position at Magh¯a. Sule et.al. refers to the commentary made by Sri Ratnagarbha Bhattacharya. “Following is the characteristic of progress of Kali age. The Saptarshi is a group of 7 stars in the shape of a cart. The first part consists of three stars in arc shape. They are Marici, Vasistha and Angiras from front to back. On the back, as the bed of the cart are four stars, Atri, Pulastya, Pulaha and Kratu in North-East, South-East, SouthWest and North-West direction, respectively. Take North-South line passing through the middle of Pulaha-Kratu which rises first and the stars next to them. Whichever nakshatra out of Ashwini etc. this line meets it will remain in the same for 100 human years.” The authors developed a computer programme and investigated the configuration at different times. The configuration in 2000 CE is shown in Fig. 4.27a when plotted for 2150 BCE the situation is shown in Fig. 4.27b. The authors prepared a table (Table 4.3) showing the nakshatras indicated by the Saptarshi pointer. They found that the duration of the pointer at a nakshatra was not constant and varied widely. Only during the period 2200 BCE to 2100 BCE the pointer stayed on a nakshatra (Pushy¯a) for 100 years. Thus they commented that the statement was based upon the observation of 2200 BCE and the rate was thought to be valid at all

Fig. 4.27 a In 2000 CE Saptarshi pointer in Purb¯as¯arh¯a, b Saptarshi pointer in Pusy¯a in 2150 BCE

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4 Descriptive Archaeoastronomical Approaches

Table 4.3 Saptarshi pointer at different era Pointer at

Era

Star

Nakshatra

Castor

Punarvasu

Pollux

Punarvasu

~4500 BCE

Praespe Cluster

Pushya

~2200 BCE

δ Hydrae

Ashlesh¯a

~1800 BCE

ε Leonis

Magh¯a

~1000 BCE

Before 8000 BCE

times by mistake. However, the matter of Saptarshi Cycle may not act as an accurate chronological clock but some hints about the antiquity of certain astronomical references can be roughly guessed.

References Daftari, K. L. – “The Astronomical Method and its Application”, Nagpur University, 1942. Filliozat, J. – “Notes on Ancient Iranian and Indian Astronomy”, Journal of Asiatique, pp. 325–350, 1962. Sule, A., Vahia, M., Joglekar, H. and Bhujle, S. – “Saptarshi’s visit to different Nakhsatras: Subtle effect of earth’s precession”, Indian Journal of History of Science, 42.2, 133–147, 2007.

Chapter 5

Archaeoastronomical Study of Ancient Indian Chronology: Dating Mah¯abh¯arata

5.1 Introductory Comments Investigating the chronological history of ancient India is a difficult task. The difficulties arise not only because of natural reasons but the major obstacles are framed by the historians and archaeologists themselves. So, a major problem is the presence of dogmatic theories which were developed in the nineteenth-century colonial India based on presumptive hypotheses in the absence of any archaeological evidence of any ancient civilization in the soil of this subcontinent. With more and more new evidences of ancient settlements, the old dogmatic theory is being given only cosmetic uplifts keeping the basic foundation intact. Using astronomical references in the ancient texts and scriptures is not a new subject. In fact the attempt to date ancient texts and descriptions using astronomical descriptions first started with the work by the Scottish mathematician John Playfair in 1790. He analyzed the observations recorded in ephemeris tables and found the starting date of the observations as 4300 BCE. Using astronomy for establishing the antiquity of ancient texts by Playfair was severely criticized by John Bentley in 1825. In his language, ’By his (Playfair’s) attempt to uphold the antiquity of Hindu books against absolute facts, he thereby supports all those horrid abuses and impositions found in them, under the pretended sanction of antiquity. Nay, his aim goes still deeper, for by the same means he endeavours to overturn the Mosaic account, and sap the very foundation of our religion: for if we are to believe in the antiquity of Hindu books, as he would wish us, then the Mosaic account is all a fable, a fiction’. Being the staunch creationist upholding Bible, he created his own analysis through which he ’proved’ that Krishra was born in 600 CE on 7th August. He also showed through his calculation that Var¯aha Mihira was contemporary of Emperor Akbar!! He declared that the ancient Indian astronomers did deliberately recorded false data through back calculation for

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 A. Ghosh, Descriptive Archaeoastronomy and Ancient Indian Chronology, https://doi.org/10.1007/978-981-15-6903-6_5

87

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5 Archaeoastronomical Study of Ancient Indian Chronology …

establishing the antiquity! However, at later times, many eminent astronomer scholars proved that such false recording based on back calculation is an impossibility. In the nineteenth century, a number of European scholars like Colebrook, Wilson, Wilford and Prat worked on Mah¯abh¯arata war and they were soon followed by Bankim Chandra Chattopadhyay. In his book ‘Krishna Charitra’ published in 1884, he showed by astronomical calculations (using the precession of the equinox) that Bh¯arata battle took place around mid-second-millennium BCE. Subsequently, many other scholars have used ancient astronomical observations to decide a chronological order for ancient India in the protohistoric period. The true sheet anchor for the history of ancient India is the Mah¯abh¯arata war and, therefore, there have been a considerable number of attempts to establish the date of this important event whose historicity is not in much doubt now. This topic will be, therefore, discussed in detail in a separate section of this chapter. A major source of confusion in deciding the chronological history of ancient India arises out of a very important point. The famous ancient fifth-century CE astronomer Aryabhata I recorded that ‘Kaliyuga’ has started on the midnight of 17th-18th February 3102 BCE. At the same time, it is well known that Kaliyuga started with the death of Krishna, a few years after the Bh¯arata battle. The astronomical references found in Mah¯abh¯arata contradict this date of Kali and indicate the midsecond-millennium BCE as the correct date! This confusion had remained as a major stumbling block for astronomical dating exercise. It was attempted to be solved by Daftari through a proposition for the existence of two types of ‘Yuga’ as explained in Sect. 3.3.1. The author of this book is not sure how well-accepted Daftari’s solution has been, as even today the 3102 BCE as the epoch for Kaliyuga is found in many research articles to date Mah¯abh¯arata. It is true that proper application of archaeoastronomical technique can give a correct idea about the antiquity of ancient description. Nevertheless, it should be always attempted to study the consistency of the results with those obtained through other techniques viz. palaeoclimatology, geology, etc. Beside astronomical descriptions, ancient Puranic texts also provide the genealogy of the kings of various dynasties. Lists of such kings ruling over India for more than 6000 years were shown to Megasthenis. Such lists can be also useful in validating the chronology derived using astronomical methods.

5.2 Ancient India’s Geographic Boundaries as Implied in Ancient Texts Identification of home lands can play an important role in establishing chronology. It is now known that there existed very close connection between the people and culture of two ancient nations---India and Persia. The languages of the ancient Zarathustian text Zend Avesta and vedas are so similar that to many linguists, they appear to be two different dialects of the same language. Thus, a number of useful information can be

5.2 Ancient India’s Geographic Boundaries as Implied in Ancient Texts

89

found in Zend Avesta and different vedas which can lead us to a proper understanding of the ancient homeland of the original vedic people. Unfortunately, the important ancient text that narrates ancient India’s historical aspects---V¯ayu Pur¯an---does not go beyond the so-called Var¯aha Kalpa i.e. 3102 BCE. The text states

Translation: ’Oh, best of the twice born the seventh Kalpa, named Padma has passed away; of them (kalpas) the present (kalpa) is Var¯aha. I shall describe its details’. Similarly Zend Avesta also limits itself to 2800 BCE. However, there are enough indications in Zend Avesta and the Vedic texts from which some idea can be formed about the original homeland of vedic Indians (often called ‘Aryans’). Daftari considered a Human Kalpa (not the astronomical Kalpa extending over hundreds of thousands of years) to last for 1000 years. Thus, the beginning of the Kalpa system must have preceded the onset of Var¯aha Kalpa by 7000 years since Var¯aha Kalpa was the 8th in the series. He thinks that a very important event took place around 10,102 BCE and the Kalpa system-based time reckoning was started then. Studying the vedic texts, Daftari conjectures that around that time the original people started their habitation in Pamir Plateau and the valleys and meadows there. It could be due to a ¯ severe change in climate that destroyed their earlier land by frost. Zend Avest¯ a also describes Pamir region from where the Aryan people expanded in different directions. In V¯ayu Pur¯an Meru (i.e. Pamir) is described as the abode of Gods.1 This is evident from the following text:

1 V¯ ayu

Pur¯an (Chap. 34).

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When translated, it reads as follows: ’There on that mountain are seen all Gods, Gandharvas, N¯agas and R¯akshasas and Apsar¯as. That mountain Meru is surrounded on the various sides by countries that support beings, namely by the four countries Bhadr¯asva, Bh¯arata, the west Ketum¯ala and the northern Kurus, where meritorious people live. In the thousand parts of that mountain adorned by various abodes, the numerous dwellings of all the Gods are situated. That which is called by the synonyms Swarga, N¯akaprishtha, Diva, etc., by those who know the vedas and its Angas, that abode of all the meritorious Gods, i.e. Devaloka, is situated on this mountain. This stated in all the Srutis’. The following passage from V¯ayu Pur¯an (Chap. 34) further identifies the location.

It shows that the Meru was the abode of Gods. It further specifies the location by the statement that it is in the middle of four countries viz., Bh¯arata, Ketum¯ala and Uttar Kurus and Bhadr¯asva. When translated the above poem reads as follows: “The Neela, the Nish¯ada and the others that are lesser than them, the Sweta, the Hemkoota, the Himav¯an and that which is Sringav¯an; between these are the seven countries called ‘Varsha’. This is the well-known country named Bh¯arata, which is near to the south of Himav¯an. Thence is the country named Kimpurusha (Tibet) near (to the south of) Hemkoota (Karakoram). Thence is the country named Harivarsha (Tartari) near (to the south of) Nish¯adha (Irekha Birga mountain) and near Hemkoota (to the north of Hemkoota). Thence (to the west) is the country named Il¯avrita) is the country named Ramyaka near Neela (north of Neela or the Suleiman mountains). Thence (to the east of Ramyaka) is the country name Hiranmaya (Mongolia or Gobi) near Sweta (south of Sweta or Tienshan mountains). Thence to the (northwest of Hiranmaya)

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is the country named Kuru near Sringav¯an (Hindukush). The two countries of the north and the south namely the Uttar Kuru and the Bh¯arata Khanda are of the form of a bow (whose string is pulled); the other four are long and Il¯avrita is the central country. The half of the Vedee (continent) which is on this side (south) of Nish¯adha is called the southern half of the Vedee; that half of the Vedee which is beyond (to the north of) Neela is called the northern half of the Vedee. There are three countries in the northern half of the continent and between the two halves of the continent is Il¯avrita; in the centre of which lies Meru’. It is not difficult to recognize Meru as Pamir since so many mountain ranges are said to have originated from the location. However, it implies that the geographical Meru is different from this Meru (or, Sumeru as sometimes called). The map in Fig. 5.1 shows the region. ¯ According to Avest¯ a, the original homeland of the Indo-Iranian people was ‘Ariianam Vaejo’. The text also mentions fifteen other neighbouring nations. ¯ Table 5.1 shows these ancient nations of the original people described in Avest¯ a (See Footnote 1). It is now well known that the key person in Zarathustrian civiliza¯ ¯ ¯ tion was ‘Ahura M¯azd¯a’. In Avest¯ a, ‘Ahura’ is the Iranian version of Asura of vedic

Fig. 5.1 Map of the region described in V¯ayu Puran

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Table 5.1 Sixteen lands mentioned in Avesta Sl No.

Avesta name

Present name

Features

1

Ariianam Vaejo

Pamir

Good & lawful climate change to sever winter

2

Sukhdho (Sogdiana)

Sugd; Northwest Tajikistan

Good land, cattle death

3

Mourum (Margiana)

Marv, South Turkmenistan

Brave, holy bloodshed

4

Bakhdhim (Bactria)

Balkh, North Afghanistan

Uplifted banner stinging ants

5

Nisiam (Parthia)

North East Iran bordering Balkh and Marv

Good land, Non-believers

6

Haroyum (Aria)

Herut northwest Afghanistan

Water abundance, poverty

7

Vaekeretem (Sattagydia)

Kabul, Eastern Afghanistan

Good land, witch craft

8

Urvam (Chorasmia)

Uzbekistan

Rich pasturs, Fyranny

9

Khentem Vehrkano (Hyrcania)

Golestan, North Iran

Good land sexual assault on children

10

Harahvaitim (Arachosia)

Kandahar, South Central Afghanistan

Beautiful, Bury the dead

11

Haetumantem (Drangiana)

Helmand, South East Afghanistan

Brilliant & glorious witch craft & sorcery

12

Rakhan (Ragai)

Tehran, North Iran

Utter disbelief

13

Chakhrem

Uncertain

Brave, cremation of dead

14

Varenem (Hyrcenia)

North Iran

Barbaria rule

15

Hapta Hendu (Indus)

G¯andhar, Punjab, Northwest India

Wide expanse, violence, hot weather

16

Ranghaya

Kurdistan, Turkey

Good land, lawless

¯ texts. As Sapta Sindhu of veda becomes ‘Hapta Hendu’ in Avest¯ a,2 Asura became ¯ ¯ ¯ Ahura. Furthermore in Avest¯ a, Ahura is glorified, whereas Devas are demonized. In the vedic texts, Asuras are demonized and Devas are praised. This implies that there was a fight between the two groups called Devas and Asuras. Asuras were defeated and they left for a different land in the west. According to Zarathustrian texts, the original king Jim Shed ruled the original homeland which had a temperate climate. Jim shed or Yima is the original form or Yama of vedic texts. Figure 5.2 shows the map of the lands described in Avestan text. There is a considerable degree of similarity in the two descriptions. So, Daftaree’s interpretation (and of many others) that there was close link with upper Punjab and northwest region of the Indian subcontinent with Pamir and, perhaps, that was the original place wherefrom the people came to Indian subcontinent before the eighthmillennium BCE, needs attention. Furthermore, Pamir and the upper northwest region of Indian subcontinent being adjoining areas, ancient vedic people, perhaps, did not 2 It

¯ is interesting to note that Mesopotemia and China do not figure at all in Avest¯ an texts.

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93

Fig. 5.2 Lands described in Avesta

looked at the phenomenon as a major migration. Thus, there is no reference to any major migration in the vedic texts, which is considered as an important evidence against Aryan Invasion Theory. Such a thing can happen if the Pamir and adjoining areas of extreme northwest region of the subcontinent was not considered to be a foreign land.

5.3 Structural Framework for Ancient Indian Chronology As emphasized earlier, ancient Indian chronology possesses two unique features. The ancient archaeological sites are in plenty and the earliest evidences of settlements have been dated from eighth to seventh-millennium BCE. These sites are also located quite a distance apart, one being at Mehergarh in eastern Baluchistan and the most recently discovered one at Bhiraana, Haryana (India). Thus, a continuous cultural development is evidenced that continued for almost 6000 years. Unfortunately, many aspects of this great Sindhu-Sarasvati civilization are shrouded in mystery. Till the Indus script is deciphered in an unambiguous manner, a total understanding of this great civilization in ancient India will remain elusive. On the other hand, a huge amount of literature exists that also dates back to many thousands of years. The richness (and vastness) has been amazing to the scholars of the world for the past two centuries. But its interrelationship with the SindhuSarasvati civilization is still not understood completely; in fact according to the standard existing theory of Aryan Invasion, there is no connection between the Indus-Sarasvati civilization and the vedic people who also lived in the same region (and, most probably also at the same time). The origin of the vedic people is also a very hotly debated subject as is known to all. Any ancient chronology of India must address these questions.

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Due to the abundance of astronomical references in the ancient literature, many attempts have been made since the early nineteenth century to date the various major events (and observations) using the astronomical references contained in these texts. A reasonably large amount of literature already exists. However, as new discoveries are being made as the time progresses, new questions are emerging requiring satisfactory explanation. Apart from this, although the references to astronomical alignments in the ancient literature are found in abundance, a large proportion of those are covered by allegory and are often presented through symbolic stories. A complete understanding of the actual astronomical observation is also, therefore, dependent on the correct interpretation of these allegorical descriptions in many cases. So, it is desirable to carefully plan the strategy that can be adopted for developing a reasonably uncontroversial result. The chronology must also be consistent with other available facts and the existing paradigm. One thing must be remembered that the exercise should not be based upon the existing standard theories which were developed during the nineteenth century by European scholars with somewhat imperfect understanding of ancient Indian philosophy and the ancient Sanskrit literature. More importantly, till the third decade of the twentieth century, the ancient Indus Valley Civilization was not discovered and it was thought that the subcontinent did not possess any ancient civilization. Thus, the original theory of ancient India’s civilization was based on incomplete knowledge and biased understanding. The strategy for preparing a chronology of ancient India needs to be decided first. It is now generally accepted that Mah¯abh¯arata battle was an actual major event in ancient India that had a major influence on India’s civilization. Furthermore, according to most scholars, Mah¯abh¯arata battle (MB) is the true sheet anchor in India’s protohistory. At the same time, the birth of Buddha is considered by many as the beginning of the historical period for India. The period between MB and the first historical king Nanda is a grey period with quite a few characters that are considered to be historical, viz. Panini. Thus, the structure of India’s chronology can be diagrammatically represented by the figure shown in Fig. 5.3. This is a composite diagram showing the astronomical and textual indications along with archaeological and geological

Fig. 5.3 Structure of ancient Indian chronology

5.3 Structural Framework for Ancient Indian Chronology

95

suggestions. A correct picture must be consistent in all aspects of ancient India’s chronological history and protohistory. Among many problems in developing a nice chronology of ancient India, one is the multiplicity of names of many kings. This has caused serious problem, and in many cases, the scholars, through their own individual interpretations, arrive at different results. It is very important, therefore, to consider a proper fit with the other phenomena possessing a temporal signature. With the advent of many scientific methods for establishing antiquity, one needs to consider the palaeoclimetological, geological and other physical indicators for matching with the chronology. Archaeological evidence is also very important and should be in agreement with the established chronology. Thus, Fig. 5.3 attempts to present the features of ancient India’s chronology as derived from the consideration of the following indicators: (i) (ii) (iii) (iv) (v)

Genealogical lists of Puranic and ancient kings Astronomical references in the ancient texts Archaeological evidence Geological and palaeoclimetological analysis of the past Existing historical references available.

Attempting to develop a chronology of the protohistorical period of Indian subcontinent without any consideration of the major archaeological discoveries of the twentieth and twenty-first centuries is not a very logical exercise. Unfortunately in many cases, the exercise is based upon the counting the numbers of generations of kings as found in pur¯anic texts and assuming an average period for each generation. As mentioned before, the lists are not simple lists and riddled with repetition of names. Most often, the concepts of Yuga, Kalpa etc. are intermingled with the descriptions creating a reasonable amount of confusion. The next very important thing is the consideration of the Sindhu-Sarasvati civilization (that includes various phases of pre-Harappan, Harappan and post-Harappan civilization) that extended over a vast region of west, northwest, north and central India. The entire period of this civilization, as evidenced by most recent archaeological discoveries, extends from the eighth-millennium BCE till the end of secondmillennium BCE. Thus, any chronology of ancient India without any reference to this looks not only strange but, perhaps, meaningless. Along with the archaeological findings, a proper chronology should also address the major questions related to major geological and climate-related issues of the concerned regions. Thus, astronomical references can play the role of a primary time indicator; but the results need to be matched with those obtained from other sources. It should be also remembered that all astronomical observations of the ancient past were with naked eye and the accuracy level of the observations was, therefore, not high. The positional inaccuracy restricts the accuracy of the dating. Thus, conclusions about only a rough idea of the periods involved can be drawn.

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5.4 Genealogy of Puranic Dynasties The vast amount of pur¯anic, vedic and other ancient Indian texts refer to a very large number of kings for many generations. Though not dated, these dynasties’ genealogy can indicate the antiquity of the periods ruled by the kings. This should also match with the dates infered by astronomical and other methods. The study of the ancient dynasties of India is a vast subject and many scholars have done extensive research in this field. One of these major studies was made by E. E. Pargiter in early twentieth century and the outcome of his research was published in the book ’Ancient Indian Historical Traditions (1922)’. Subsequently, many others have conducted similar studies resulting in many publications. Though the results of various studies provide a reasonable idea about the chronology of ancient India, in some cases the results are not very consistent and the accuracy of the results and conclusions is questionable. Nevertheless, this dynastic chronologies help in forming a reasonable idea about the chronology of ancient India. The ancient scriptures of India state that world’s creation and destruction is a cyclic phenomenon. Each period is called a ‘Kalpa’. The current age of our existence is called the ’Sveta-Bar¯aha Kalpa’. Furthermore in Sveta-Bar¯aha Kalpa, there are two stages. The earlier one is predeluvian and the other one is postdeluvian. The survivors from the primary creation lead to the secondary creation after the deluge. Growth of human civilization has been influenced by the past climate of the world. As determined by the scientists. the world climate for the past 1,20,000 years is indicated in Fig. 5.4.

Fig. 5.4 India’s protohistoric period

5.4 Genealogy of Puranic Dynasties

97

A concise amount of the ancient protohistoric period of India is presented in Fig. 7.9 and the detailed dynastic genealogical trees are presented in Appendix C. The figure shows the beginning of ancestory with Manu Svyambhuva, the son of god Brahma. Brahma also created the Bramharishis, eight Rudras, four Kumaras and Dharma. Manu Svyambhuva had two sons Priyavrata and Utt¯anp¯ad and two ¯ daughters---Prasuti and Akuti. Priyavrata’s decendents ruled for about thirty generations, the last one being Viswagajyoti after which there was a 907 years of kingless deluge period. In the lineage of Utt¯anp¯ad, there were twelve kings and ten Prachet¯as the last member being Daksha Praj¯apati and gods alongwith their adversaries--Datiyas and D¯anavas. After the deluge period, the second creation starts with K¯ashyapa, and after three generations, Manu Vaivasvata is the main character whose two sons, Ila and Iksh¯aku,3 started the lunar and solar dynasties, respectively. The main figure in the solar dynasty was R¯ama (D¯asarathi) and this ended with Brihadvala, who was killed by Abhimanyu in the Mah¯abh¯arata war. The lunar dynasty’s major characters were Lord Krishna and the five P¯andavas. Abhimanyu’s son Parikshit, the only survivor (after Yudhisthir abdicated and left for Him¯alaya) continued the lineage. After Parikshit, it was 1015 years when Mahapadma Nanda ascended the throne according to Vishnu Pur¯an as indicated below:

With this the protohistoric era of ancient India ends and the historical era begins as shown. Since Chandragupta Maurya began his rule in 321 BCE, the connection between the protohistory and history of India gets established. As Chandragupta and Alexander of Macedonia were contemporaries, western scholars consider this event as the sheet anchor of Indian history. It is interesting to note that the lists of Puranic dynasties, as collected from various Pur¯anas, are reasonably consistent! Besides, the statement of Megasthenis, Chandragupta’s contemporary, that he was shown 153 generations of kings who ruled India also matches well with the Puranic list. From Manu Vaivasvata to Parikshit, there are 99 generations, and from Parikshit to Chandragupta, there are 55 generations. Thus, in the postdeluvian period, there were (99 + 55 =) 154 generations of kings. However, the total period from Manu Svyambhuva can be found out as shown below: Predeluvian Period: Number of generations of kings = 31 Deluge period Postdeluvian period: Number of generations of kings = 154 T otal period be f or e Chandragupta 3 River

≡ 620 years ≡ 907 years ≡ 3080 years = 4607 year s

Oxus’s original Sanskrit name ‘Bakshu’ originated from the name Iksh¯aku.

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As Chandragupta Maurya is dated 321 BCE, the era of Manu Svyambhuva goes back to (4607 + 321 =) 4928 BCE, or, roughly 5000 BCE.

5.5 Date of Mah¯abh¯arata It has already been emphasized that the real sheet anchor of ancient India’s protohistory is the battle of Mah¯abh¯arata. Currently, hardly any scholar disagrees with the reality of the event. Many reasons for which the historicity of Mah¯abh¯arata was doubted have been sorted out. Thorough analysis has also established that the final compilation of this great epic took place much later but the real event is of much higher antiquity. Of course, till date, no archaeological or epigraphic evidence of Mah¯abh¯arata battle has been found. The form in which Mah¯abh¯arata is found at present started being complied since the Maurya period; to substantiate that in several places in Mah¯abh¯arata, there are mentions of Buddhist monks. Through the analysis of certain astronomical descriptions, Sengupta (Sengupta 1947) has shown that the final compilation could have been during the period 400--300 BCE. As mentioned in Asval¯ayana Grihya Sutra, the original book Jay¯a consisted of about 8000 slokas. At a later period, the book Bh¯arata expanded to 24,000 slokas. In the final compilation, the two books got combined into one. It is not easy to find out the original portions and later additions; but an excellent discussion can be seen in Bankim Chandra Chattopadhyay’s famous book ‘Krishna Charitra’. However, since the time of Gupta dynasty in the early centuries of the Common Era, it is known that Mah¯abh¯arata has hundred thousand slokas. So, there have not been much further additions to Mah¯abh¯arata during the last two millennia! A considerable amount of research for dating Mah¯abh¯arata has been carried out by a number of scholars since the last two centuries. The results are wide apart. The dates arrived at by these scholars vary from 5000 BCE to 400 BCE. One of the major source of confusion is the common belief that Kali Yuga started with the death of Krishna 36 years after the Bh¯arata battle. This, along with Aryabhata’s Kali era epoch as 3102 BCE, has resulted in the very high antiquity of Mah¯abh¯arata. Unfortunately, this date contradicts the dating done by using the astronomical references. Apart from this fourth-millennium date of Mah¯abh¯arata also goes against the genealogical order of Puranic kings and also the geological evidence for vedic river Sarasvati. In one of the most recent work, Bhatnagar (Bhatnagar 2017) has carefully considered only the consistent references. In fact, Bankim Chandra Chattopadhyay’s analysis was almost similar and the result obtained by him agrees well with most of the conditions. Bhatnagar has also mentioned about the problem of using eclipses as guidelines for dating purpose. One of the key points many scholars have stressed upon is the beginning of Kali era with the death of Krishna and Aryabhata’s dating of Kali era as 3102 BCE. However, this identification was based upon a calculated grand conjunction of the sun, moon and five planets at the starting point of Aries---‘Mes¯adi’. But, the data available with Aryabhata were not accurate enough and in reality no such grand conjunction occured on 17th--18th February 3102 BCE.

5.5 Date of Mah¯abh¯arata

99

5.5.1 Types of Astronomical References Before starting a detailed discussion, it is desirable to have an idea about the types of astronomical references which are found in Mah¯abh¯arata (and in most ancient texts in general). These are indicated below in tabular format. Bhatnagar also mentioned that Planetarium Gold software is preferable as this software is based upon tropical year instead of sideral year. Thus, the dates for the cardinal days and the seasons remain unchanged (Table 5.2). Some major astronomical references are again presented in a tabular format (Table 5.3) for a quick appraisal.

5.5.2 Dating Mah¯abh¯arata War As mentioned earlier, some of the astronomical references are self-contradictory and some are simply wrong. Particularly, the astrological references to planetary positions are self-contradictory and not trustworthy. Therefore, such descriptions should be ignored. In the references given in Table 5.3, all are not very dependable. Apart from the references mentioned in Table 5.3, it is known that when Krishna went to negotiate peace with Duryodhana, on a day during that period the moon was near Pushy¯a nakshatra. It is better to construct the astronomical scenario of the war period first considering the most definite, unambiguous and dependable astronomical references, and, then fit the rest of the references as far possible. The most definite astronomical reference is the death of Bhisma. It is very specific on the fact that the day of his death (or the day just before that) was the winter solstice day. The few other very unambiguous information are (i) the war lasted for 18 days, (ii) Bhisma fell on the tenth day of the war and (iii) he lay on his death bed (of arrows as per common knowledge) for 58 days. Figure 5.5 shows the astronomical references of Mah¯abh¯arata which helps in dating. Table 5.2 Types of astronomical references Type

Contents

A

Calendric

Detailed positions of moon along nakshatras, moon’s phases and titihis, number counts of days, year and months for given event

B

Seasonal

Positions of the solstices and equinoxes, onset of seasons; reference to sacrifices etc.

C

Planet positions

Planetary positions among the nakshatras for the purpose of astrological predictions

D

Special events

Solar and lunar eclipses; major floods; major droughts

E

Special objects

Comets, meteors

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Table 5.3 Major astronomical references in Mah¯abh¯arata Sl No. Reference

Type

1

In ‘Vana Parva’ there is detailed description of a K¯artika full moon. The rains were over, the sky was clear of dust and clouds; the stars shone brightly; the nights were cool

A

2

In ‘Udyog Parva’ there is a description that gives the month of K¯artika under A&B nakshatra ‘Revati’ and the season represented transition from autumn to winter

3

After the failure of peace talks, Krishna told Karna that war will start after seven days on the K¯artika am¯avasy¯a under ‘nakshatra’ Jyesth¯a (whose presiding deity was Indra). So the start of the war was on a ‘new moon’ day and the sun was at ‘Jyesth¯a-Rohini’ according to one sloka. But on the eve of the war beginning, the moon was near full, may be two days before full moon, according to another statement

4

On the fourteenth day of the war, Jayadrath was killed. The fight continued till A almost midnight. But it was resumed again towards the end of the night before dawn. The crescent moon rose and it was described as the horns of a bull. This matches with the statement of Vyas to Dhritarashtra on the eve of the war beginning that he finds the near full moon at Krittika

5

Bhisma died on the (or the next day) winter solstice day after 67 days from the B start of the war

6

Bhisma died on the Shukl¯astami day in the month of ‘M¯agha’. It coincided with the winter solstice at ‘Dhanistha’ nakshatra

A

7

A pair of solar and lunar eclipses occured within a period of 13 days

D

8

A solar eclipse after 36 years after the war

D

9

Balar¯ama went along Sarasvati on pilgrimage up to ‘Vin¯asana’ where the river vanished in the desert. This is a geological and climatological reference. When he went, it was 42 days before the end of the war and the moon was at Pushy¯a. The moon was at Shravan¯a at the last day of the war

A

One thing is clear from this that the start of the war was around a new moon day as otherwise it could not have been a full moon after 75 days. Other descriptions which do not match this description should be rejected. Figure 5.6 shows the diagram for deciding the date of Mah¯abh¯arata war. This view is from the south celestial pole. Figure 5.7 shows the sky map for the winter solstice day in 2400 BCE. From this position of the full moon, it is evident that the sun must be at the farthest southerly position since the moon is in opposition at the northern most position of the ecliptic and the full moon is in nakshatra Magh¯a. Using the planetarium software, the following data are obtained (i) In the year 1898 BCE on January 5, the sun was at the winter solstice position. (ii) On January 13 of 1898 BCE, the moon was at 6.6 h R.A. and the sun was at 18.6 h R.A. Thus, 13th January was the full moon day. (iii) The full moon was at nakshatra Magh¯a.

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101

Fig. 5.5 Major astronomical and calendric references in Mah¯abh¯arata

Fig. 5.6 Astronomical dating of Mah¯abh¯arata

Hence, the winter solstice day was in the month of M¯agha and the tithi was Shuklastami.4 From Fig. 5.6, it is seen that in 2400 BCE, the winter solstice day was the full moon day and the full moon was in nakshatra Magh¯a. Assuming Bhisma’s death was one day after the winter solstice and seven days before full moon as indicated, the configuration of the day in question is shown in Fig. 5.6. This (7 + 1) day’s difference causes the year to be given by −2400 +

7+1 × 28500 = −1835.29 365.5

or, about 1835 BCE. 4 Eight

days before the full moon is actually Shukla Saptami; but such minor variation is always possible.

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Fig. 5.7 Sky map for the winter solstice day in 2400 BCE

This is quite close to the year found by the planetarium software. Another point that should be remembered is that naked-eye observations in ancient times always involved a certain amount of inaccuracy in angular positions.5 This needs an error margin of about ±300 years to be incorporated. Furthermore, an error of ±1 day in determining the winter solstice day is also quite possible. Since 75 days elapsed from the start of the war till the Magh¯a full moon (seven days after the winter solstice which was 68 days from the start of the war), it is quite obvious that the war started near a new moon day. So the interpretation of Vyasa’s remark on the eve of the war beginning should be reconsidered. Another calculation (again approximate, of course) can be made using the period required for the sun to go from Jyesth¯a to the winter solstice position. In 1900 CE, it takes the sun 20.8 days to travel from Jyesth¯a to the winter solstice position, whereas it took about 67–68 days during the Mah¯abh¯arata era. Thus, the winter solstice position shifted by (68 − 20.8) × 360◦ = 46.6◦ 365 Considering the rate of precession of the equinox as 1° per 72 years, the Mah¯abh¯arata time preceded 1900 CE by 46.6 × 72 years = 3352 years or, the period was (3352 − 1900 =) 1452 BCE. Of course an error margin of ±300 years should be remembered. 5 Apart

from the observational inaccuracy, it is to be noted that each ‘nakshatra’ occupied about 13° along the ecliptic and it takes more than 900 years for the equinoctial and solticial positions to cover this. It should be also noted that winter solstice occured in Dhanisth¯a during the period 2250 BCE to 1280 BCE.

5.5 Date of Mah¯abh¯arata

103

Sengupta arrived at a date 2432 BCE considering the onset of the war to be on a (or, near a) full moon day. He also considered a ‘purnim¯anta’ month reckoning and Bhisma’s death was after the month Magh¯a completed 34 th part. This is little difficult to understand when Fig. 5.5 is examined. Since the full moon was after seven days of Bhisma’s death (irrespective of the system of month reckoning since it happened in ‘shuklapaksha’ as per very clear statement of Bhisma), then the total number of days from the start of the war till the full moon at Magh¯a has to be around 75. But if the war started on a full moon (or near a full moon) day, the subsequent full moon’s will be after approximately 30, 60 and 90 days. Bhatnagar’s recent work (Bhatnagar 2017) considered Bhisma’s death on (or a day after) the winter solstice day that was the eighth day of M¯agha in the first half, i.e. shuklapaksha. Three fourth of the month still remained. He also clearly showed the evidence in Mah¯abh¯arata that an am¯anta system used to be followed during Mah¯abh¯arata period. Using an advanced planetarium software (Planetarium Gold), he arrived at the date 1773 BCE. Bhatnagar further strengthened his finding by analyzing the various eclipses within a period of 13 days, which was considered ominous, being very rare. Finally, he concludes that Mah¯abh¯arata war started on 13th October, 1792 (or 1793) BCE on ‘Am¯avasy¯a’ as declared by Krishna, and Bhisma died on 20th December after 68 days at the onset of uttar¯ayana. Bhatnagar’s paper also discusses the lack of dependability of many other poetic references which can be considered to be astronomical in nature. A detailed table of all the meaningful and relevant astronomical references in Mah¯abh¯arata in his paper is a valuable resource. Daftari (Daftari 1942) also conducted analysis of the astronomical references in detail. He used the eclipses and the planetary positions. According to him Mah¯abh¯arata, date should be after Ved¯anga Jyotisha that is dated 1400 BCE. The reason he gives is that am¯anta system was followed in Mah¯abh¯arata period and Ved¯anga Jyotisha mentions the am¯anta system. This is a very weak reasoning of course. The date arrived at by him is 1197 BCE. It should be also mentioned that there have been many attempts to date Mah¯abh¯arata war. Following Aryabhata’s Kali era concept, the war is dated back to the fourth-millennium BCE. Var¯ahamihir puts the war in the third-millennium BCE. Another astronomical reference in scriptures is found that has both annoyed and baffled the generations of astronomers. It is related to the Saptarshi Cycle. The pur¯anic reference to the concept has already been presented in Sect. 4.6. This very ill understood phenomenon has also been employed in determining the antiquity of Mah¯abh¯arata. Sengupta has demonstrated that different interpretations of the scheme can lead to very different results. Anyhow a brief account of the connection of Saptarshi Cycle with Mah¯abh¯arata dating can be presented here. According to pur¯anic text the Saptarshi was at Magh¯a at the time of Yudhisthira and shifted to Purv¯as¯adh¯a at the time of Mah¯apadma Nanda. When the Andhra dynasty came to an end the Saptarshi was at Satabhisaj. (Vayu Pur¯an, 99.423)

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5 Archaeoastronomical Study of Ancient Indian Chronology …

Table 5.4 Mah¯abh¯arata war date according to various researchers Sl No.

Researcher

Mah¯abh¯arata Date

1

Aryabhata I (Since Kali era started on 3102 BCE and the war preceded it by 35 years)

3137 BCE

2

Var¯ahamihira (Since as per Vriddha Garga Yudhisthir ruled 2526 years before the start of Saka era---77 BCE)

2449 BCE

3

Vishnu Pur¯an (1050 years elapsed between Parikshit and Nanda. Evidence of a submerged temple at Dw¯arak¯a in the middle of second-millennium BCE supports this)

1424 BCE

4

Bankim Chandra Chattopadhyay (Krishna Charitra, 1880)

1430 BCE

5

P. C. Sengupta

2449 BCE

6

K. L. Daftari & Dieter Koch

1197 BCE

7

A. K. Bhatnagar (Bhisma’s death on WS day that was seven days 1793 BCE before full moon at Magh¯a + Vishnu Pur¯an with a slight variation)

8

L. M. Kar (Natural catastrophic, genealogical list of kings)

1924 BCE

Now from Magh¯a to Purv¯asadh¯a, the gap is ten nakshatras. Again Satabhisaj is four more nakshatra from Purvas¯adha. Thus, according to the Saptarshi Cycle tradition, the period between Mah¯apadma Nanda and Yudhisthir is (10 × 100 =) 1000 years and the interval between Nanda and Andhra’s end becomes (4 × 100 =) 400 years. Although the interval between Yudhisthira and Nanda is reasonably acceptable, that between Nanda and Andhra’s ending is wrong. Historically, it is known to be 800 years. Many feel that the motion of Saptarshi pointer is nonuniform and it must have been 200 years per nakshatra. In this way, the average rate of Saptarshi pointer’s movement could be 150 years during the period between Yudhisthira and Nanda. In that case, the Saptarshi Calendar yields a date of (1500 + 100 + 321 =) 1921 BCE. This is of course, a very rough estimate, but the order of magnitude tallies with those from other analyses. Table 5.4 shows the results arrived at by various researchers.

5.5.3 Consistency of Mah¯abh¯arata Date with Other Sources It can increase the level of confidence in dating Mah¯abh¯arata war if it is corroborated by other sources. In this regard, the genealogical list of kings can be very useful and the information contained in Pur¯anas can be employed for verification of the date obtained. The Pur¯anas which are relevant for this purpose are the following according their chronological order. (i) (ii) (iii) (iv)

The Matsya Pur¯an The V¯ayu Pur¯an The Vishnu Pur¯an The Bh¯agvata Pur¯an.

5.5 Date of Mah¯abh¯arata

105

Table 5.5 Years of rule by various dynasties Sl No. Dynastic Kings

Total years of rule

1

Brihadrthas of Magadha from Mah¯abh¯arata war (Som¯adhi to 967 Ripunjaya)

2

Pradyotas of Avanti

173

3

Sisun¯agas of Magadha

360

4

Mahapadma Nanda & Nandas

100

5

Chandragupta (Maurya) took over

1600 years after Parikshit

1500

This chronological order has been arrived at by studying the astronomical references contained in these texts. Particularly, the location of the winter solstices mentioned in these Pur¯anas has become useful in ordering these texts chronologically. Among these, the Matsya and V¯ayu Pur¯ana can provide most reliable information. Genealogical lists of the kings mentioned in the Pur¯anas, when compiled, yield the following data in a condensed form (Table 5.5). Coronation of Mah¯apadma Nanda from the time of Parikshit is therefore 1500 years according to the dynastic lists of kings mentioned in the Pur¯anas. This is also supported by a sloka in Vishnu Pur¯ana as presented in Sect. 5.4. It means ’From the birth of Parikshit to the accession of Mah¯apadma Nanda, the interval is known to be one thousand and fifty five hundred years’.6 Now, it is known that Chandragupta Maurya started his rule in the year 321 BCE. Adding the above period to this puts the end of Mah¯abh¯arata battle (i.e. also the birth of Parikshit) in 1921 BCE. The result also matches roughly with the astronomically determined date. If the period between Parikshit and Mah¯apadma Nanda be 1050 years according to the other version of the Pur¯anic sloka, then Mah¯abh¯arata war is dated as (1050 + 100 +321 =) 1471 BCE. This date matches with the calculation based on the time taken by the sun at Dhanishth¯a to winter solstice as 67 days. This has been discussed in the previous section. There is some indication for the war date in the geological and climatological information contained in Mah¯abh¯arata itself. Recent research on vedic river Sarasvati has established that the river started losing its glory from 3000 BCE7 onwards and dried up in 1900 BCE. Towards the end of its life, Sarasvati stopped flowing to the sea and was lost in the Thar desert at a place which was called ‘Vin¯asana’ in the Puranic period. In Mah¯abh¯arata, there is a description of Balar¯ama going on a pilgrimage along the banks of river Sarasvati and reached ‘Vin¯asana’. This shows that during the Mah¯abh¯arata period, Sarasvati was on the verge of its extinction indicating a period near about 1900 BCE. The other geological and climate related information

6 There 7A

are variations and the period is mentioned as 1050 and 1015 in the different recessions. more detailed discussion on Sarasvati will be presented in Chap. 7.

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5 Archaeoastronomical Study of Ancient Indian Chronology …

Fig. 5.8 Sea level change during the historic and protohistoric periods

have been analyzed.8 Benedetti mentions that in the later part of the 1500 BCE, the Kurukshetra area had Late Harappan settelments. Pottery from Harappan civilization and Painted Grey Ware (PGW), dating from 1400 BCE, are found. It is felt by some eminent archaeologists like B. B. Lal that such ware is related to Mah¯abh¯arata period since these are found in the places mentioned in Mah¯abh¯arata viz. Indraprastha (this is identified with the place where Purana Qila, Delhi is located), Hastin¯apur, Ahichchhatra and Kaus¯ambi. An interesting tradition exists regarding Hastin¯apur and Kaus¯ambi, that king Nicaksu (fifth generation from parikshit) had to abandon the first city as it was destroyed by a Gang¯a flood.9 According to archaeologists like Lal, the evidence of such a flood is confirmed at the PGW and Ochre Coloured Pottery(OCP) levels at Hastin¯apur. As per the archaeologists like Lal, the excavations unearthed the settlements belonging to the second-millennium BCE. Again in Gujarat, archaeologist S. R. Rao (Rao 1999) has discovered a submerged settlement near the Bet Dv¯ark¯a island that is dated mid-second-millennium BCE. According to Rao, this Dv¯arak¯a town was built around 1500 BCE when the sea level was lower than the present level. Submergence could have been around 1400 BCE. It is interesting to note that the Sindhu-Sarasvati civilization came to an end around the same time. Figure 5.8 shows the change of mean sea level during the historic and protohistoric period. Examining the change of the mean sea level, it is found that around 2500 BCE, the level was low enough to make the bridge connection between mainland India and Sri Lanka to be possible as found in R¯am¯ayana. D¯asharathi R¯ama was 22 generations before Krishna and discussion on R¯am¯ayana date will be taken up in Chap. 7. Figure 5.9 shows a composite diagram with various interconnections between Mah¯abh¯arata and other events in the historic and protohistoric periods.

8 Benedetti,

Giacomo, ’The Chronology of Puranic Rings and Rigvedic Risis in Comparison with the Phases of the Sindhu-Sarasvati Civilization’, Chap. 6. 9 Ibid Pargiter.

5.5 Date of Mah¯abh¯arata

107

Fig. 5.9 Interrelation between Mah¯abh¯arata war and other events

References Bhatnagar, A. K., “Date of Mah¯abh¯arata War Based on Astronomical References – A Reassessment”, Indian Journal of History of Science, 52.4 (2017). Bhatnagar, A. K., “Date of Mah¯abh¯arata War Based on Astronomical References”, Indian Journal of History of Science, Pub: Indian National Science Academy, New Delhi, 52.4 (2017), 369–394. Daftari, K. L., “The Astronomical Method and its Application to the Chronology of Ancient India”, Nagpur University, 1942. Rao, S. R., “The Lost City of Dv¯arka”, National Institute of Oceanography, 1999. Sengupta, P. C., “Ancient Indian Chronology”, Calcutta University Press, 1947, pp. 2.

Chapter 6

Chronology of Vedic and Ved¯anga Periods

6.1 Introduction Many consider the vedas to be the oldest texts of the world. The root of the word ‘Veda’ is ‘Vid’ meaning ‘to know’. Thus, ‘Veda’ implies ‘knowledge’ or book of knowledge. The vedic corpus is vast and is divided into the following four vedas—‘Rik’, ‘Sam’, ‘Yajur’ and ‘Atharva’. Each veda has the original hymns called ‘Samhita’ followed by a commentary portion called ‘Br¯ahmana’ which guide people ¯ to perform sacrificial rites. Two other divisions are ‘Aranyakas’ and ‘Upanishads’. ¯ ‘Aranyakas’ are meant for hermits who prepare for taking sany¯as in the forests. ‘Upanishads’ deal with the philosophical aspects of life. Among all the vedas, Rigveda is the oldest and richest in its volume. Rigveda is a collection of 1028 hymns and 10,600 verses organized into ten books (‘Mandalas’). The four vedas consist of 20,358 verses. It takes more than two thousands printed pages. By linguistic analysis, it has been found that Rigveda is the oldest followed by S¯amveda, Yajurveda and Atharvaveda. In a very brief form, the vedic corpus is shown below

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 A. Ghosh, Descriptive Archaeoastronomy and Ancient Indian Chronology, https://doi.org/10.1007/978-981-15-6903-6_6

109

110

6 Chronology of Vedic and Ved¯anga Periods ¯ Aranyaka

Veda

Samhit¯a

Br¯ahmana

Rigveda

Rik

Aitareya Aitareya Aitareya Kaushitiki, Sankh¯ayana Kaushitiki, Sankh¯ayana Kaushitiki

S¯amveda

S¯ama

Panchavimsa, Sadvimsa Jaiminiya

Yajurveda

Taittiriya Taittiriya Kathaka Kath¯a Maitray¯ani Satapatha V¯ajaseneyi

Atharvaveda Atharva

Gopatha

Upanishad

Chh¯andogya Kena Taittiriya Kath¯a

Taittiriya Kath¯a Maitri Brihad¯aranyaka Mundaka Mundukya

It is one of the strangest things that for thousands of years, this huge volume of literature has been preserved with exceptional fidelity. But it is not easy to understand the meaning clearly in many cases. Particularly, in many instances, the texts are couched in allegorical stories. It remained like this till the fourteenth century when S¯ayana, a great scholar of Vijayanagar, South India, authored the most comprehensive commentary. Unfortunately, even S¯ayana’s commentary was related to the outer meaning of vedas. In many cases, the real deeper meaning has remained unraveled till the present times. Once the translation of Rigveda was published in the nineteenth century, considerable interest was created among the western scholars and many started research on the antiquity of this text, thought to be the oldest. The antiquity of ancient India’s astronomical knowledge was already a burning topic characterized by controversies, debates, insuniations and even rage. By that time already the connection between Sanskrit and other languages of Europe (and Iran) was established after the seminal lecture by Sir William Jones in Calcutta. The concept of an original common language, termed as Indo-European, was already going round the scholarly world and a new subject---comparative linguistics---was already raising its head. The obvious result was the emergence of a concept of a race, called Aryan, as the bearer of this Indo-European (or Indo-Aryan as some called it), invading India from its northwest boundary. According to this hypothesis, these invading Aryans brought the Sanskrit language to India and laid the foundation of India’s culture and civilization, which became known as Hinduism at a later time. This hypothesis was termed as Aryan Invasion Theory (AIT) as has already been discussed earlier in this volume. The prime mover behind this theory was the reputed Indologist Fredric Max Mueller. To fit with the Biblical genesis, he proposed the era of this event as 1500 BCE. Starting from this assumed date of arrival of the Sanskrit-speaking Aryans, he concluded that the first of the vedas---Rigveda---was composed in 1200 BCE and giving a period of 200 year between each consecutive vedas, he concluded that the last one was composed around 600 BCE. This hypothesis has continued to be the main stream standard theory about the origin of Indian civilization and composition of the vedas. This theory became so dear to the ruling Britishers and the majority of the western

6.1 Introduction

111

(and some Indian) scholars, that even today, the academia has not been able to get rid of AIT. The original dating of veda’s composition was done primarily through an adhoc approach to fit it with the known history of India that began with Gautama Buddha. The period for each stage was decided by some assumed language-based procedure. Finally, Max Mueller himself was unhappy with his dating of Rigveda and declared that no one on the earth is capable of dating this most ancient text of the world. Subsequently, it was felt by many scholars that, if properly interpreted, many astronomical references (in allegorical form in most cases, of course) contained in Rik and other vedas, may yield a reasonable guess about the antiquity of these compositions. A very large number of competent astronomers and vedic scholars have remained engaged in this task since the time of B. G. Tilak, towards the end of the nineteenth century. Besides, as mentioned in the previous chapter, the prepared genealogical list of pur¯anic kings can also be useful in mapping the vedic period. Mah¯abh¯arata being the sheet anchor of India’s protohistory, an appropriate mapping with Mah¯abh¯arata along with the genealogical list of kings can lead to approximate dates which can be matched with the astronomically determined dates. Corroboration with the geological history of northwest India can provide further substance to the arrived antiquity. Recently, it is also being attempted to consider the archaeological data from the Sindhu--Sarasvati civilization (and the earlier phases of civilization in the region starting from 7000 BCE) providing further clues to the study of this topic. Although equating Harappan civilization with the ancient vedic civilization is still not considered to be the main stream idea, and gradually, many evidences are emerging which prove the interaction of the vedic people with the contemporaneous Harappan people. Among the geological evidences, the most prominent one is the vedic river Sarasvati. A section on Sarasvati in this book will be very useful for the study of certain aspects of ancient climate of this region yielding very interesting ideas and also hints at the antiquity of vedic era. It is quite obvious that any discussion on establishing the antiquity of the vedas is bound to be intimately connected with the Aryan Invasion Theory. As a result, study and discussion on vedic antiquity get politically entangled as AIT has been very heavily politicized from its very inception. Of course in the recent time, increased application of scientific methods is gradually bringing more facts into the light and the academia is not so hostile to reopening the subject as it used to be before. Extensive analysis of the astronomical references found in vedic literature has been carried out by quite a few scholars in the past, and the most notable among them is P. C. Sengupta. Thus, this chapter draws, very heavily, material from his published results. Subsequent researchers have done extensive work using advanced planetarium softwares. However, not much significant change in the results is evidenced.

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6 Chronology of Vedic and Ved¯anga Periods

6.2 Hints to High Antiquity of Vedas Before proceeding with detailed discussion on the antiquity of vedas, in this section, a very definite and unambiguous astronomical reference will be presented that undoubtedly hints at high antiquity of Rik and other vedas. It can act as an appetizer and strengthen the interest and curiosity of any investigator. The high antiquity of vedic texts is indicated by the tradition of a reference to a polestar as ‘Dhruva Nakshatra’. A relook into Fig. 2.15 makes it clear that due to the precessional rotation of the earth’s axis, the north (and also south) celestial pole continues to move along a circle of an angular diameter of 47° with the ecliptic pole as the centre. Figure 6.1 shows the circle along which the north celestial pole moves taking 25,800 years in completing one rotation. Currently, there is a star, Polaris, very near to the point on the celestial sphere that represents the north celestial pole. However, the figure shows that Polaris must be a recent entry to the position around 1000 CE when it was still at a distance of 6° from the actual pole position. In the year 1547 CE, its position was 3° 7 from the true north celestial pole, and the current declination of Polaris is 89° 15 50.8 . Or, it is about only 44 9 angular distance away from the centre. Thus, it appears as virtually still. Before 1000 CE, no star could have been described as a pole star. But many ancient texts quite empathetically refers to a north Pole Star as ‘Dhruva’; the only possible way it could have happened as the reference to a Pole Star in ancient vedic texts. The figure shows quite clearly that there was no visible star near the pole position unless one goes back to 2800 BCE when the star Thuban (α Draconis) occupied the position of the pole. Its distance from the pole was only 5 of arc and, obviously, the star appeared to be absolutely still. Figure 6.2 shows how the distance of Thuban changed in the third millennium and early second millennium BCE. It is

Fig. 6.1 Circle described by the north celestial pole

6.2 Hints to High Antiquity of Vedas

113

Fig. 6.2 Change in the angular distance of Thuban from the north celestial pole

clear that even by the middle of the third millennium BCE the angular distance of Thuban became almost double the diameter of the full moon. By 1700 BCE, Thuban’s distance from the true pole point increased to 6°, i.e. 12 full moon diameters. Obviously, its motion could be easily noticed. This phenomenon has been discussed in ancient texts as ‘running away’ of the star. In Maitryupanisad, this phenomenon has been described as a harbringer of disasters (Mai Up 1.4): But what am I talking of these! Moreover there is also the drying up of great oceans, the collapsing of mountains, the swerving of the pole star, the cutting through of the wind strings, the drowning of the earth, the running away of the gods from their abode, in this kind of course of the world, how can one enjoy desires when, as can be seen whoever relies on them, must return again and again!

Thuban’s motion was originally so inprecebtable that ‘Dhruva’ was the symbol of permanence and nuptial knots used to be desired to be as permanent as ‘Dhruva’. Even now, in India, terms like ‘Dhruva satya’ is often used. It was thought that all the stars and constellations were connected to the ‘Dhruva’ by invisible strings allowing them to move in circles with the Dhruva Nakshatra at the centre. There has been a suggestion that the desired Pole Star could be κ Draconis which reached the minimum distance of 4° 40 in the second millennium BCE. But as pointed out by R. N. Iyenger this could not be the case as in texts Dhruva is mentioned to be a star in the tail of a constellation called ‘Simsum¯ara’. From 1700 BCE till 1000 CE, there was no visible star near enough to the pole. So ancient texts mentioning ‘Dhruva’ and again its ‘running away’ must refer to Thuban and the era dates back to early third millennium BCE, establishing high antiquity of the vedic texts and the corresponding period of their composition. This rule out any possibility of the vedic texts to be younger than at least 4500 years old.

114

6 Chronology of Vedic and Ved¯anga Periods

6.3 Astronomical References in Vedic and Other Ancient Texts As already mentioned that most extensive work in this topic was done by P. C. Sengupta, Professor of Astronomy, Calcutta University, during the thirties and forties in the twentieth century. Similar work was also done by K. L. Daftari and quite a few other researchers. Before starting the study and analyses of these astronomical references, it may be advantageous if these are grouped and collated in a tabular format. Table 6.1 shows the important astronomical references. As evident from the table, the most dependable references are those which relate the position of the equinoxes and solstices along the Zodiac (or, the ecliptic). The other type of observation that can yield dependable result is the simultaneous crossing of meridian by stars and also the alignment of stars along the same longitude as explained in Fig. 2.19. There are many more astronomical references in Br¯ahmana texts and Ved¯anga Jyotisha. Ved¯anga Jyotisha’s antiquity will be discussed seperately. It is further stressed that the list of astronomical references mentioned in Table 6.1 is neither complete nor extensive. Only some very prominent ones have been taken as examples. As was done in the case of Mah¯abh¯arata dating for establishing the chronology of vedic India consistency with the genealogical list of kings will be checked.

6.3.1 Heliacal Rising of Ashvins at Winter Solstice This is the earliest astronomical reference in Rigveda (Rigveda V, 77, 1α2). According to this, Ashvin used to rise heliacally on the winter solstice day. α Arietis (Hamal)1 is the main star and its magnitude and current position are given by m = 2, α ≡ R.A. = 2 h 7 m 10 s and δ = 23° 27 46 . Since its magnitude is 2, for heliacal rising, its approximate longitude can be found out by (A.22). Using Sapta-Sindhu latitude of 30°N (λs − λ) is approximately 17.1°. On the winter solstice day the sun’s longitude is 270°; for heliacal rising of Hamal, it should have a longitude of ~(270° − 17.1° =) 252.9°. Now in degrees 2 h 7 m 10 s ≡ 31.8◦ Converting to the ecliptic system of coordinates using (2.1.2), the following value of the current longitude is obtained as λ = 37.72◦ and β = 9.6◦

1 The

principal star of Ashvin.

6.3 Astronomical References in Vedic and Other Ancient Texts

115

Table 6.1 Astronomical references in Vedic and other ancient texts S. No.

Nature of the phenomenon

Astronimcal phenomenon

References

1

Equinox position

Orion’s head near vernal equinox

2

Summer solstice position

Heliacal rising of α Leonis (Magh¯a) on the summer solstice day

3

Heliacal rising

Madhu Vidy¯a; Heliacal rising Rig Veda, M.I 34.2, M.I of α Triangulum and α and β 157.3, M.I 34.9, M.I 47.2, Arietis (Ashvins) after two M.I 118.2 months from winter solstice

4

Equinoctial position and the stars

Vernal equinox near λ Orionis, Summer solstice near β Leonis, Autumal equinox near λ Scorpionis, Winter solstice near α Pegasi

5

Solar eclipse

A solar eclipse on the summer Rig Veda, V 40.5.9 solstice day taking place in Kausitiki Br¯ahmana XXIV, the fourth part of the day 3.4 visible in northwest India

6

Star alignment

Dogs of Yama—α Canis majoris and α Canis minoris being on the same meridian pointing to south

7

Star alignment

Praj¯apati Rohini legend. Aitareya Br¯ahmana III Simultaneous crossing of the 36,13,9 meridian by δ Auriga and α Rig Veda X, 61.6 Tauri on the Autumal equinox day on a full moon night

8

Month of M¯agha and five-yearly Yuga

Beginning of five-yearly Yuga system in the month of M¯agha on the winter solstice day

9

Nakshatra Krittika

Nakshatra Krittik¯a never Shatapatha Br¯ahmana II swerves from the east (when 1,2.3 it rises) implying it was on the equinoctial point

10

Winter solstice

Heliacal rising of Ashvins at winter solstice (earliest reference)

Rig Veda, M.X.23.2

Atharva Veda XIII, 1.6, Taittiriya Br¯ahmana

Rig Veda, X, 14.10.11, Atharva Veda, XVIII, 2,11

Rig Veda V 77, 1&2

Since longitude increases with time due to precession, the amount of increase from a longitude of 252.9° to 37.72° is equal to 360◦ + 37.72◦ − 252.9◦ = 144.82◦

116

6 Chronology of Vedic and Ved¯anga Periods

Considering a shift of 50.4 per year, the time required, T, for a shift of 144.82° is found out as follows: T = (144.82 × 3600)/50.4 years = 10344 years Hence, the reported event could be observed around 10344 − 2018 = 8326 BCE This is the earliest astronomical event that has been reported in Rigvedic text. Undoubtedly, it is of a very high antiquity level and needs careful reconsideration. Of course, the result is quite approximate as the analysis did not consider the declination into consideration. For stars near the ecliptic, this approximate method is acceptable. In Atharvaveda, heliacal rising of λ and γ Scorpionis is found as shown below:

Analysing the slokas, the interpretation, according to Whitney, there was a time in vedic era when the heliacal rising of λ Scorpionis marked the onset of ‘Hemanta ritu’. At that time of the year, the sun’s longitude is around 210°. Sengupta has shown by mathematical analysis that the required celestial longitude required for heliacal rising of the star is around 190°. The current celestial longitude of λ Scorpionis is 264.77°. So the magnitude of the shift is 74.77° implying the date of the observation recorded to be (5299 − 2018 =) 3281 BCE.

6.3.2 Madhu Vidy¯a and Heliacal Rising of Ashvin Rigveda gives a clear instruction for identifying the onset of the spring. As mentioned earlier, the season spring used to be called ‘Madhu Ritu’. At the onset of spring,

6.3 Astronomical References in Vedic and Other Ancient Texts

117

everything becomes very comfortable and sweet. Particularly, in the northwest India, the winter used to be quite severe and the onset of spring used to be full of sweet feelings. Thus, Rigveda says (Rigveda M.I.90.68)

meaning ‘Sweetness is blown by the winds and sweetness is discharged by the rivers; may the herbs be full of sweetness to us. May the nights and twilights be sweet to us, may the dust of the earth be sweet, may the sky-father to us be full of sweetness. May the trees be full of sweetness to us, may the sun be full of sweetness, may our wine be sweet to us’. It is very clear that arrival of spring used to fill the hearts of the people with joy and happiness. This was also the time for harvesting the crop. The trees become full of new leaves and the trees become ready to yield fruits. The weather, of course, used to become comfortable and warmer. Thus, it is no wonder that this event got considerable importance. The Rigveda (M.I.117.22) states

meaning2 ‘You replaced, Ashvins, with the head of a horse, Dadhichi, the son of Atharvan, and true to his promise he revealed to you the science of ‘Madhu’ which he had learnt from Tv¯astri and which was a jealously guarded secret’. This ‘Madhu vidy¯a’ or the science of spring is nothing but recognizing the celestial signals to the onset of spring. The ‘Ashvins’ are generally identified with the main stars in nakshatra ‘Ashvini’— α and β Arietis. As mentioned by Sengupta the combination of the stars α Triangulum, α and β Arietis forms a triangle resembling a horse’s head. The Ashvins are thought of as riding in their three-wheeled, spring-bearing chariot. Rigveda (M.I, 157.3) states

2 Sengupta

(1947).

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meaning1 ‘May the three-wheeled car of the Ashvins, which is the harbringer of spring-Madhu V¯ahana-drawn by the swift horses, three canopied, filled with treasure, and every way auspicious, come to our presence and bring prosperity to our people and our cattle’. There are a number of verses in Rigveda M.X.41.8, M.I.34.9, M.I.47.2 and M.I.115.2 which describe the Ashvins as the harbringer of the spring season. One of this M.X.41.2 clearly mention ‘harnessed in dawn and set in motion at dawn’. This is undoubtedly a reference to the heliacal rising of Ashvins at the onset of spring season. Which is usually two months after the winter solstice, i.e. when sun’s longitude is around 330°. It has clearly been shown that the current longitude of α Arietis, the main star of ‘Ashvins’, is 37.72°. As shown earlier for heliacal rising, the longitude of α Arietis should be about 17.1° less than that of the sun or around (330° − 17.1° =) 312.9°. So the increase of its longitude till 2018 is 306◦ + 37.72◦ − 312.9◦ = 84.82◦ This requires a time interval of (84.82 × 3600/50.4) years or, 6059 years approximately. So the period of the above-mentioned heliacal rising was (6059 − 2018 =) 4041 BCE. This is also a very approximate analysis. Considering the inclination of the ecliptic after two months of winter solstice, the period comes as 4539 BCE, approximately. According to Sengupta, the longitude difference for heliacal rising should be 18°. With this condition, the longitude of α Arietis should have been (330° − 18° =) 312° and the increase in longitude till 2018 is 360◦ + 37.72◦ − 312◦ = 85.72◦ and the time elapsed is (85.72 × 3600/50.4 =) 6123 years. Thus, the era under consideration is (6123 − 2018 =) 4105 BCE. Thus, the early era of Rigveda goes back to the sixth millennium BCE as hinted by these astronomical references. Figure 6.3 shows the situation in 4000 BCE when α Arietis rose heliacally after two months of the winter solstice.

6.3.3 Orion’s Head Near Vernal Equinox B. G. Tilak3 in his famous book ‘The Orion’ had shown through extensive analysis that there are references in vedic texts that the head of the constellation Orion was near the vernal equinox. The year beginning was reckoned from the day when sun occupied the vernal equinoctial point. This could be judged by the ancient Indian 3 Tilak,

B. G. – ‘The Orion‘’.

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Fig. 6.3 Heliacal rising of Ashvins

astronomical observers by noticing the nakshatra located at this position. It can be estimated how far long back in time the head of Orion was nearest to the vernal equinox. Since the constellation Orion is situated at reasonably southern celestial latitude, it cannot be on the equinoctial position. But around 4000 BCE, the sky map very clearly shows how the head of Orion was quite conspicuously near the vernal equinox. Figure 6.4 shows the sky configuration around 4000 BCE. A simple analysis can show the result as follow: The main star at Orion’s head is Meissa (λ Orionis) and its current position is given by R.A.—5 h 35 m 8.28 s and declination—+9° 56 2.96 . When transformed to the ecliptic system, the longitude and declination of the star are determined as α = 83.785◦ and δ = 9.934◦ with the help of (2.1.1). Thus, λ = cos−1



cos δ cos α cos β

 and β = sin(sin δ cos ϕ − cos δ sin ϕ sin α)

and substituting the values one gets λ = 83.7° and β = −13.956°. When Orion’s head (λ Orionis) was near the vernal equinox, its celestial longitude was almost 0°. Thus, till date, the increase of Orion’s head’s longitude is 83.7°. This requires (83.7◦ × 3600)/50.4 = 5979 years

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Fig. 6.4 Orion’s head near vernal equinox in 4000 BCE

Thus, the period when the observation was made was (5979 − 2018 =) 3961 BCE (almost 4000 BCE).

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6.3.4 Heliacal Rising of Magh¯a (α Leonis) on Summer Solstice Day There are ample references in Rigveda to Indra as the ‘shedder of rain’. Rishi Hiranyastupa describes Indra’s great deeds in Rigveda (M.I. 32)4

A few parts of the translation in its allegorical form are given here. ‘I declare the former valorous deeds of Indra, which the Thunderer has achieved; he clove the cloud; he cast the waters down; he broke (a way) for the torrents of the mountain. He clove the cloud, seeking refuge on the mountain; Tvastri sharpened his far-whirling bolt; the flowing waters quickly hastened to the ocean, like cows hastening to their calves…. Maghavan took his shaft, the thunder-bolt, and with it struck the first born of the clouds … with his vast destroying thunder-bolt Indra struck the darkling mutilated Vritra, as the trunks of trees are felled by the axe, so lies Ahi prostrate on 4 Sengupta

(1947).

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the earth … the waters that delight the minds of men, flow over him recumbent on this earth, as a river bursts through its broken banks. Ahi has been prostrated beneath the feet of waters which Vritra by his might had obstructed. The waters carry off the nameless body of Vritra, tossed into the midst of the never-stopping, never-resting currents. The foe of Indra has slept a long darkness … when the single repledent Vritra returned to blow, Indra, by the thunder-bolt, thou becommest (furious) like a horse’s tail. Thou hast rescued the kine; thou hast won, Hero, the Soma juice; thou hast let loose the seven rivers to flow’. [Wilson’s Rigveda translation taken from Sengupta]. Vedic scholars are unanimous in their opinion that the above allegorical description is nothing but the onset of the rainy season. The clouds carrying water is considered as a demon unwilling to release their water until Indra hurls thunder-bolt to the demonic clouds to release the rain water. Ahi (i.e. Vritra) is considered as a demon and the onset of the rainy season is because of a fight with Indra, who finally wins. The mentioned seven rivers obviously refer to the seven rivers of the Sapta-Sindhu region where the hymns were composed. During vedic periods, the astronomical observers noticed that the sun remains almost motionless (that is why the term ‘solstice’) for almost 21 days during summer (and also winter) solstice. The middle day, or the eleventh day of this period was recognized as the real solstice day. This was termed as ‘Ekavimsa’ (21). In Aitareya Br¯ahmana (XVIII.18), it is mentioned ‘by this Ekavimsa, the gods raised up the sun towards the highest point of the heavens’. Rigveda (M.I.10.1) further identifies Indra as the sun in the hymn ‘The chanters of G¯ayatri hymn thee, Satakratu, the worshippers of the sun praise thee, the Br¯ahmanas raise thee aloft like bamboo pole’. Rigveda also states (M.I.7.3) that ‘Indra in order to make the duration of light longer elevates the sun in the sky’. To further specify the situation (onset of the rains), Rigveda (M.X.23.2) states ‘Indra by the Magh¯a become Maghavan, and thus became the slayer of Vritra’. Now, Indra becoming Maghavan is interpreted as the heliacal rising of nakshatra Magh¯a. Magh¯a consists of α, η, γ , δ, μ and e Leonis. In those ancient times, the onset of various seasons used to be identified by observing the heliacal rising of some prominent stars.5 Therefore, during the Rigveda time, the rains started when the star α Leonis used to rise heliacally. Sengupta has presented a detailed analysis of this heliacal rising. An approximate calculation can be as follows: At summer solstice, the sun’s longitude is 90° and, so for heliacal rising, [using (A.22) and m = 1.4] α Leonis should be at (90° − 9.7° =) 80.3° longitude. Current position of α Leonis (Regulus) is given by α(R.A) = 10 h 8 m 22.311 s and δ = 11◦ 58 2 or, 5 With

naked-eye astronomy observing heliacal rising of some prominent stars used to be the most convenient method for identifying the period in a tropical year.

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α = 152.093◦ and δ = 11.967◦ Using (2.1.1) λ = cos

−1



cos δ cos α cos β



where β = sin(sin δ cos − cos δ sin sin α) After substituting the values λ = 149.83◦ and β = −2.81◦ Thus, the increase in longitude of α Leonis during the intervening period is (149.83° − 80.3° =) 69.53°. This takes (69.53 × 3600)/50.4 years ≈ 4966 years Thus, the approximate date comes out as 4966 − 2018 = 2948 BCE If Sengupta’s value of 18° is considered as the difference in the longitude of the sun and Magh¯a, then the required increase in the longitude becomes 149.83° − (90° − 18°) = 77.83° increasing the length of the interval to (77.83 × 3600)/50.4 years = 5559 years and the period in question becomes6 5559 − 2018 = 3541 BCE

6.3.5 Dogs of Yama and the Direction to Pitriloka There is a very intriguing hymn in Rigveda that provides information on the accurate direction to the south. From the latitude of Sapta-Sindhu, it was not possible to observe the south pole. In the ancient times, the world was divided into two regions--‘Devaloka’ and ‘Pitriloka’---as mentioned in ‘Satapatha Br¯ahmana’ 6 More

accurate calculation by Sengupta shows the date to be 4170 BCE.

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When translated, these shlokas mean Two worlds in truth there are, they say, the ‘world of the gods’ and the ‘world of the fathers’ The world of the gods is in the north and the world of the fathers in the south.

From the very ancient time, in the Hindu faith, the ‘Yamaloka’ and the ‘Pitriloka’ are situated in the south. After death, the departed souls follow the southernly ‘Pitriy¯ana’ route towards the south. This route is guarded by Yama’s two ‘spotted four-eyed dogs’ as mentioned in Rigveda:

Wilson’s and Whitney’s translations of the above hymns are given below: Pass by the secure path beyond the two spotted four-eyed dogs, the progeny of Saram¯a, and join the wise ‘Pitris’ who rejoice fully with Yama. Entrust him, O King, to thy two dogs, which are thy protectors, Yama, the four-eyed guardians of the road, renowned by men, and grant him prosperity and health. (Wilson)

The translations of the Atharva Veda hymns by Whitney are as follows: Run thou past the two four-eyed, brindled dogs of Saram¯a, by a happy road; then go to the benificient fathers, who revel in common revelry with Yama. What two defending dogs thou has, O Yama, four eyed, sitting by the road, men watching, with them, O king, do thou surround him; assign to him well-being and freedom from desease. (Whitney)

During the vedic and early vedic era, the two stars α Canis Minoris and α Canis Majoris were considered as the two dogs guarding the southernly route. The astronomical interpretation of the above allegorical hymns is that when these two stars α Canis Minoris and α Canis Majoris are joined by an imaginary line it points directly to the south. In other words, the Right Ascension of the two stars were the same (or almost same). The current positions are as given below:

6.3 Astronomical References in Vedic and Other Ancient Texts Coordinates

α Canis Minoris

α Canis Majoris

Right Assension

7 h 39 m 18.12 s

6 h 45 m 9 s

Declination

5° 13 30

– 16° 42 58.02

125

It is clear from the above that at present, these two stars do not lie on the same meridian. Before proceeding further, an interesting point should be noted. In the Rigvedic time, these two stars were described as Dog Stars. Again one finds that these two stars’ names in Hellenistic astronomy also imply their description as dogs (Canis). In other places also Rigvedic hymns refer α Canis Majoris as the Dog Star. It is very surprising how the two civilizations a couple of millennia apart considered the same stars as dogs. It needs a thorough study to find out if there was some connection between the naming of these stars as dogs by Hellenistic astronomers and the sages of the Rigvedic era. Equation (A.20) shows how α and δ vary with time due to the precession of the earth’s axis. This pair of differential equations represents two coupled nonlinear equations of first order and can be solved by computer. Figure 6.5 shows the plot of α versus time (towards the past) and it is seen that α for α Canis Minoris reduces at a rate faster than that of α Canis Majoris. Thus, the R.A’s of the two stars became the same almost 63 centuries before present. Figure 6.6 shows the situation in 4350 BCE and 2018 CE. It is clearly seen that in the Rigvedic time, the line joining α Canis Minoris and α Canis Majoris used to point towards the south celestial pole. Now, it does not do so is clearly visible in figure.

Fig. 6.5 Change of R.A for the stars with time

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Star alignment in 4100 BCE

Star alignment in 2018 CE

Fig. 6.6 Alignments of Canis Minoris and Canis Majoris in 4100 BCE and 2018 CE

The plot shows the variation of R.A. for α Cannis Minoris (star 1) and α Cannis Majoris (star 2) when the time axis is reversed. They are almost same 61 centuries before present.

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127

6.3.6 Praj¯apati-Rohini Legend It is a very well-known legend originating from Aitareya Br¯ahmana of Rigveda. This has attracted the attention of many scholars of ancient Indian astronomy including B. G. Tilak, S. B. Dixit, P. C. Sengupta and many others. The legend in a nut shell is about Prajapati feeling love for his daughter Rohini and his attempt to mate her (who became a deer) taking the form of a stag. Seeing this, the gods wanted to punish him and the fiercest among them, Rudra, pierced him with an arrow. There have been a number of interpretations of the story but all agree it to be an allegorical form of an astronomical event. Some like Tilak and Dixit considered the legend to refer to the event when the vernal equinox was at Mrigashira cluster consisting of α, ϕ 1 and ϕ 2 of Orionis. But comparing and studying the various statements of the legend found in other ancient scriptures Sengupta interpreted the legend (devoid of the allegory) to refer to the simultaneous crossing of meridian by the stars δ Auriga (Prajapati) and α Tauri (Aldebaran or Rohini). The three stars forming the Orion’s belt and α Tauri are almost collinear. The present coordinates of δ Auriga and α Tauri are as follows: Coordinates

δ Auriga

α Tauri

Right assension

5 h 59 m 31.6 s

4 h 35 m 55.24 s

Declination

54° 17 4.77 N

16° 30 33.49 N

Using the solution of A.20, shown in Fig. 6.7, it is found that the R.A.’s of the two stars were almost same during the year 3300 BCE. Sengupta has shown that on the

Fig. 6.7 Change of R.A for δ Auriga and α Tauri with time

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Star alignment in 3400 BCE δ Auriga and α Tauri have almost same meridian

Star alignment in 2018 CE δ Auriga and α Tauri have different meridian

Fig. 6.8 Sky map in 3300 BCE showing δ Auriga and α Tauri crossing meridian simultaneously

full moon night when the sun was at the autumnal equinox, the vernal equinox colure passed almost straight through these two stars. He has given adequate explanation for taking δ Auriga as the Prajapati. Figure 6.8 shows the sky map for the situation.

6.3.7 Solar Eclipse Recorded in Rigveda and T¯andya Br¯ahmana It has been mentioned earlier that using eclipse for the determination of ancient dates is difficult. This is so because eclipse is not a rare event when the periods involving many millennia are concerned. Furthermore, the degree of an eclipse may not be always recorded. However, total and annular solar eclipse at a particular location on a particular day of the tropical year at a particular hour of the day is, surely, a very unique event. The dates arrived at by the consideration of various stellar alignments discussed in the previous sections can only provide an approximate idea of the antiquity. Only through temporal traiangulations7 a somewhat precise idea about the antiquity can be found out. On the other hand a unique event involving a solar eclipse, as mentioned above, can pin point the date of the event. But clear cut descriptions of such eclipses are very rare. One such unique solar eclipse’s description is found in Rigveda described by sage Atri. This reference to a total solar eclipse (or annular eclipse) has been researched extensively; however, no unique result has been arrived at. The original hymn (Rigveda V, 40, 5-9) is reproduced below:

7 Dating

an event using more than two references.

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129

The translation by Wilson8 is given below: 5. When O Surya, the son of asura Svarbh¯anu, overspread (rather ‘struck’) thee with darkness, the world were beheld like one bewildered not knowing his place. 6. When, Indra thou wast dissipating those illusion of Svarbh¯anu which were spread below the sun, then Atri, by his fourth sacred prayer (Turiyena Br¯ahmana), discovered (rather ‘rescued’) the sun concealed by the darkness impending his functions. 7. [Surya speaks]; Let not the violater, Atri, through hunger, swallow with fearful (darkness) me who am thine; thou art Mitra whose wealth is truth; do thou and the royal Varuna both protect me. 8. Thou the Br¯ahmana (Atri), applying the stones togeather, propitating the gods with praise, and adoring them with reverence, placed the eye of Surya (sun) in the sky; he dissipated the delusions of Svarabh¯anu. 9. The sun, when the asura Svarabh¯anu enveloped (rather ‘struck’) with darkness, the sons of Atri subsequently recovered; no others were able (to effect his release).

As illustrated by Sengupta the concerned day, on which the eclipse took place, the following passage from Kausitaki Br¯ahman (XXIV,3,4) can be refered to:

The english translation by Keith9 is given below: Svarabh¯anu, an Asura, pierced with darkness the sun; the Atris were fain to smite away its darkness; they performed before the Visuvant, this set of three days, with saptadasa 8 Wilson 9 Keith

(1866). (1920).

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(seventeen) stoma. They smote away the darkness in front of it; that settled behind, they performed the same three day rite after Visuvant; they smote away the darkness behind it. Those who perform knowing thus, this three day (rite) with Saptadasa stoma on both sides of the Visuvant, verily those sacrifices smite away evil from both worlds. They call them the Svaras¯amans; by them the Atri’s rescued (apasprnvata) the sun from the darkness; in that they rescued, therefore, are the Svaras¯amans. This is declared in a rik. The sun which Svarabh¯anu The Asura pierced with darkness. The Atris found it, None other could do so.

The descriptions given in Rigveda and Kausitiki Br¯ahmana of Rigveda as presented above undoubtedly refer to a solar eclipse that could be near total. The first attempt to date the described eclipse was made by Prof. A. Ludwig of Prague10 (the first translator of Rigveda beside Hermann Grassmann). Quite naturally, he was severely criticized by Prof. W. D. Whitney of New Haven, Connecticut. He was of very negative opinion about the abilities for any scientific capability of ancient Indians as evidenced through his all published opinions. However, Ludwig’s interpretation that there were references to four eclipses has not been agreed to by Sengupta. In his opinion, only one reference (Rigveda, V, 40, 5-9) can be considered as a solar eclipse. Subsequently, Sengupta and some others, most notably S. Balakrishna have analyzed the description to find out the antiquity of the event. Sengupta did not have any help from any computer in the 1940s whereas Balakrishna has employed advanced planetarium software for his analysis. To date a solar eclipse, the following information are necessary: (i) The day of the eclipse in the year (ii) The time of the eclipse on that day (iii) The location of the observer It is assumed that any remarkable eclipse has to be central and at least near total. Once it is decided that the riks 5–9 in Rigveda V.40 refer to a solar eclipse, the scholars proceeded in the following manner to get some idea about the three points mentioned above. From the description given in the Kausitiki Br¯ahmana (presented above), the day of the eclipse in relation to the tropical solar year, point no. (i) can be decided. For that purpose, the mention of the word ‘Visuvant’ is critical. There are two opinions on that. According to Sengupta ‘Visuvant’ can refer to either of the solstice days. He shows that Kausitiki Br¯ahmana says that ‘the sun starting northward from the winter solstice on the new moon day of M¯agha, reached the Visuvant after six months’. Apart from this Aitareya Br¯ahmana states that ‘the Visuvant and the Ekavimsa day was the same day, the day on which the gods raised up the sun to the highest point in the heavens…’. The highest point in the heaven is reached by the sun on the summer solstice day. Considering these two statements, Sengupta concludes that the eclipse must have taken place on the summer solstice day or a day after 10 Ludwig

(1885).

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131

that. Much later, in T¯andya Br¯ahmana and Taittiriya Samhit¯a, the word Visuvant was used to mean the middle day in a sacrificial year beginning on the vernal equinoctial day. This means the autumnal equinoctial day. Balakrishna has taken the day of the eclipse near the autumnal equinox and using planetarium software decided to date of the eclipse to be three day prior to autumnal equinox in the year 4677 BCE, and according to him, the location of the event was at Chitrakoot (about 25°N latitude). However, considering the Rigveda Br¯ahmana texts, Sengupta considered the day to be near the summer solstice day. From rik no. 6 presented above, the interpretation of ‘…by his fourth sacred prayer…’ has been ‘the fourth part of the day’. It is also concluded based on the description given that the eclipse was an annular eclipse and it was over before the day end (at Kurukshetra meridian). To determine the place of observation by Atri, some Rigveda riks are used by Sengupta for guidance. Those are I,51,3; I,112,7; I,116,8; I,119,6; I,139,9; I,180,4; I 183,5; V,73,6-7; VII,68,5; VII,71,5; VIII,35,19; VIII,36,7; VIII,37,7; VIII,42,5; X,39,9; X,143,1-3 and X,150,5. Quoting Sengupta after his study of these riks ‘it would appear that Atri took shelter in a cave with a hundred doors or openings, where he felt scorching heat, which was allayed by a thaw of ice from the snow capped top of the mountain peak, at the bottom of which the cave was situated’. This description can match if the latitude of the place corresponds to the start of Himalaya/Karakoram mountains, since the riks mention ‘scorching heat was quenched with snow’. Sengupta, after detailed analysis, found the date to be July 26, 3928 BCE. Assuming the event to be 2 or 3 days before the exact summer solstice day Sengupta found out another possible date as July 24, 4058 BCE when an annular eclipse took place with a magnitude of 0.79 at a place on the ◦ meridian of Kurukshetra and 33 21 N latitude (taking it to the foot of the mountains). Both these dates fall in the Rigvedic era as decided from other references.

6.4 Astronomical References in Br¯ahmanas A considerable number of references to astronomical alignments are also found in the Br¯ahmana texts. There are about a dozen Br¯ahmanas. These texts consist primarily of explanations of the vedic hymns and provide practical instructions to the priests for conducting various sacrificial rituals. Br¯ahmanas also contain a number of astronomical references which can provide guidance for dating these observations. A few examples are being presented in the section.

6.4.1 Krittik¯a Never Swerves from the East Since nakshatra ‘Krittik¯a’ was considered to have ‘Agni’ as the presiding deity, it played an important role in ancient Indian astronomical system. In Satapatha Br¯ahmana, the following verse is found (Sat.B.2.1.2):

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An english translation of the above verse is as follows: ‘Krittik¯as alone consists of many stars, other asterisms (consisting of) one, two, three or only four stars. (He who performs the agny¯adh¯ana ceremony on this nakshatra) gets plentifulness of this star; that is why ‘fire should be lit’ on Krittik¯as. These are the only stars which do not swerve from the east while all others do. He who does the ceremony on this nakshatra gets two of his ‘agnis’ i.e. fires firmly established in the east, and that is why fire should first be lit on Krittik¯as’. Satapatha Br¯ahmana also refers to other nakshatras Rohini, Mrigasir¯a, Ph¯alguni, Hasta and Chitr¯a in the verses 2.1.2.1–13. Now, the description that it (Krittik¯a) never swerves from the east implies that Krittik¯a was situated on the celestial equator. But the nakshatras are along the ecliptic. Thus, the only possible solution is that krittika was at the junction of the celestial equator and the ecliptic. Hence, it must have been at (or very near to) an equinoctial point. Again Taittiriya Br¯ahmana (1.5.2) shows that Krittik¯a was the first nakshatra and Vish¯akh¯a was the last.

The translation of the above verse is ‘Krittik¯as are the first and Vis¯akh¯a the last; these constitute devine nakshatra; Anur¯adh¯a is the first and Apabharani is the last; these constitute Yama nakshatra! The divine stars turn from south (to north) and the Yama from north to south’. Since spring used to be the start of the devine period (when the sun was in the north of the equator) for six months, the location of Krittik¯a was near the vernal equinoctial point. Taking η Tauri as the principal star of Krittik¯a nakshatra, the antiquity can be determined easily. η Tauri does not lie on the ecliptic. Thus, exact rising of the star in the east implies that its declination must have been zero at that period. Using (2.1.1) and (2.1.2), the problem can be solved, and the result comes out as 2926 BCE. Figure 6.9 shows the star alignment when Krittik¯a used to rise exactly in the east (i.e. had zero declination) and the current situation.

6.4.2 Solar Eclipse and Heliacal Rising Described in Br¯ahmanas The solar eclipse described in Rigveda has been discussed in Sect. 6.3 using the analysis provided by Sengupta. He also paid attention to the references to solar eclipses mentioned in T¯andya Br¯ahmana. The three references to this solar eclipse are given below:

6.4 Astronomical References in Br¯ahmanas

133

Fig. 6.9 Rising of Krittik¯a (η Tauri) in 2926 BCE and 2018 CE

Sengupta arrives at a date in 2451 BCE for such an eclipse visible from the Brhm¯avarata location. Again an astronomical reference in Jaiminiya Br¯ahmana has been studied according to which the winter solstice day was marked by the heliacal rising of α, β, γ , δ and ε Delphinis (Dhanisth¯a). This yields a date in 1625 BCE. S¯amkh¯ayana Br¯ahmana gives a reference to the heliacal rising of α and β Geminorum

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(Punarvasu) on the summer solstice day. This refers to an approximate date 1022 BCE. There are quite a few other references of astronomical nature.

6.5 Ved¯anga Jyotisha This ved¯anga has been preserved along with other vedic literature as a part of the whole family of vedic corpus. Ved¯anga Jyotisha is a text on pre-siddh¯antic astronomy and provides many useful information on ancient Indian astronomy. Using the descriptions contained in it, it is possible to decide its date with a reasonable degree of confidence. Ved¯anga Jyotisha11 is found in two recensions---‘Rik Jyotisha’ and ‘Yajur Jyotisha’. Rik Jyotisha contains 36 verses and Yajur Jyotisha consists of 43 verses. But out of these 43 verses, 30 are common with Rik Jyotisha. Hence, there are in total 49 verses. These verses are nothing but algorithms for astronomical computation. At the very beginning, the writer mentions a sage Lagadha to be the real author. The important astronomical references found in Ved¯anga Jyotisha are quite clear and unambiguous. Verses 6 and 7 of Yajur Jyotisha mentions that at the time of Lagadha, the winter solstice was at the beginning of nakshatra Sravisth¯a and the summer solstice was at the middle of nakshatra Aslesh¯a. These verses are given below:

The meaning of the above verses as provided in the edition published by the Academy is as follows: when the Sun and the Moon occupy the same region of the zodiac together with the asterism Sravisth¯a, at that time begins the yuga, and the (synodic) month of M¯agha, the (solar seasonal) month called Tapas, the bright fortnight (of the synodic month, here M¯agha), and their northward course (uttaram ayanam). (YJ – 6) when situated at the beginning of the Sravisth¯a segment, the Sun and the Moon begin to move north. When they reach the midpoint of the Alesh¯a segment, they begin moving south. In the case of the Sun, this happens always in the month of M¯agha and Sr¯avana, respectively.

From the known rate of precession, it can be easily shown that the above situations were possible in around 1400 BCE. It is also mentioned in the text that the duration of daylight periods in summer and winter were 18 and 12 ‘ghatis’, respectively. 11 Ved¯ anga

Delhi.

Jyotisha of Lagadha – Edited and translated; Indian National Science Academy, New

6.5 Ved¯anga Jyotisha

135

Using this relative proportion, one can determine the latitude of the location where Ved¯anga Jyotisha was composed. It comes out as 34.5°N. This is the latitude of the Sapta-Sindhu region where vedic texts were composed.

6.6 Dating Through Astrological References In the ancient times, astronomy used to be intimately mixed up with astrology. Therefore, there is an abundance of descriptions of the sky with reference to astrological significance. In some cases, these sky descriptions of astrological nature can be also used for the purpose of deciding the antiquity of such astrological references. Though alignment and conjunction of the planets used to be an important phenomena with important astrological significance, such descriptions are mostly not suitable for the dating purpose. This is primarily because the accuracy of such alignments used to be not very dependable and frequency of occurrence of such planetary alignments was not rare enough for dating purpose involving a few millennia. However, one type of astrological reference can be effectively used for the dating purpose. In Sect. 4.3, the technique of using the references to the exaltation of planets for dating purpose was explained. Amongst all, the exaltation of planet mars is most spectacular as explained in Sect. 4.3. Dating of ancient astrological reference giving the nakshatra of exalted mars has been done by Rana.12 He considered the longitude of the exaltation of mars referred to in ancient astronomical/astrological references. He noticed that the ancient astronomers of India specified the location of exaltation of mars at a longitude very near to that of the perihelion of the planets orbit. The perihelion position of mars’ orbit precesses at a rate taking about 225 years to rotate through 1°. Thus, the positions of the perihelion can be back calculated from the present position. According to the referred position (longitude) of the exalted mars, it is found to be 298°. Of course the actual reference was based upon the ancient nakshatra system (and its finer divisions). As mentioned earlier, in the Indian system, the longitude is ‘nir¯ayana’ longitude. Rana showed that the motion of the perihelion of mars in the ‘nir¯ayana’ system can be accurately expressed as follows: 312◦ 12 117.7 + 1598.0459163T − 0.623275T 2 . . . T being in centuries. Thus, the movement of the perihelion of mars’ orbit through 312° 12 can be approximately found out as follows (neglecting the higher order terms): 298◦ ≈ 312◦ 12 + 1598T or, 12 Rana

(1990).

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6 Chronology of Vedic and Ved¯anga Periods

T ≈ (298◦ − 312◦ 12/1598)centuries ≈ −32 centuries ≈ −3200 years Thus, the period of the observation mentioned is approximately 1200 BCE.

6.7 The Emerging Picture A quick glance over the general scenario of the chronology of the protohistoric period of ancient India can provide an overall picture. It has been noticed in the sections presenting the astronomical dating of Mah¯abh¯arata war, considered as the sheet anchor of India’s protohistory, and the ancient scriptures like the Vedas and Ved¯angas that very accurate results cannot be expected. One among the many reasons is, of course, the inherent inaccuracy involved in the naked-eye astronomical observations. Except in a few cases of very specific situations involving equinoctial days, solsticial days and some spectacular events like total solar eclipse, only an approximate idea can be formed through the dating procedure using ancient astronomical references. However, even getting a reasonable idea of the approximate degree of antiquity is a considerable achievement. Even the modern scientific techniques for dating like Carbon-14 dating also provide an approximate idea of the antiquity. In many cases, even this rough picture can help in understanding the history of civilization in India. Before closing the chapter, a consolidated picture of the results is presented below in Table 6.2. Table 6.2 Astronomically derived dates

Era

Astronomically derived various dates

Prevedic and early vedic

8326 BCE 4677 BCE 4539 BCE 4350 BCE 4105 BCE

Vedic

3961 BCE 3928 BCE 3541 BCE 3281 BCE 2926 BCE 2948 BCE

Mah¯abharata war

2449, 1924, 1793, 1430, 1424, 1197 BCE

Ved¯anga Jyotisha and Astrological References

1400 BCE 1200 BCE

References

137

References Keith, A. B. – “Rigveda Br¯ahmanas: The Aitareya and Kausitiki Br¯ahamanas of Rigveda”, Harvard University Press, 1920. Ludwig, A. – “On the mention of solar eclipses in the Rig-Veda”, Sïtzungberichte, Bohemian Academy of Sciences, May 1885. Rana, N. C. – “On the Chronology of Hindu Astronomy”, Bull. Astr. Soc. India (1990), 18, pp. 85-87. Translation in Sengupta, P. C. – “Ancient Indian Chronology”, Calcutta University Press, 1947. Wilson, H. H. – “Rig-Veda Samhita”, N. Triibner & Co., London, 1866.

Chapter 7

Archeaological, Geological and Genealogical Indications of Ancient Chronology

7.1 Consistency of Astronomical Dating As has been emphasized earlier, it is very important to check the approximate consistency of the astronomically derived chronology with other available information from different sources. In this respect, there are three major sources which can indicate the antiquity of the ancient chronology of protohistoric India. These are (i) geological and climatological, (ii) archaeological and (iii) genealogical evidences. Rigveda refers to a number of contemporary geological features of the Sapta-Sindhu region in the northwest part of the subcontinent. Similarly, a large amount of information has been accumulated through archaeological excavations and research; and even at present, many new findings are continuously changing the concept of protohistoric India. It has been now established that the civilization in Indian subcontinent is a continuous development from the eighth-millennium BCE till the beginning of the historical period that started with a shift of the base to the Gangetic Valley. It is not wise to delink the archaeologically established picture from that obtained from the ancient texts. The third source that can help to provide further support to the astronomically derived antiquity is the genealogical tables of Puranic kings found from various sources. As mentioned earlier, the Mah¯abh¯arata war is the sheet anchor of the protohistory of India. All the Puranic references and the genealogical lists relate to Mah¯abh¯arata; and, so, such lists can provide idea about the periods when various kings ruled relative to the war. Mah¯abh¯arata war has also connection with the historic period. Thus, an absolute dating, based on the genealogical lists, can be achieved. In last chapter of this volume, some discussions on the consistency of the astronomically derived chronology is checked with information available from other sources.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 A. Ghosh, Descriptive Archaeoastronomy and Ancient Indian Chronology, https://doi.org/10.1007/978-981-15-6903-6_7

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7.2 Lost River Sarasvati The case of the vedic river Sarasvati is unique in human history. In Rigveda, this river has been praised as the mightiest and the best among all rivers known to the Rigvedic seers. In Rigveda, there are sixty references to river Sarasvati whereas Ganges is mentioned only in three places. Rigveda describes Sarasvati as the best of mothers, best or rivers and the best of goddesses. It says

When translated it means Best among the mothers, best among the rivers, The best among the goddesses, O Sarasvati, we are living in misery, bring prosperity to us.

At the dawn of human civilization, this is how the vedic seers described river Sarasvati. The civilization of India first developed on the banks of this mighty river. But the river vedic Sarasvati also remained a great mystery to most historians and scholars as no trace is found of a mighty river carrying water from Himalaya to the sea, named Sarasvati. Rigveda mentions very clearly

There cannot be any doubt about the location of the river vedic Sarasvati since in Rigveda ‘Nadistuti’ clearly locates the river. The ‘Nadistuti’ is given below:

The above verse not only gives the names of all the major rivers of northwest and northern India but also places them in correct order, starting from the east and going towards west. When translated the ‘Nadistuti’ reads as follows1 :

1 Danino

(2010).

7.2 Lost River Sarasvati

141

O Gang¯a, Yamun¯a, Sarasvati, Shutudri (Sutlej), Parushni (Iravati), hear my praise! Hear my call, O Asikni (Chandrabhaga), Marudvridh¯a (Maruvardhan), ¯ Vitasta (Jhelum) with Arjikriy¯ a and Sushom¯a. First you flow united with Trishtam¯a, with Susartu and Ras¯a, and with Svety¯a, O Sindhu with Kubh¯a (Kabul) to Gomati (Gomal) with Mehatnu to Krumu (Kurram), with whom you proceed together.

There is hardly any scope for misunderstanding the location of river Sarasvati--it is described to be flowing between Yamuna and Shatadru. Furthermore, the above verse clearly shows the deep geographical knowledge of the Rigvedic seers! ¯ Two more rivers, Drish¯advati and Apaya, have also been described in Rigveda as tributaries to Sarasvati. Unfortunatly, no major river exists now in the region. This led to a considerable amount of controversy about the location where Rigveda was composed. Many also doubted the dependability of the Rigvedic text and all these descriptions were considered as the figment of imagination of the ancient Indian seers. Nevertheless, a few geologists continued with their investigation for discovering the channel of this river in the nineteenth century. R. D. Oldham and C. F. Oldham, two geologists of the Geological Survey of India, published the results of their research in 1886 and 1893, respectively. Both of them suspected the channel of the rivers Ghaggar (in India), Hakra and Nara (both in Pakistan) as the channel of the lost river Sarasvati. Figure 7.1 shows the map prepared by them. Soon after independence of India, the first Indian Director General of the Archaeological Survey of India, Amalananda Ghose, conducted investigation on the banks of the dried up channel of river Ghaggar in Rajasthan, and discovered a large number of Harappan settlements. Similarly, in the Pakistan part of the same river (called Nara), Mughal discovered a large number of Harappan settlements on the two banks. Figure 7.2 shows the distribution of these settlements. The total number of the settlements on the banks of the Ghaggar-Hakra rose to 2378. Looking at these large numbers of ancient settlements belonging to the Harappan civilization, the conclusion that Ghaggar-Hakra-Nara represents the ancient vedic Sarasvati became firmly authenticated. Such a large number of human settlements can flourish only when there is adequate water supply which only the river Sarasvati could supply as per the description found in Rigveda. Finally, when USA released the LANDSAT pictures in the early 1970 s’, the palaeochannels of this region were clearly visible. These are shown in Fig. 7.3. These palaeochannels not only provided the evidence for the existence of a major river in this region but also provided clues to the reasons for the disappearance of it.1 The disappearance of vedic river Sarasvati gives a considerable amount of geological and palaeoclimetological information that can be useful to the dating of Rigveda and other Puranic texts. The picture of the palaeochannels gives a clear indication that in the ancient times, river Shatadru used to be a tributary to Ghaggar-Hakra,

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7 Archeaological, Geological and Genealogical Indications …

Fig. 7.1 Course of Sarasvati as suspected by Oldham

i.e. ancient Sarasvati. That is why after Shatrana, the width of the palaeochannel increases to 8–-9 km indicating the existence of a huge river in ancient times. The description matches well with the description of Sarasvati as found in Rigveda. Most of the palaeochannels have disappeared below the sands of Thar desert and their existence get revealed through infrared images which shows the increased moisture content below the surface of the present desert like terrains. Later, it took a sharp turn at Ropar (Punjab) towards west and met the tributories of river Indus as shown in Fig. 7.4. The palaeochannels also indicate that in the ancient period, a branch of river Yamuna also used to meet river Sarasvati. Another river Drishadvati was also a tributary of Sarasvati in Rigvedic period. The shift of the river courses were primarily due to tectonic disturbances, one major cause for that is the gradual rise of the subterranean ridge of Aravalli (Fig. 7.4). The gradual shift of the course of ancient Sarasvati due to these tectonic disturbances is shown in Fig. 7.5.

7.2 Lost River Sarasvati

143

Fig. 7.2 Harappan settlements along the dry channel of river Ghaggar-Hakra

The Carbon-14 dating of the objects found in the settlements on the banks of Sarasvati yields the antiquity to go back to 7500 BCE at Bhiraana.2 This, alongwith the discovery of Mehergarh, (7000 BCE) has given evidence that civilization in the subcontinent has been the result of a continuous cultural development. These ancient settlements in a region that is also considered to be the home of vedic seers suggest a strong relationship between these settlements and Vedic civilization. This will be discussed in more details in the next section. 2 Sarkar

et al. (2016).

144

7 Archeaological, Geological and Genealogical Indications …

Fig. 7.3 Palaeochannels in the vedic area as found from LANDSAT image

Gradual drying up of Sarasvati was not only due to the shift of the courses of Shatadru and a part of Yamuna. Almost 4000 years before present, the rainfall in the region was reduced by 70%. After the end of the last glaciation period, monsoon in the region was very intense. That, in combination with larger volume of glacier melt caused the rivers in the region to have large flow of water. But the palynological studies3 by Gurdip Singh and quite a few others indicate a sharp decline in monsoon rain fall sometime during 2000 BCE. There is also mention of a long spell of draught in Mah¯abh¯arata. Even before that, Sarasvati stopped being a perennial river due to the diversion of Shatadru and Yamuna (branch) although the monsoon water was reasonably enough for the rivers to have some flow. Sarkar’s recent investigation also indicates the intensification of monsoon from 7000 BCE to 5000 BCE. But monsoon started declining monotonically after 5000 BCE and reduced drastically around 2000 BCE. Around this time, Sarasvati vanished in the desert at a place called Vin¯asan¯a. This is described in details in Mah¯abh¯arata where the pilgrimage of Balar¯ama along the river Sarasvati is described. The periods match quite well. The decline of the Harappan civilization is nowadays attributed to this setting of aridity instead of any invasion by outside Aryans. This drying up of Sarasvati caused the migration of the whole civilization towards the Gangetic Valley. 3 Palynology

conditions.

is the science of studying pollen (fossilized pollen) for investigating ancient climate

7.2 Lost River Sarasvati

145

Fig. 7.4 The river system in northwest India and the subterranean ridge of Aravalli

Not depending only on the LANDSAT images, a considerable research and investigation are being conducted on the water in the subterranean palaeochannels of Sarasvati. A lot of research is also being done on the ancient clay and sand found in the channels. One type of investigation studies the Tritium (3H) content of the water found below the ground along the palaeochannel of Sarasvati in the present desert. Along the dried up Sarasvati, a considerable amount of water is found to exist 40-–100 m below the surface. The age of this water, established by the study of the radioactive Tritium in rain water, is found to be between 5000 and 9000 years before present! Apart from being very old, the supply of this water is also abundant and this subterranean body of ancient water is not still, but is moving from the north-east direction to the south-west at a speed of about 5 m per year! It has been unambiguously established that there has been no recharging of the subterranean palaeochannel of Sarasvati after 3000 BCE.

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7 Archeaological, Geological and Genealogical Indications …

Fig. 7.5 Gradual shift of the course of ancient Sarasvati

The study of the sedimentation and the sand in Sarasvati’s palaeochannel also indicates the antiquity. As one goes down, the age is found to increase as shown below: Depth of the layer (m)

Approximate age (years)

0.8

2900 ± 200

1.3

3400 ± 200

1.6

3000 ± 200

3.6

5600 ± 200

4.7

5900 ± 200

7.2 Lost River Sarasvati

147

Time (BCE)

9000 – 5000

5000 – 3000

3000 – 2000

2000 –

Climate

Post glacial

Gradual

Gradual setting

Dry spell start

very heavy

decrease in

in of aridity

monsoon

monsoon intensity

Geological

Shatadru,

Drishadvati,

Shatadru shifts

Sand dunes

condition

Drishadvati &

Yamuna stops

westward

advance

a branch of

flowing water to

Yamuna were

Sarasvati

Still a mighty

A monsoon

River slowly

river

water fed river

vanished

Rig Vedic

Later Vedic

Puranic &

tributaries Sarasvati

Era

Mighty river

Pre Vedic

Vedānga

Fig. 7.6 Life cycle of Sarasvati

This data makes it clear that the river stopped being active after 1500 BCE as evidenced in various Puranic texts. The time line for the river vedic Sarasvati is graphically represented in Fig. 7.6.

7.3 Changing Sea Level It has been now scientifically established that the mean sea level is not constant and undergoes substantial amount of variation due to various reasons. Figure 7.7 shows how the sea level changed during the Holocene period. During the last Ice age, the mean sea level was about 130 m below the present level. Such low sea level causes the connectivity among various land masses to be far more extensive than what is found at present. This helped the migration of modern man to spread along all the continents including Australia. The results of the changing sea level have left indelible signatures in the history of ancient India. This information can be suitably used in forming some approximate idea about the antiquity of some past records in the ancient texts. Of course any accurate dating is not possible and some

148

7 Archeaological, Geological and Genealogical Indications …

Fig. 7.7 Sea-level variation during the last 7000 years

discussion is being presented primarily to check the consistency of the chronology determined from astronomical references. As shown in Figs. 5.8 and 7.7, the sea level rose steadily after the last glaciation period and reached near the present level around 7300 years ago. After 5300 BCE, there was major flooding and the level rose to near the present level. This high sea level continued till 3800 BCE. During the next few centuries, the level was lower than the current level by about 2–-3 m. Again during 3400-–2000 BCE, the sea level suffered temporary increase as shown. The figure indicates two relatively stable periods. During the period 10,500-–7300 BCE, the sea level remained steady at a level 80 m below the current level. After that, there was a very fast rise in sea level to reach 30 m below the present level and remained some what stable for almost 1000 years. After this, the level again rose steadily to reach near the current level around 5300 BCE. This variation is validated by the discovery of 7500 old Neolithic settlements in the Gulf of Khambat 30-–40 m below the current sea level. The somewhat stable sea level for almost 1000 years gave adequate time for this civilization to flourish before it was engulfed by the sea again. The reputed marine archaeologist S.R. Rao discovered the Harappan port town of Lothal which had a dockyard. Now, it is land locked. But during the period 5300– -3800 BCE, the sea level was high and, so Lothal could function as a sea port town which is now land locked. This shows that Lothal stopped functioning as a port town after 2500 BCE. An interesting reference in Mah¯abh¯arata exists that mentions about Krishna reclaiming land from the sea to build the city of Dwarka. This kind of reclamation is possible when the sea water recedes. From the sea-level curve, it appears that such a process could be done when the sea level started falling after 2000 BCE. Later, when the sea level started rising again, the city of Dwarka got submerged again around 1500 BCE. The sea-level-change record matches well with this epic reference, and it commemorates the tentative date of Mah¯abh¯arata around 1500 BCE.

7.3 Changing Sea Level

149

Fig. 7.8 Satellite picture of R¯am Setu (or, Adam’s bridge)

Another major controversy is raging in India for many decades that can have implications related to the sea-level change. R¯am¯ayana describes the building of a bridge connecting India and Sri Lanka. The satellite picture of this bridge is shown in Fig. 7.8. The very narrow bridge like connection between India and Sri Lanka is very intriguing. Since it looks like an artificial structure, there has been a claim that this is the ancient bridge referred to in R¯am¯ayana as ‘Setu bandhan’. However, the claim is disputed and scientific studies are still going on as no clear cut evidence of the structure being natural has been found. On the contrary, the geological structure revels certain features that point to its artificial (man made) character. The study by a senior scientist from the Geological Survey of India revealed a very strange feature. This bridge is about 35 km long and quite narrow. Till a couple of centuries before the ‘bridge’ was above sea level and till 1480 CE, it was possible to reach Sri Lanka by walk from India. This is mentioned in a book by Alexander Hamilton.4 Since the ‘bridge’ is only a few metre below the sea level, a lower sea level could have made it possible to walk over the structure. The study by the Geological Survey of India team led by Dr. Badrinarayan5 has revealed that the sand of the lower layers in the structure is younger in age than the stone and coral boulders in the upper layer. This indicates the possibility that the upper layer material was placed artificially by human hand. At present the bridge’s upper surface is about 3–3.5 m below the sea level and when the sea level is lower the bridge 4 Hamilton

(1744). R. – “http://specials.rediff.com/news/207.

5 Badrinarayan,

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7 Archeaological, Geological and Genealogical Indications …

comes above the sea level. Figure 7.7 shows that around 3500 BCE the sea level was about 3.5 m lower than the present level and the bridge was quite usable. Perhaps during this period the upper layers were placed for gaining access to Sri Lanka by walk. This matches with the description in R¯am¯ayana. This geological study also indicates the antiquity of the R¯am¯ayana period to be about 3000 BCE. Astronomical dating of R¯am¯ayana period has been attempted by quite a few scholars.6 However, the astronomical references found in this epic are predominantly based upon planetary alignment and not related to the precession of the equinox. There is a strong possibility that many of these references are of astrological nature and are later projections. It is quite possible that in the third-millennium BCE only jupiter, venus and probably mars were known to the naked-eye astronomers. Furthermore, planetary alignments based upon naked-eye astronomy cannot be accurate. But the geological evidence from the Adam’s bridge (also called Setubandha in ancient Indian texts) can yield some idea about the R¯am¯ayana era.

7.4 Genealogical Sources for Investigating Ancient Indian Chronology Apart from astronomical and geological studies, hints to the chronology of the protohistoric India can be found in the genealogical lists found in various pur¯anas and other ancient texts. It has already been mentioned in the earlier sections of this book that Megasthenes recorded in his travelogue to India in the third-century BCE that he was shown by the contemporary scholars a list of 154 kings who reigned over 6451 years and 3 months.7 Arrian8 recorded that ‘From the time of Dionysos to Sandrakottos the Indians counted 153 kings and a period of 6042 years (but among these a republic was thrice established) … and another to 300 years and another 120 years’. These descriptions show that India’s political history was extended up to more that six thousand years before the third century BCE! Count Bjornstjerna9 in his ‘Thogny of the Hindu’ states ‘Megasthenes, the envoy of Alexander to Kandragupso (Chandragupta), king of the Gangarides, discovered chronological tables at Polybhotra, the residence of this king, which contain a series of no less than 153 kings, with all their names from Dionysos to Kandrogupso and specifying the duration of every one of these kings, together amounting to 6451 years which would place the reign of Dionysos nearly to 7000 years BCE and consequently 1000 years before the old king found in the Egyptian tables of Menetho (viz. the head of the Tinite Thabanie dynasty) who reigned at 5867 years BCE and 2000 years before Saufi, the founder 6 Bhatnagar 7 McCrindle

(2011). (2008)

8 Ibid. 9 Bjomstjerna

(1844).

7.4 Genealogical Sources for Investigating Ancient Indian Chronology

151

of the Gizeh pyramid’. Though, such detailed lists were found in the third-century BCE, India currently such lists have to be created only using various Pur¯anas. The first attempt in this direction was made by Pargiter10 by extensively analysing the different Pur¯anas and other ancient texts. Subsequently, other modern researchers have made significant contribution in this direction, one of the most notable researchers being Chandra11 in the 1970s. These genealogical trees can yield useful information on the chronology of the protohistoric period of India. But that needs some idea about the average period of each king. It has been found that there are some gaps in these lists and only those kings, whose periods were not very short, found mention in the references. Thus, the chronology will not be very accurate but a reasonable idea about the antiquity can be gained. The detailed compiled lists can be found in the work of Chandra and some of these are given in Appendix C for ready reference. However, for the purpose of discussion and quick reference, an abridged genealogical tree is shown in Fig. 7.9. The whole protohistoric period is divided into four sections as mentioned below:

(i)

Pre deluvial

(ii)

Post deluvial and pre Bhārata war

(iii)

Post Bhārata war

(iv)

Historical period

Proto historic period Historic period

Geneaological trees can be used to decide on the chronology approximately. But to do that one needs to have some idea about the average period for each king in the absence of any information about the duration directly from the sources. In this respect, there is substantial difference of opinion among various scholars. One direct method some have followed is to divide the period 6451 years by the number of listed kings 154. This yields the average period for each king as 41.9 years. As shown by Chandra that it is not totally improbable by considering the matter in case of the known kings during the historical period. In case of France, there were seven kings from 987 to 1223 CE yielding the average period as 34 years. In England, eight kings ruled from Henry II to Richard II covering a period from 1154 to 1399 CE resulting in an average period of about 30 years. In more recent times, in England, five kings (queen) ruled for 188 years starting from George I to Queen Victoria. This yields the average period as 37 and 1/2 years. Similarly, the history of Kashmir states that 21 kings ruled from Gonarda III to Yudhistira covering a period spanning over 987 years and 8 months and 29 days. This provides a value of about 49 and ½ years for each king. So Chandra has used the average duration of each king as 40 years approximatley. However, in some cases, the total duration has been specified directly. Estimating the average period of the kings may not be very accurate as there are a number of gaps in the lists. So, some reference to the absolute length of a 10 Pargiter

(1922). (1980).

11 Chandra

152

7 Archeaological, Geological and Genealogical Indications …

Fig. 7.9 Composite genealogical diagram for ancient India

period mentioned can be helpful. For example, the period between Parikshit and Chandragupta is given directly as about 1600 years by the detailed account. At the same time, according Vishnu Pur¯ana, the period between Parikshit and Mah¯apadma Nanda is 1050 years. Then, the Nandas ruled for 100 years till Chandragupta ascended the throne of Magadha. Pargiter considered the average duration of kings as 18 years, but scholars like Benedetti12 thinks that it can be raised to 19 years to match with the data available from archaeological excavations. The value being almost half of the value taken by Indian scholars, this lowers down the antiquity subsequently. Unless 12 Benedetti,

G. – ‘The chronology of puranic kings and Rigvedic rishi; In comparison with the phases of the Sindhu-Sarasvati civilization’.

7.4 Genealogical Sources for Investigating Ancient Indian Chronology

153

further studies provide a more dependable value any definite answer to the antiquity may not be possible that will be acceptable to the western scholars. In a sense, the situation is somewhat similar to Max Muller’s arbitrary fixing of 200 years for each stage of the vedic corpus. In this section, some corroboration with the astronomical and geological data will be attempted. As suggested by Daftari, some idea can be had about the period of composition of the vedas by studying the latest king (and rishi) mentioned in the texts. Rigveda’s last referred person is Dev¯api, a rishi very close to Santanu. Santanu was three generations before Arjuna. Hence, it can be assumed that composition of hymns in the vedas stopped around this time. This is also close to the period of Veda Vyas who organized the whole vedic corpus and classified the vedas into four parts. So the vedas can be dated prior to (1921 + 2 × 40 =) 2001 BCE or, by other reckoning prior to (1471 + 2 × 40 =) 1551 BCE. But the beginning of the vedic period goes far back in time as can be seen in the genealogical list and also from the characteristics of river Sarasvati as discussed earlier. The dates estimated by using the genealogical lists are reasonably close to the dates arrived at by the descriptive archaeoastronomical techniques as presented in Table 6.2. Of course such agreement has to be very approximate for obvious reasons. The dates also match the indications from the geological history. For example, the period of R¯ama derived from the genealogical tree is around 3200 BCE and it is close to the date indicated by the sea-level record. The antiquity of the deluge (that covered a major part of the land by water as mentioned in the ancient texts) is found to be established from the genealogical tree. It occured around 7579 BCE and lasted for more than eight centuries. The earliest date found from the start of the genealogical tree is found as 8939 BCE that is very close to the end of the last ice age. This marks as the onset of the civilization in the Indian subcontinent.

7.5 Archaeological Discoveries and Ancient Indian Chronology Till the beginning of the third decade of the twentieth century, no trace of any ancient civilization was found in Indian subcontinent, and, this was one of the major factors that led to the proposal of Aryan Invasion. However, there were enough early indications; but these were not recognized properly. In 1826, Charls Masson saw at Harappa, the ruin of the brick castle. Similarly, James Tod described the ancient site Kalibangan while writing on the antiquity of Bikaner. In a later period, Alexander Burnes noticed the ruined brick castle at Harappa on the river bank. Subsequently, in the archaeological survey of Harappa by Alexander Cunnigham, the first Director General of Archaeological Survey of India, in 1853 reported the extensive mounds along the banks of river Ravi. But its real significance remained unrevealed to all of them. Till that time, the majority of the scholars were of the opinion that the civilization of India is a foreign export. The Aryan Invasion Theory (AIT), proposed

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7 Archeaological, Geological and Genealogical Indications …

by the eminent Indologist, Prof. Max Mueller, became very popular and explained quite a few features beside the linguistic similarity among, Sanskrit and the European languages. Since then AIT has remained as an integral part of ancient Indian history though the theory has no support from all the traditional knowledge corpus of ancient India. The accepted fact was that a race called ‘Aryan’ invaded India crossing the mountains of the northwest India and composed the vedic literature and founded the Indian civilization. Two brothers John and William Brunton got the contract for laying the rail track from Lahore to Karachi (as a part of the East Indian Railway network) in the year 1856. The elder brother John wrote a memoir after his retirement and described the way he collected the bricks from an ancient ruin at Br¯ahminabad for the required ballast. They never realized that the bricks they were using for ballast were several thousand years old! Only in the year 1921, systematic excavation of Harappa was taken up by Daya Ram Sahni. Excavation of Mohenjodaro was taken up by Rakhal Das Banerjee in 1922. Fortunately, Mohenjodaro was less damaged compared to that in the case of Harappa. The contemporary Director General of Archaeological Survey of India was Sir John Marshall. In one push, the antiquity of ancient India’s civilization was pushed back by more than two millennia. But AIT had to be saved, and, it was immediately concluded that the invading nomadic Aryans destroyed these cities and set up their own vedic culture. By carbon dating method it was found that the Harappan cities were more than 4500 years old. Subsequent studies led the scholars to announce that the Harappan civilization existed from 2600 to 1500 BCE. This also matched very well with Mueller’s suggested date of Aryan Invasion of 1500 BCE. Thus, the matter was nicely settled. Or was it! After a few decades the picture started changing and the understanding of protohistoric India became very different from that proposed by the majority of the Eurocentric scholars. It was found that the Indus civilization’s extent (both spatial and temporal) was really extensive. A very large majority of the settlements belonging to Indus civilization, as it was termed, were in the deseart areas along the banks of the palaeochannels of Sarasvati and Drisadvati (current name Chautang). Figure 7.10 shows the Indus civilization’s extent in Indian subcontinent and Afghanistan. The total number of settlements discovered so far is around 3781 as indicated in Table 7.1. It is seen very clearly that a majority of these settlements belong to the valley of now vanished river Sarasvati. Because of this, many scholars prefer to rename the civilization as Indus--Sarasvati civilization. The subject is huge and beyond the scope and objective of this volume. Instead, a brief discussion on the chronology of the evolution of civilization in northwest India will be presented. Attempt will be also made to investigate the relationship between the evolutions of the vedic society. Till 1970s, the period of Indus civilization was considered to be confined to 2600 BCE and 1500 BCE determined by the Carbon-14 dating method applied to the objects found in Harappa and Mahenjodaro. Later, further investigations led to the classification of Indus (Harappan) civilization into three phases as shown below

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Fig. 7.10 Area covered by the settlements belonging to Indus civilization

Table 7.1 Distribution of Harappan settlements discovered sofar Region

Number of Harappan sites discovered

Total number

Early stage

Mature stage

Late stage

Sarasvati Valley

640

360

1378

2378

Uttar Pradesh

2

32

10

44

Himachal, Jammu, Delhi

1

–

4

5

Gujrat

11

310

198

519

Indus valley and Western Pakistan

385

438

12

835

Total

1039

1140

1602

3781

Early Harappan Phase

2600-–2450 BCE

Mature Harappan Phase

2450-–2000 BCE

Late Harappan Phase

2000-–1500 BCE

Since the vedic age was traditionally supposed to have started after 1500 BCE, the Harappan and vedic societies were considered to be totally delinked. Since the Harappan society was a highly developed urban society, it was very perplexing and the origin of this civilization was covered in mistery. This is so as evolution of a civilization to such advanced level of urbanization takes not centuries but millennia.

156

7 Archeaological, Geological and Genealogical Indications …

Fig. 7.11 Conventional and revised chronology of Harappan civilization based upon Bhirrana excavations

Most scholars thought that this civilization had its origin in Mesopotemia. This suspision became stronger when in 1970s Mehergarh was discovered in Baluchistan and it was dated 6500 BCE. Thus, the concept and theory of eastward migration of civilization became very popular. Since the antiquity of the Indus civilization was pushed back by almost four thousand years before the Harappan civilization a further revised chronology for the civilization was proposed that is presented below.13 Mesolithic and Neolithic

Early Food Production Era (Mehergarh Phase)

7000-–5500 BCE

Early Harappan Phase 5500–-2600 BCE (Hakra, Ravi, Sherikhan Tarekai, Balakot, Amri, Kot Daji, Nal, Sothi, Tochi—Gomal) Chalcolithic

Harappan Phase

Chalcolithic and Iron Age Later Harappan Phase

2600–-1900 BCE 1900-–1300 BCE

The gradual shift of the settlements towards the east has been now conclusively proven to be due to climate change, disapperance of Sarasvati and onset of aridity, not a part of migration from Mesopotemia. Subsequently, further excavations and research14 have revealed the indigenous nature of the civilization from 7000 BCE. Excavations were carried out at Bhirrana, Haryana, India. It was a part of the intensive Harappan settlements along the river Sarasvati. The excavations revealed many layers of continuous development of civilization as was earlier suggested by Possehl.15 Figure 7.11 shows the cultural levels alongwith the depth of the layers and approximate age alongwith general climatic condition. Since Bhirrana is located in the region between ancient Sarasvati and Drisadvati, it shows the indigenous nature of the civilization in the northwest and north India that has an antiquity going back to 9000 years before present. This also conclusively proves that the Indus civilization does not have a foreign origin. 13 Kenoyer

(2011). et al. (2016). 15 Possehl (2002). 14 Sarkar

7.5 Archaeological Discoveries and Ancient Indian Chronology

157

Benedetti has attempted to detect archaeological corroboration of Mah¯abh¯arata war and other very major events described in the ancient literature. Of course the task is not easy and may not be completely unambiguous. But the suggestions of the possible links are quite strong. A few of these are quoted from Benedetti’s work. Potteries related to Indus civilization viz Painted Gray Ware (PGW) and Ochre Coloured Pottery (OCP) are found in the places mentioned in Mah¯abh¯arata. In case of Hastin¯apur and Kaus¯ambi, major settlements in Kuru and Panch¯al also show this trend. There is a statement in ancient texts that the fifth successor of Parikhit, Nicasku had to abandon his first city at Hastinapur as it was carried away by a major flood in the Ganges. Traces of this flood are found from archaeological excavations at Kaus¯ambi and Hastin¯apur. Archaeological excavations suggest from the potteries at Kh¯andavprastha (which later became Indraprastha of the Pandavas) to belong to around 1500 BCE, i.e. a little before Mah¯abh¯arata war (according to the astronomical dating by many scholars). Thus, the area was covered by the Late Harappan civilization. Again investigation by archaeologist S.R. Rao has discovered an undersea city’s remains at Dwarak¯a. This has been identified with the city that got inundated as the sea level rose as described in Mah¯abh¯arata. This also happened towards the end of Late Harappan period around 1400 BCE. This submergence forced Lord Krishna to call Arjuna to take the surviving Y¯adavas for resettlement at different places. It is mentioned that Arjuna settled them at a few places and the majority was brought to Indraprastha and Arjuna crowned Vajra, the last of the Vrisna Prince as the king. Thus, according to Benedetti ‘Archaeologically the beginning of Kali Yuga (with the death of Lord Krishna) seems to be connected with the end of Sindhu-Sarasvati civilization with the arising of the new Gangetic civilization’. Mah¯abh¯arata16 also refers to ancient destructive events by the Haihaya king Arjuna K¯arttavirya. The Haihayas were supposed to start from their original city M¯ahismati on the river Narmada. Their conquest proceeded towards the north and the northeastern direction reaching up to the Doab region of Punjab, Ayodhy¯a and Varanasi. Therefore, the Haihaya king Arjuna K¯arttavirya was described as samr¯aj and chakravartin.17 He was described to have burnt the world’s seven continents alongwith the cities. The happening continued in the memory of the people and even long after the event; in Mah¯abh¯arata, it is described as the burning of villages, towns, cities and camps of the herdsmen through Arjuna’s arrows. The carnage stopped ¯ at the hermitage of Risi Apava Vasistha near the Himalayas. The archaeological investigation reveals burnt layers in some early Harappan sites before the arrival of mature Harappan culture. Quoting the excavator F. A. Khan of Kot Daji ‘A thick deposit of burned and charred material on top of layer, spreading over the entire site, completely sealed the lower levels (Kot Daji) from the upper ones (Mature Harappan). This strongly suggests that the last occupation level of the early settlers (that is Kot 16 Mah¯ abh¯arata 17 Mah¯ abh¯arata

12.49.33 12.49.30-31

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7 Archeaological, Geological and Genealogical Indications …

Daji) was violently disturbed, and, probably totally burnt and destroyed’.18 Apart from this, the early Harappan sites at places like Amri, Nausharo, Gumla, etc., show burnt stratums containing ash, debris, charcoal and broken bricks. Possehl observes Several points seem to be evident: the fires at these sites were large; this large scale burning is associated with the Early Harappan – Mature Harappan junction; there is little, if any, evidence for such conflagrations at these or other sites in the region prior to or after the Early Harappan – Mature Harappan junction. These observations point to a pattern in the canflagrations, and, while it is true that fires begin for many reasons, a pattern like this might be telling us that they have a common cause.

Therefore, there is archaeological evidence for extensive burning of cities that was remembered in the tradition as the work of Arjuna K¯arttavirya who was about 70 generations before Mah¯abh¯arata. This puts the beginning of Mature Harappan phase about 70 generations before Mah¯abh¯arata. More extensive study indicates quite a few other corroborations, of course, of a more subtle nature, of the archaeological findings with the puranic texts. This provides a reasonable degree of credibility to the ancient chronology arrived at by the astronomical methods. Beside the region of Sindhu--Sarasvati civilization, the Gangetic Valley has also been found to have flourished since a long time. Even king Suhotra, a descendent of king Bh¯arata, who was remembered as a great conqueror belonging to an era about 50 generations before the Mah¯abh¯arata war, married an Aiksh¯aku princess to establish contact with the eastern region. At Lahurdeva, near Gorakhpur, traces of civilization belonging to the fourth- and fifth-millennium BCE have been discovered. Similarly the onset of agriculture in the third- and fourth-millennium BCE has been established in the Pratapgarh district. So, the rule of the Solar dynasty in Ayodhya gets some archaeological corroboration and this civilization being as old as the Sindhu-Sarasvati civilization refutes the suggestion that the Sindhu--Sarasvati civilization was a transport from West Asia. Rakhigarhi19 is another major site in Haryana which also represents a large Harappan settlement of urban character. A large part of the area is already occupied and cannot be excavated. The study of the various layers of the excavated areas shows the earlier levels to be of early Harappan era and dates back to the fourth- and fifth-millennium BCE. The layers belonging to the mature phase show very wellplanned township with all amenities as found in Mohenjodaro. These layers date back to the third-millennium BCE. The name of the state, where it is located, ‘Haryana’ finds mention even in Rigveda (8.25.22). The name used is ‘Harayane’. Various later Puranas also refer to the region as ‘Harayane’, ‘Hareyanaka’ etc. Similarly, the connection of Rigveda with Harappa is also found in the text. Rigveda states that the kings of Aja, Sighru and Oksu presented Indra with a horse’s head. Further, the Rusams gave Indra 4000 cows, coveted as a major wealth. It further states that Indra killed the descendents of Vrich¯avane, son of Varsikha in the eastern part of Hariupi¯a. It is quite suggestive. Oksu is river Oxus (Amu Daria), Rusams could be Russia and 18 Cited 19 Nath

in Possehl (2002). (2014).

7.5 Archaeological Discoveries and Ancient Indian Chronology

159

Hariupi¯a is nothing but Harappa. The study of the burials shows the burial system to be according to the vedic descriptions. The well-structured town shows citadels, living houses, planned streets and drainage systems, dug wells and also fire alters as per the descriptions given in Rigveda. There are enough indications that the residents were fire worshippers. According to the traditional wisdom, this region was under the King Arjuna K¯arttavirya who killed the sage J¯amdagni, father of Parashur¯am. Later, Parashur¯am killed Arjuna in revenge. Thus, the brief discussion in the previous paragraphs indicates a strong relationship of the pre-Harappan and Harappan civilization with the vedic society. There are enough indirect archaeological evidences supporting some major events described in the vedic and Puranic texts. The chronology also is in reasonable agreement with the scientifically derived dates of the archaeological findings. All these point towards the continuous development of civilization in South Asia from a period soon after the last glaciation dating back to almost tenth millennium before the Common Era. It also becomes evident that many of the Puranic literature are based on real happenings in the ancient past.

References Bhatnagar, P. – “Dating the Era of Lord Ram”, Rupa Publications India Pvt. Ltd., 2011. Bjomstjerna, Count M. – “The Theogony of the Hindoos: with their systems of philosophy and cosmogony”, J. Murray, London, 1844. Chandra, A. N. – “The Rig Vedic Culture and the Indus Civilization”, Ratna Prakashna, Kolkata, 1980. Danino, Michel – “The Lost River: On the Trail of the Sarasvati”, Penguin Books, 2010. Hamilton, Alexander – “A New Account of the East Indies”, 1744. Kenoyer, J. M. – “Changing Perspectives of the Indus Civilization: New Discoveries and Challenges”, Presidential address of the Indian Archaeological Society, New Delhi, Puratattva, no.41, 2011. McCrindle, J. W. – “Ancient India as described by Megasthenes and Arrian”, Munshiram Manoharlal Publishers, New Delhi, 2008. Nath, Amarendra – “Excavations at Rakhigarhi”, Archaeological Survey of India, 2014. Pargiter, F. E. – “Ancient Indian Historical Tradition”, Oxford University Press, London, 1922. Possehl, G. L. – “The Indus Civilization: A Contemporary Perspective”, Altamira Press, Lanham, 2002. Sarkar, A. et. al. – “Oxygen isotope in archaeological bioapetites from India: Implications to climate change and decline of Bronze Age Harappan Civilization”, Nature Scientific Reports (6.26555), 10.1038/srep.2655 (2016).

Concluding Remarks

Archaeoastronomy is a highly interdisciplinary subject and has been applied to many prehistoric structures like Stonehenge. In all such cases, the primary objective has been to note the awareness among the prehistoric people of the solistial and equinoctial days in a solar year. Since these directions are not dependent on the precession of the equinox, any kind of dating is not possible. The primary aim of these studies is to understand the cultural aspects related to astronomy in these ancient societies. Because of this, one scholar has defined archaeoastronomy as a horizon-based science. However, the unique situation in the case of India is the availability of a large volume of ancient literature rich in astronomical references. Thus, descriptions of the ancient sky can be used for establishing chronology. The main exception is the pyramids of Egypt whose alignments can be analyzed for dating purpose. The astronomically derived chronology matches reasonably well with the genealogical tradition. There are enough supports to the archaeoastronomical dating by the results of the palaeoclimatological and geological investigations. Finally, the recent archaeological excavations and studies indicate a continuous evolution of civilization leading to the highly developed urban society of the Sindhu–Sarasvati region. In quite a few cases, the archaeological evidence of some major events described in the Puranic literature provides a strong support in favour of the reality of such descriptions. Thus, many parts of the ancient texts refer to the real historical facts and are not just figments of imagination of ancient poets and sages as has been always suggested by a large section of the scholars engaged in Indological research. The subject is still in its nascent state, and descriptive archaeoastronomy is relevant only in the case of ancient India. This is so as in no other civilization of the world such a huge volume of ancient literature exists. Thus, the responsibility of developing the subject ‘Descriptive Archaeoastronomy’ lies on the scholars working on the history and chronology of ancient India. It has been found that an attempt to derive the antiquity of an event with the help of only one astronomical reference is less reliable. Thus, a technique should be developed that can fix the era of a particular major event through a number of astronomical and other references. This can be made possible by

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 A. Ghosh, Descriptive Archaeoastronomy and Ancient Indian Chronology, https://doi.org/10.1007/978-981-15-6903-6

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Concluding Remarks

creating extensive data base that will include astronomical, climatological, geological and genealogical information, and a suitable computer software can be developed that can correlate various sources while estimating the antiquity. This book has been aimed at general readers primarily to make them curious and interested in the subject. The trends in recent archaeological discoveries unambiguously establish that what has been discovered is the tip of an iceberg only. Many more remarkable discoveries will surely be made, and the future generations of scholars interested in the history of ancient India will unreavel the biggest mystery of human civilization—the story of ancient India.

Appendix A

Spherical Trigonometry and Astronomy

A.1 Celestial Sphere and Spherical Trigonometry As mentioned earlier, the sky, along with all the heavenly objects, appears as a celestial dome. Thus, the relative alignments and positions are described on this imaginary sphere called the celestial sphere. On a plane surface, coordinate systems are developed using straight lines. So, it is necessary to define an equivalent of straight lines for prescribing positions on a sphere. It should be also remembered that what is possible in positional astronomy observation is only the direction in which an object is seen. Thus, the distance or separation between two objects in the sky is the angle between the two viewing lines. As discussed is Sect. 2.1.2, the equivalent to straight lines on plane surfaces is great circles on spherical surfaces. Great circles are the lines of intersection of a spherical surface with a plane passing through the sphere’s centre as

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 A. Ghosh, Descriptive Archaeoastronomy and Ancient Indian Chronology, https://doi.org/10.1007/978-981-15-6903-6

163

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Appendix A: Spherical Trigonometry and Astronomy

Fig. A.1 Basic definitions in spherical trigonometry

shown in Fig. 2.11. Let two great circles 1 and 2 intersect at a point P as shown in Fig. A.1. The angle between the two great circles at the point of intersection is defined by the angle between the two tangents to the great circles at the point of intersection. Thus, in the case shown in Fig. A.1, the spherical angle is ψ. Since the celestial sphere is unique, its radius may be treated as unity. The length of a segment of a great circle is defined by the angle subtended by the segmental arc at the centre. So, the length AB is defined by ∠AO B as shown in Fig. A.1. When three great circles intersect, a spherical triangle is formed as shown in Fig. A.2. The segments AB, BC and CA form a spherical triangle with sides a, b and c all defined by the corresponding subtended angles at the sphere centre O as mentioned above. The opposite angles are spherical angles A, B and C, each opposite to the corresponding sides with lengths (as subtended angles, of course) a, b and c as shown in the figure. The line OD intersects the sphere at B, the line OE intersects the sphere at C, and the line OA’s intersection point is A. According to the definition, a = ∠BOC, b = ∠AOC and c = ∠BOA. The plane defined by the plane triangle ADE touches the sphere at point A. So, according to the definition of spherical angle, A is given by ∠DAE as line AD is tangent to the segment AB and the line AE is tangent to the segment AC at A. It is also obvious that in the OAD, ∠OAD = 90° and ∠AOD = c (≡ ∠AOB). Therefore AD = O A tan c and O D = O A sec c

(A.1)

Appendix A: Spherical Trigonometry and Astronomy

165

Fig. A.2 Deriving basic relations of a spherical triangles

Similarly AE = O A tan b and O E = O A sec b

(A.2)

Now, considering the plane triangle DAE, the following relation is obtained: D E 2 = AD 2 + AE 2 − 2 · AD · AE cos ∠D AE = O A2 tan2 c + O A2 tan2 b − 2 · O A2 · tan c tan b cos ∠D O E Again as the plane angle ∠AOE (≡ ∠BOC) is equal to a as per definition D E 2 = O D 2 + O E 2 − 2 · O D · O E cos a = O A2 sec2 c + O A2 sec2 b − 2 · O A2 · sec c sec b cos a

166

Appendix A: Spherical Trigonometry and Astronomy

Combining the R.H.S of the above two expressions for DE 2 , one obtains the following relation: tan2 c + tan2 b − 2 tan c · tan b · cos A = sec2 c + sec2 b − 2 sec c · sec b · cos a since ∠DOE = A (as per the definition of spherical angle). The above equation can be rearranged to yield the fundamental formula of spherical trigonometry given below: cos a = cos b cos c + sin b sin c cos A

(A.3a)

The two other similar formulae are cos b = cos c cos a + sin c sin a cos B

(A.3b)

cos c = cos a cos b + sin a sin b cos C

(A.3c)

All other important relations can be derived from the above laws. A sine-formula is sometimes very useful and is given below: sin B sin C sin A = = sin a sin b sin c

(A.4)

Relations involving all three sides and the angles can be expressed as given below: sin a cos B = cos b sin c − sin b cos c cos A

(A.5a)

sin a cos C = cos c sin b − sin c cos b cos A

(A.5b)

and,

A.2 Transformation of Coordinates Quite often it becomes necessary to transform the position coordinates from one system to another. For example, one observer may take the positional data in the horizontal system but may require to define the same positional data in another system viz. equatorial system. It has already been mentioned earlier that the horizontal system is convenient in many situations, but it is a position dependent system; however, the equatorial system is position independent.

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167

Figure A.3a shows the horizontal system in which Z represents the zenith point, vertically above the observer O. N W S great circle represents the horizon, and P is the north celestial pole. The great circle passing through Z and P intersects the horizon circle at point N that is called the ‘north point’. Accordingly S and W are the south and west points on the horizon, respectively. If X be the position of the object whose coordinates are to be specified, a great circle is drawn passing through Z and X, and it intersects the horizon circle at B. The angle ∠B O X is called the altitude a. When the object is in the western half of the celestial sphere (as in the case shown in Fig. A.3a), the angle ∠N O B is called the azimuth, A. On the other hand, if the object is in the eastern part of the celestial dome as shown in Fig. A.3b, the azimuth is given by ∠N O B  . The angle ∠P O Z is the latitude of the observer γ = 90◦ − φ, when the latitude of the observer’s position is φ. Now, two common problems associated with the spherical triangle PZX can be taken up for analysis and solution. The first problem is, given the observer’s latitude φ, the hour angle (H) and the declination (δ) of an object as shown in Fig. A.4, to determine the azimuth (A) and altitude (a). The hour angle is the angular distance of the object’s meridian from the prime meridian, that is the meridian passing through the pole P and the zenith Z. Thus, according to Fig. A.4, the hour angle is the spherical angle ∠Z P X or ∠D OC. Using Eq. (A.3a) and considering the three sides of the spherical triangle PZX, PZ, ZX and XP (and also remembering that the sides of a spherical triangle are also angles subtended at the sphere’s centre) cos Z X = cos P Z cos P X + sin P Z sin P X cos ∠Z P X or, sin a = sin ϕ sin δ + cos ϕ cos δ cos H

(A.6)

Fig. A.3 a Horizontal system of position coordinates when the object is in the western half of the celestial dome and b horizontal system when the object is in the eastern half of the celestial dome

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Appendix A: Spherical Trigonometry and Astronomy

since a = 90° − z. Again using Eq. (A.3a) cos P X = cos P Z cos X Z + sin P Z sin Z X cos ∠P Z X or, sin δ = sin ϕ cos z + cos ϕ sin z cos A or, sin δ = sin ϕ sin a + cos ϕ cos a cos A or, cos A = (sin δ − sin ϕ sin a)/ cos ϕ cos a

(A.7a)

(A.7b)

The hour angle depends on the observers’ meridian. So if the observers’ position from the reference is known from where the R.A. is measured, the hour angle H and the right ascension R.A. can be related by the following relation. If the R.A. of the observers’ meridianbe (R.A.)O and the hour angle of the celestial object be H, then the right ascension of the celestial object, X (R.A.) X = (R.A.) O − H

(A.8)

or, α X = α O − H. The second problem is just the opposite. If the observers’ latitude (ϕ), the azimuth (A) and the altitude (a) be given, the α (or H) and the declination (δ) are to be determined. Using Eq. (A.7a) one gets sin δ = sin ϕ cos a + cos φ · cos a · cos A Fig. A.4 Transformation from horizontal system to equatorial system

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169

Fig. A.5 Rising and setting azimuth of a celestial object

Since ϕ, a and A are specified, the declination, δ, can be calculated. Once, δ is known using Eq. (A.6), the hour angle H can be calculated from the following relation: cos H =

sin a − sin ϕ sin δ cos ϕ cos δ

A.3 Rising and Setting of Celestial Objects Figure A.5 shows an object X along with its position described in both the equatorial system and horizontal system. A circle, parallel to the celestial equator, is drawn through X which is the latitude circle of X. It represents the path taken by object X in the sky during one day (and night). The two points U and V where this latitude circle of X intersects the horizon circle are the rising and setting points of X, respectively. Hence, for the conditions indicated, ∠N OU is the rising azimuth of X. Since at the rising point the altitude of X is zero from Eq. (A.7b), the azimuth of the rising point is given by cos AU =

sin δ cos ϕ

(A.9)

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Appendix A: Spherical Trigonometry and Astronomy

Fig. A.6 Range of rising and setting positions

where ϕ is the latitude of the observer and δ is the declination of the object. Thus, for the summer solstice day when the sun’s declination is equal to 23.5 °N, the azimuth of the rising point of the sun as observed from a location at latitude ϕ is given by AUSS

= cos

−1



sin 23.5◦ cos ϕ

 = cos

−1



0.3987 cos ϕ

 (A.10)

Again on the winter solstice day, the sun’s declination is −23.5°. So from the same location, the rising azimuth will be     0.3987 0.3987 = 90◦ + cos−1 AUW S = cos−1 − cos ϕ cos ϕ = 90◦ + AUW S

(A.11)

This shows that AUW S − AUSS = 90◦ . Again at a latitude (90° − 23.5°), the value of = 0. This latitude defines the arctic circle, and on the summer solstice day, there is no rising and no setting of the sun. As seen from Fig. A.5, the rising and the setting points on the horizon circle are symmetrically positioned about the north–south line. Thus, the rising and the setting diagram for the extreme positions becomes as shown in Fig. A.6. It should be noted that these positions are not affected by the precession of the equinox. However, the change in the inclination of the earth’s axis affects the azimuths. At a latitude of 60°, the azimuth for the rising sun on the summer solstice day will change by 1.5° if the tilt changes from current value of 23.5°–23°. AUSS

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171

Fig. A.7 Change of position coordinates with the shift of the pole

A.4 Effect of Precession of the Equinoxes Due to the precessional motion of the earth’s axis, thecelestial poles change their position and describe a circle of about 47° angular diameter. Since a longitude great circle (or meridian line) starts at thecelestial pole, the shift of the celestial pole causes a change in the coordinates of an object’s position in the celestial sphere. Figure A.7 shows the situation in an exaggerated fashion. When the north celestial pole changes its position from P to P, the celestial equator changes from ε to ε. The meridian line also changes from PXC to P XC. Then, changes of the coordinates can be determined as discussed below. Figure A.8 shows the celestial sphere with the northcelestial pole at P, and point K represents the ecliptic pole K around which the north celestial pole P rotates due to precession completing the circle in about 25,800 years. Since the earth’s axis is tilted to the plane of the ecliptic at an angle (the present value being 23.5°), the arc KP is equal to . Again from the plan view of the celestial sphere, it is clear that the celestial equator and the ecliptic intersect at two diametrically opposite points UU that is perpendicular to the great circle passing through K and P. Now, due to precessional motion of the earth’s axis, thencelestial pole will take a new position P after some time as indicated in Fig. A.8. At this instant, the ecliptic and the celestial equator will intersect at points U1 and U1  , again U1 U1  being a diameter that is perpendicular to the line KP1 . So, great circles passing through K and P are perpendicular to the great circle passing through K and the equinoctial point U. Similarly, KP1 is normal to the great circle through K and U1 . Hence, the spherical angle PKP1 to the angle U1 OU. The shifting westward motion of the equinoctial point U along the ecliptic is

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Appendix A: Spherical Trigonometry and Astronomy

Fig. A.8 Shift of celestial pole due to precession and its effect or celestial coordinate

known. It is 360°/25,800 or 50.231 of arc per year. Now, the effect of precession on right ascension (α) and declination (δ) can be determined as explained below: If the position of a star be at S, the spherical triangle KPS changes to KP1 S after an interval of time due to precession. The rate at which the equinoctial point shifts is known to be 50.4 per year. So at an interval of one year, the angle PKP1 is equal to ∠U1 OU which is equal to ψ (=50.23 ). If the right ascension and declination of the star S be (α, δ) and (α 1 , δ 1 ) at the starting instant and after one year, respectively, then P S = 90◦ − δ, P1 S = 90◦ − δ1 ∠K P S = 90◦ + α, ∠K P1 S = 90◦ + α1 K S = 90◦ − β, ∠P K S = 90◦ − λ, ∠P1 K S = 90◦ − λ1

1 Another

value of 50.4 has also been used by a majority of scholars.

(A.12)

Appendix A: Spherical Trigonometry and Astronomy

173

where β is the latitude of the star S, λ and λ1 are the longitudes of S at the start and at the end of one year period. It is also known KP = KP1 = . The change in declination is given by δ 1 − δ. Let an arc P1 Q be drawn from P1 , perpendicular to PS. Since ψ (=50.23 ) is very small QS may be considered to be equal to P1 S. So Q S ≈ 90◦ − δ1 and P Q ≈ δ1 − δ = δ Now from Fig. A.8, it is char that P1 P is almost normal to KP (for very small value of PP1 ) and ∠KPQ is equal to 90° + α. Hence, ∠P1 PQ ≈ α and δ ≈ P Q = P P1 cos α

(A.13)

∠P K P1 = and P P1 = ∠P K P1 sin = ψ sin

(A.14)

Now

From the above two equations, the change in declination per year δ1 − δ ≈ δ = ψ sin cos α

(A.15)

The change in right ascension per year can be denoted by α = α 1 − α. From the spherical triangle KPS using (A.3a) and noting the relations given in (A.12), sin β = cos sin δ − sin cos δ sin α

(A.16)

Similarly, considering the spherical triangle KP1 S sin β = cos sin δ1 − sin cos δ1 sin α1

(A.17)

It should be remembered that due to precession the reference point, U shifts along the ecliptic resulting in variation in the longitude only keeping latitude β unaltered. In (A.17), the declination δ 1 and R.A. α 1 are written as δ1 = δ + δ and α1 = α + α

174

Appendix A: Spherical Trigonometry and Astronomy

Since both δ and α are small quantities, (A.17) can be expanded, and only the first-order terms in δ and α can be kept. Noting that sin δ1 ≈ sin δ + δ cos δ cos δ1 ≈ cos δ − δ sin δ sin α1 ≈ sin α + α cos α Eq. (A.17) can be approximately written as follows sin β = cos (sin δ + δ cos δ) − sin (cos δ − δ sin δ) × (sin α + α cos α) (A.18) Subtracting (A.16) from (A.18) and neglecting the terms with products of the small quantities, the following equation is obtained: sin cos α cos δ · α ≈ (cos cos δ + sin sin α sin δ)δ

(A.19)

Relations given in (A.15) and (A.19) can be used to estimate the yearly change of R.A. and declination of a star due to the precessional motion of the earth’s axis. It should be remembered that using the relations derived, changes in the coordinates can be estimated not for very long time intervals. Since α and δ both become time-dependent functions, (A.15) and (A.19) need to be integrated to determine the changes when the time interval is very long. Writing ψ = Ω dt where Ω is the rate of precessional motion (A.15) and (A.19) can be expressed in the form of the following two differential equations: dδ =  sin · cos α dt dα = Ω(cos + sin ε sin α · tan δ) and dt

(A.20)

(A.20) represents two coupled nonlinear differential equations which can be solved numerically. Planetarium softwares have built in computer programmes. It should be noted that an oscillating motion exists superimposed, on the precessional motion that is called ‘nutation’. For more accurate analysis, nutation has to be considered. A MATLAB programme for solving (A.20) is given below:

Appendix A: Spherical Trigonometry and Astronomy clear all;

% Initial conditions in degrees x0=24.11;

% range: -30 to 80

y0=56.87;

% range: 0 to 350

% Timestep size in centuries dt=1;

% Total time in centuries T=70;

% Defining symbolic variables symsx; symsy;

% E, B, x, y are in degrees B=23.5*pi/180; E=-1.42*pi/180;

k=E*sin(B)*cos(y);

% Rate of change of x

l=E*(cos(B)+sin(B)*tan(x)*sin(y)); % Rate of change of y

Y(1)=y0*pi/180; y=y0*pi/180; X(1)=x0*pi/180; x=x0*pi/180;

i=2; % Counter for updating time in the loop % Runge-Kutta fourth order for time integration for t=0:dt:T-dt xn=x; yn=y; k1=double(subs(k)); l1=double(subs(l)); x=xn+dt*k1/2; y=yn+dt*l1/2; k2=subs(k); l2=subs(l); x=xn+dt*k2/2; y=yn+dt*l2/2; k3=subs(k); l3=double(subs(l)); x=xn+dt*k3; y=yn+dt*l3; k4=double(subs(k)); l4=double(subs(l)); x=xn+dt*double((k1+2*k2+2*k3+k4)/6); X(i)=x; y=yn+dt*double((l1+2*l2+2*l3+l4)/6); Y(i)=y; i=i+1; end t=0:dt:T; plot(t,Y);hold on; ylabel('Y(radians)'); xlabel('Time(centuries)');

175

176

Appendix A: Spherical Trigonometry and Astronomy

Fig. A.9 Heliacal rising of a star

A.5 Heliacal Rising of a Star It is needless to mention that the stars are there in the day sky but are not visible due to presence of the bright sun. Thus, when the dawn approaches in the eastern , the glare of the approaching sun gradually makes these stars invisible from the earth’s surface. Figure A.9 shows the phenomenon. In the early morning, a star S (a little ahead of the sun that is still below the horizon) is seen to rise just before the sun rises, and this phenomenon is called the heliacal rising of star S. It is obvious that brighter the star lesser will be its longitudinal distance from the sun when it can be seen to rise before the sun. Apart from the brightness of the star, the other things which decide the visibility of a heliacally rising star are the weather condition, pollution, refraction and parallex. As the sun advances by about 1° every day along the ecliptic towards the east, stars come out of its obstruction as soon as the longitude difference exceeds a value depending on the star’s brightness. Thus, on a particular early morning, a star reappears for a short time (after a period of its invisibility) before being plunged in the daylight. To determine the condition for heliacal rising of a particular star, a thumb rule has been proposed by Alexander Thom.2 According to this thumb rule, it has to be considered when a star of magnitude m is at its minimum visible altitude |m|° and the sun in at an altitude −4|m| (in degrees) below the horizon. Thus, a star of magnitude 2 is visible at an altitude of 2° when the sun is about 8° below the horizon. One point needs to be kept in mind is that these simple thumb rules can be applied when the heliacally rising star’s celestial latitude is within a small range. A star at longitude λ and latitude β can be seen to rise heliacally from a location on the earth at latitude of φ when the following condition is satisfied (on a clear day, of course).

2 See

Footnote 1.

Appendix A: Spherical Trigonometry and Astronomy

177

Fig. A.10 Approximate configuration for heliacal rising

(λs − λ) cos ν + β sin ν ≈ 5|m| (in degrees)

(A.21)

where λs is the longitude of the sun and ν is the inclination of the ecliptic line from vertical (locally). The value of ν varies depending on the day of the year; on the summer and winter solstice days, ν is equal to φ for obvious reasons. So, for helical rising on the solstice days, the longitude difference between the star and the sun should be (λs − λ) ≈

5|m|(degrees) + β sin φ cos φ

(A.22)

This of course is a very approximate analysis on the basis of Fig. A.10. For an approximate calculation referred to days other than solstices ν can be replaced by ν eq where νeq ≈ φ + 23.5◦ cos α

(A.23)

For the Sapta-Sindhu region, φ ≈ 30°, and the final form of the required longitude difference for heliacal rising of stars with small declinations becomes (λs − λ) ≈

5|m|(degrees) + β sin νeq cos νeq

(A.24)

Appendix B

Positions of Nakshatras and Zodiacal Signs

S. no.

R¯asi

Nir¯ayana Longitude

S. no.

Nakshatra

Nir¯ayana Longitude

1

Mesa

0°–30°

1

Asvini

0° 00 –13° 20

2

Bharani

13° 20 –26° 40

3

Krittik¯a

26° 40 –40° 00

4

Rohini

40° 00 –53° 20

5

Mrigasir¯a

53° 20 –66° 40

6

¯ a Ardr¯

66° 40 –80° 00

7

Punarvasu

80° 00 –93° 20

8

Pusy¯a

93° 20 –106° 40

9

Asles¯a

106° 40 –120° 00

10

Magh¯a

120° 00 –133° 20

11

Purva Ph¯alguni

133° 20 –146° 40

12

Uttar Ph¯alguni

146° 40 –160° 00

13

Hasta

160° 00 –173° 20

14

Chitr¯a

173° 20 –186° 40

2

3

4

5

6

Vrisabha

Mithuna

Karkata

Singha

Kany¯a

30°–60°

60°–90°

90°–120°

120°–150°

150°–180°

(continued)

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 A. Ghosh, Descriptive Archaeoastronomy and Ancient Indian Chronology, https://doi.org/10.1007/978-981-15-6903-6

179

180

Appendix B: Positions of Nakshatras and Zodiacal Signs

(continued) S. no.

R¯asi

Nir¯ayana Longitude

7

Tul¯a

180°–210°

8

9

10

11

12

Vrischika

Dhanus

Makara

Kumbha

Mina

S. no.

Nakshatra

Nir¯ayana Longitude

15

Sv¯ati

186° 40 –200° 00

16

Vis¯akh¯a

200° 00 –213° 20

17

Anur¯adh¯a

213° 20 –226° 40

18

Jyesth¯a

226° 40 –240° 00

19

Mul¯a

240° 00 –253° 20

20

Purv¯as¯adh¯a

253° 20 –266° 40

21

Uttar¯as¯adh¯a

266° 40 –280° 00

22

Sravan¯a

280° 00 –293° 20

23

Dhanisth¯a

293° 20 –306° 40

24

Satabisaj

306° 40 –320° 00

25

Purvabh¯adrapada

320° 00 –333° 20

26

Uttarbh¯adrapada

333° 20 –346° 40

27

Revati

346° 40 –360° 00

210°–240°

240°–270°

270°–300°

300°–330°

330°–360°

NB: In the year 2000 CE, the Anayanamsa for the vernal equinoctial point was 28.3°. So, the Nirayana longitude of a celestial object can be found out by adding (Year-2000) × 50.4/3600 degrees to the Sayana longitude

Appendix C

Genealogical Lists of Puranic Kings

C.1 Predeluvian Dynasties

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 A. Ghosh, Descriptive Archaeoastronomy and Ancient Indian Chronology, https://doi.org/10.1007/978-981-15-6903-6

181

Sikhandini

(10 Prachetas)

Barhisada Gaya Sukla Krishna Satya Jitāvrata

Habirdhana

Vijitasva Dhumra Kesa Haraya Kesa Dravin Brika

Manasyu Vauvan Tustu Virāja Rāja Satajita Viswagajyoti

Samarata Marichi Vindumāna Madhu Viravrata

Chitrarath

Bhuma Udgitha Prastaba Bibhu Prithusena Nakta Gaya

Dharma

Brahma

Sugathi

Pramantha

Avirodhan

Aja

(10 Brahmarishis) (4 Kumaras) (8 Rudras) Bhrigu Rudra Sanaka Pulastya Sanātana Bhava Uttānpāda Priyavrata Prasuti Akuli Sadānanda Pulaha Sarva Agnidhara Dhruva Sanat Kumā Ishāna Kratu Pashupati Angiras Harivarsa Maru Kuru Hiranmaya Ranyaka Kituman Marichi Kimpurush Bhima Bhadraswa Ila Bhima Atri Ugra Rishava Mahādeva Vashistha Batsar Kalpa Nārada Kustha Ketu Vadrasena Indraspaka Vidarva Kikata Ruchi Ila Brahma Bharata Maru Pusparna Tigma Isha Urja Vasti Jaya Vrata Vrata Vrata Pravandhyana Pippal Avihotra Dravira Chamas Karavajana Kusthu Nishitha Pradosha Sāyam Madhyāndin Kari Hari Antariksha Chakshu Rāstravrita Sudarsana Sumati Avaran Dhumraketu Manu (Nadvala) Devtajit Devadmna Ulmukh Shribi Pradyumna Atirātra Agni Dhrita Salyavan Dumna Rita Kristna Puru Paramusthri Pratiha Anga Sumona Svati Kratu Angiras Gayā Vena Pratiharta Udgatha Prihu Paritosta

Manu Svaymbhuva

182 Appendix C: Genealogical Lists of Puranic Kings

Appendix C: Genealogical Lists of Puranic Kings

C.2 Postdeluvial Solar Dynasty of Ikshaku

183

Dandaka

Muchukunda

Ambarish

Purukusta

Trasadashyu Sambhuta Anaranya Prisadasva (Trasadashyu) Haryasva

Vadrasva

Drirasva Haryasva Nikumbha Samhatasva Krisasva Prasenjit Yuvanāsva Māndhāta

Kerkutsa (other names Puranjaya, Indrabāho) Anena Prithu Visvagandha Adra Yuvanasva Svavastha Brihadasva Kuvalaysva

Bikukshi

Kapilasva

Nimi

Diti

Ila

*Harischandr Rohitāshva Harita Chancha Vijaya Ruruka Vrika Vahuk Sagara Asamanjas Amsumāna Dilipa *Bhagiratha Sruta Navaga Ambarish Sindhudwip Ajutayu Rituparna Sarvakāma Sudāsa Saudāsa (Kalmaspada) Asmaka Urukama Mulaka Sataratha

Danu

Kiitasarma Viswasha Dilipa Dirghavāhu Raghu Aja Dasaratha *Rāma Kusha Atithi Nisādha Nala Nava Pundarika Kshemadhanya Devanika Ahingu Paripatra Bala Dala Udraka Bajranar Sankhapara Bathitasva Viswasva Hiranyava Vrihatvanu Pushya Dhrubasandhi Sudarshan Agnivarna

Savitur Mitra Varuna Bhaga

(12 Adityas)

Aditi+Kāshyap

(Lunar Dynasty – Main line of Purus)

Kavi Dista Prishada Ikshāku Karusha Dhrista Nriga Nariswanta

Manu Vaivasvat

Anga Vishnu Indra Aryaman Dhuti Vivasvat Tvashtri Pushan

(Ikshāku Solar Dynasty)

907 years of kings deluge period 60 daughters of Daksha Prajapati (Brahma’s son in a former life)

Maru Prashsruta Vridhyasarma Sushandhi Amarsha Mahaswan Visrutavara Brihadvala (Contemporary of Pandavas)

Vinata

184 Appendix C: Genealogical Lists of Puranic Kings

Appendix C: Genealogical Lists of Puranic Kings

C.3 Lunar Dynasty—Main Line of Purus (Incomplete)

185

Riksha Priya Sambaran Kuru (Founder of Kuru dynasty

Medhadi Nila Brihadishu Santi Susanti Puruja Arka Vadrasva

Hasti (Gap of 34 generations) Ajmira

*Puru Janmejaya Prachihanan Pravina Manashu Charupada Sudyumna Bahugava Samjati Ahamjati Raudrasva Riteyu Rantiman

Jyoti

Rambha

Samjati

Nahusha

Ajati

Ahalya (+Gotama)

Jati

Anu

*Divodāsa Mitrayu Chavyan Sudāsa Sahadeva Somaka

Drutsyu Bavau Setu Aravdha Gandhara Dharma Dhrita Durmada

Ragi

Anena

Riksha Sambaran *Kuru Janhu Suratha Biduratha Sarvabhaum Jayatsena Rādhik Dyuman Akrodhāna Devatithi Riksha Dilipa Pratipa Balhika *Santanu Devapi(Rishi)

Sutiotra Chavan Kriti Vasu Vrihadratha Jarasandha Sahadeva

(Gap of 15 generations)

Parikshit Sudhanu Nishāda

Prisat

(Prochetas who left for the north)

(Through Sharmistha)

Yajati

(12 Adityas)

Sanjay Campilla Javinar Muagai Brihadisva Bramhista Indramadha Bridhyasva

Sudhanta

Gauri (Daughter) Prativatha Kanva Medhatithi

Pravir *Dusyanta (+Sakuntala) *Bharata Bitatha Varanmanyu Brihatkshetra

Tamsu Surrodha

Suhota Gaya Suhota Garga Kapila

Anagna

Subahu

List 4

Yadu

(Through Devyani)

Vindhyasarma

Ila (Budha) Pururava Ayu

*Bhisma

Pandu

Vichitravirya Bidura

*Parikshit

Abhimanyu

*Yudhisthira Bhima Arjuna Nakula Sahadeva

Duryodhana

Dhritarastra

186 Appendix C: Genealogical Lists of Puranic Kings

Appendix C: Genealogical Lists of Puranic Kings

C.4 Line of Yadu Dynasty (Incomplete)

187

Sahasrajit Satajit

Nila

Ripu

Payoda Krosta Vrijvana Swahita Visadgu Renuhaya Haya *Haihaya Chitrurath Dharma Sasavindu Netra Prithusrav Kartya Tama Sohagni Dharma Mahisman Ushana Vadrasrenya Siteyu Durdama Ruchak Dhanka Purujit Kritavirya Kritanja Kritavarma Kritagni Jamagha Vidarva *Arjuna (Kārtavirya) Krama Romapada Surasena Sura Dhrisna Krishna Jayadhvaja Kunti Bavru Vrishni Talajangha Kriti Nivriti Bitihotra Ustik Dasarta Madhu Chedi Voyama Vrisni Jimuta Bikriti Bhimaratha Navaratha 36 Dasaratha names Sakuni are Karambhi missing Devarat Devakshatra Madhu Anabarata Kuruvasta Anuratha Puruhotra Amsa Ayu Satwata

Yadu

Vrishni

Divya Devavridha Vajaman Bavru Nimlochi Kinkin Dhristi

Kukur Suchi Kambalbarhi Vajaman Sumitra Yudhajit Sini Bidurath Dhrista Satwak Sura Vrishni Yuyudhan Biloma Sini Jaya Swambhoja Kapotroma Kuni Bilomak Hridika Yugandhar Bhaba Anu Andhak Devamirha Dundavi Sura Abhijit *Basudev Punarvasu Ahuk (Father of Lord Devak Ugrasena Krishna) Devaki Kangsa* *Krishna

Andhaka Mahabhoja Vaji

188 Appendix C: Genealogical Lists of Puranic Kings

Appendix C: Genealogical Lists of Puranic Kings

C.5 Post Mah¯abh¯arata Dynasties

189

Ikshāku

Urukshepa Vatsa Vatsavyuha Prativyoman Divakara Sahadeva Brihadasva Bhanuratha Prateetasva Supratitha Marudeva Sunakshatra Kinnara Antariksha Suvarna Amitrajit Vrihadrāja Dharman Kritānjaya Rananjaya Sanjaya Kshudraka Kundaka Suratha Sumitra Shuddodhana Gautama (Siddhārtha) Rāhul Prasenjit

Ayodhyā Line (Incomplete)

About 1150 years after Mahābhārata War

About 7 names missing

100 years

Descendents of Brihadvala, killed by Abhimanyu Shrutavat Ayutāyus Niranitra Sukshatra Vrihatkarmah Senajit Shrutanjaya Vipra Shuchi Kshemya Subrata Dhara Sushuma Drihadasenā Sumati Suvala Sunita Satyajit Vishvajit Ripunjaya Pradyota Palaka Vishakayupa Janaka Nandivardhana Sisunaga Kākavarma Kshemadharman Kshatrujas Bimbisāra Ajatashatru Dharbaka Udayasva Nandivardhana Mananda *Mahapadma Nanda *Chandragupta

Magadha Line

9 Nandas – 100 years

About 1050 years after Parikshit according to Vishnu Purān

Janamejaya Shatanika Ashvamedhadatta Asima – Krishna Nichakra (Due to destruction of Hastinapur by flood the capital was shifted to Kaushambi) Usna Chitraratha Vrishnimat Sunita Richa Nrichakshu Sukhibala Pariplava Sunaya Medhavin Nripanjaya Mridu Tigma Vrihadratha Vasudana Shatanika Udayana Ahinaru Khandapāni Niranitra Kshemka

Pandava Line initially at Hastinapur

190 Appendix C: Genealogical Lists of Puranic Kings

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Index

A Advance of perihelion, 21, 80 Agastya –heliacal rising, 71 Ahargana, 58–60 Ahichchhatra, 106 ¯ Ahura M¯azd¯a, 91 Alexander, 5, 46, 97, 150, 153, 176 Altitude, 20, 167–169, 176 Am¯anta system, 13, 48, 54, 103 Ancient Indian astronomy –rediscovery, 43, 44 Anumati, 48 Aphelion, 13, 41, 75, 80, 81 Apogee, 74, 75 ¯ Aranyaka, 109, 110 Archaeoastronomy –descriptive, vii, 3, 28–30, 37, 38, 43, 61, 153, 161 –physical, vii Arctic circle, 32, 170 Arcus visionis, 68, 69 Ardhar¯atrika system, 48 Ariianam Vaejo, 91, 92 Arjuna –K¯arttavirya, 157–159 –Pandav, 157 Aryabhata I, 7, 47, 88, 104 Aryan, 5, 6, 89, 110, 144, 153, 154 Aryan Invasion Theory, 6, 93, 110, 111, 153, 154 Astronomy –hellenistic, 46, 50, 56, 57, 125 –positional, vii, viii, 2, 3, 11, 23, 25, 26, 65, 163 –presiddh¯antic, 45–50, 53, 57, 134

–siddh¯antic, 45, 48, 50, 52, 56–59 Asura, 91, 92, 129, 130 Asval¯ayana Grihya Sutra, 98 Atri, 85, 128–131 Ayanachalana, 58 Ayanas –dev¯ayana, 49 –pitriy¯ana, 49, 124 Azimuth, 20, 30, 32, 33, 35, 167–170

B Badrinarayan, R., 149 Bailly, J. S., 44 Baluchistan, 93, 156 Banerjee, R. D., 154 Barahamihira, 57 Benedetti, G., 106, 152, 157 Bhadr¯asva, 90 Bh-amsa, 54, 55 Bh¯arata, 88, 90, 91, 98, 158 Bhaskaracharya, 57 Bhatnagar, A. K., viii, 98, 99, 103, 104 Bhattacharya, R., 85 Bhirrana, 93, 143, 156 Bhisma, 99–101, 103, 104 Brahmagupta, 57 Br¯ahmana, 1, 47, 51, 109, 110, 114, 115, 122, 127, 129–133 Br¯ahmin¯ab¯ad, 154 Brennand, W., 44 Brunton, J., 154 Brunton, W., 154 Buddha, 2, 5, 94, 111 Burgess, J., 44

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 A. Ghosh, Descriptive Archaeoastronomy and Ancient Indian Chronology, https://doi.org/10.1007/978-981-15-6903-6

193

194 C Carbon 14, 29 Cardinal days, 32, 33, 35, 65, 66, 73, 99 Cassini, G., 44 Celestial coordinates, 18 Celestial pole, 16, 18, 20, 25, 37–39, 62, 67, 85, 100, 112, 125, 167, 171 Celestial sphere, 2, 11, 14, 15, 17–19, 25, 69, 78, 112, 163, 164, 167, 171 Chandra, A. N., 151 Chandragupta, 97, 98, 105, 150, 152, 189 Chattopadhyay, B. C., 88, 98, 104 Chronology, viii, 2–10, 30, 35, 37, 43, 57, 72, 73, 84, 88, 93–96, 114, 136, 139, 148, 150–154, 156, 158, 159, 161 Circumpolar, 62, 67 Comets, 12, 57, 99 Conjunction –of moon, 27, 73, 74, 78, 98 Coordinate system –ecliptic, 19 –equatorial, 18, 20, 166, 169 –horizontal, 20, 166, 167, 169 Cunningham, A., 153

D Daftari, K. L., 52, 88, 89, 103, 104, 114, 153 Dakshin¯ayan, 49, 54 Day –civil, 48, 50, 54–56, 58, 60, 80 –s¯avana, 48, 54, 56 Declination, 18–20, 32, 33, 69, 71, 112, 116, 119, 125, 127, 132, 167–170, 172–174, 177 Dhruva Nakshatra, 112, 113 Dhruva Tara, 50 Division of day, 50 Dixit, S. B., 44, 52, 127 Draconis, 37, 112, 113 Drisadvati, 154, 156 Dv¯ark¯a, 106

E Earth axis –tilt, 13, 21, 32, 35, 63, 81, 82, 84, 171 Earth’s spin –slow down of, 21, 23 Eccentricity of earth orbit, 21, 40, 80 Eclipse –lunar, 26–28, 40, 72–74, 80, 99, 100

Index –solar, vii, 2, 7, 11, 22, 26–28, 38–40, 61, 72–76, 79, 80, 99, 100, 115, 128, 130, 132, 136 –year, 28, 78 Ecliptic –plane of the, 13–15, 27, 28, 33, 73, 77, 82, 171 Ekavimsa, 122, 130 Epoch, 3, 7, 8, 32, 38, 58–60, 82–84, 88, 98 Equator –celestial, 14, 16, 18, 25, 26, 30, 65, 132, 169, 171 –terrestrial, 14 Equinoctial point, 18, 25, 38, 58, 62, 65, 72, 115, 118, 132, 171, 172, 180 Equinox –autumnal, 17, 25, 49, 115, 128, 131 –vernal, 17, 18, 25, 26, 32, 38, 54, 58, 65, 81, 84, 115, 118, 119, 127, 128, 131, 132, 180 Exaltation –of mars, 2, 8, 38, 40, 41, 61, 135 –of planet, viii, 2, 8, 38, 41, 61, 71, 135

F Father du Champ, 44 Fire alters –vedic, 50, 159 Fred, E. K., 80

G Garga, 185 –Vriddha, 57, 104 Genealogy –Puranic dynasties, 96, 97 Ghaggar, 141 Ghose, A., 141 Great circle, 18–20, 25, 58, 67, 69, 163, 164, 167, 171

H Haihaya, 157, 187 Hakra, 141, 156 Hamilton, A., 149 Hapta Hendu, 92 Harappa, 153, 154, 158, 159 Harappan, 95, 106, 111, 141, 144, 148, 154–159 Hariupi¯a, 158, 159 Harivarsha, 90 Haryana, 93, 156, 158

Index Hastin¯apur, 106, 157 Hemkoota, 90 Himav¯an, 90 Hindu religion, 6 Hiranmaya, 90, 181 Holocene, 2, 147

I Il¯avrita, 90, 91 Indraprastha, 106, 157 Indus-Sarasvati civilization, 44, 154 Indus Valley, 5, 6, 44, 94, 155 International Astronomical Union, 30 Iyenger, R. N., 113

J Jacobi, Carl G. J., 44 Jarvis, H., 52 Jay¯a, 98 Jean, M., 80 Jim Shed, 92 Jones, W., 110 Julian day, 80 Jupiter, 12, 45, 46, 50, 57, 60, 150 Jyotisha –Rik, 52, 109–112, 134 –Vedanga, 52–58, 103, 114, 134–136 –Yajur, 52, 55, 109, 110, 134

K Kaliyuga, 58, 88 Kalpa, 58, 89, 95, 96 Kar, L. M., 104 Kaus¯ambi, 106, 157 Kay, G. R., 44 Ketu, 50, 181 Ketum¯ala, 90 Kimpurusha, 90 Kochab, 35, 37 Koch, D., 104 Kot Daji, 156–158 Krishna, 88, 97–100, 103, 104, 106, 148, 157, 181, 187, 189 Krittik¯a, 46, 100, 115, 131, 132, 179 Kuhu, 48 Kuru, 90, 91, 157, 181, 185 Kurukshetra, 106, 131

L Lahurdeva, 158

195 LANDSAT, 141, 145 Laplace, P. S., 44 Latitude –celestial, 19, 26, 119, 176 –terrestrial, 18 Le Gentil, G., 44 Light year, 11 Longitude –celestial, 19, 25, 26, 48, 116, 119 –terrestrial, 19 Lothal, 148 Loubere, L. A., 44 Ludwig, A., 130 Lunar period –Sidereal, 13, 17, 20, 53, 54, 56, 57, 77, 99 –Synodic, 13, 17, 56, 134 Lunation, 56 Luni-Solar calendar, viii, 43, 47, 48, 59

M Madhu Vidy¯a, 115–117 Madhyam¯adhik¯ara, 58 Mah¯abh¯arata, viii, 3, 6, 52, 56, 88, 94, 97– 100, 102–106, 111, 136, 139, 144, 148, 157, 158, 189 –dating of, 88, 98–100, 103, 104, 114, 136, 148 Mah¯ayuga, 58, 60 Manu –Svyambhuva, 97, 98 –Vaivasvata, 97 Manus, 58 Manvantara, 58 Mars, 2, 8, 12, 13, 38, 40, 41, 45, 60, 61, 72, 135, 150 Marshall, J., 154 M¯as¯a, 13, 47 Matsya Pur¯an, 84, 104 Max Mueller, 5, 6, 110, 111, 154 Megalithic –arrangements, 9, 30, 33 –sites, 30, 33, 44 Megasthenes, 150 Mehergarh, 93, 143, 156 Mercury, 12, 13, 45, 60 Meridian, 38, 44, 58, 62, 67, 114, 115, 125, 127, 131, 167, 168, 171 –prime, 58, 67, 167 Meru, 89–91 Mesh¯adi, 58 Milky Way

196 –galaxy, 11 Mizar, 35, 37 Modak, J. B., 52 Mohenjodaro, 154, 158 Month –am¯anta, 13, 48, 54, 103 –intercalary, 49, 53, 60 –lunar, 7, 8, 13, 17, 47–49, 53, 54, 58, 60, 63 –purnim¯anta, 13, 48, 54, 103 –solar, 49, 54, 60 Moon, 7, 8, 12–17, 21, 24, 26, 27, 28, 31, 33, 35, 39, 40, 44, 45, 47, 48, 50, 52– 54, 56–60, 63, 65, 66, 73–79, 98–104, 113, 115, 128, 130, 134 Moon’s orbit –plane of, 12, 13, 27, 28, 33, 73 Mukherjee, K., 44

N Nadistuti, 140 Nakshatra –system, 7, 45, 49, 135 Nanda –Mah¯apadma, 103–105, 152, 189 Nara, 141 Neela, 90, 91 Nicaksu, 106 Nir¯ayana, 58, 72, 135, 179, 180 Nish¯adha, 90, 91 Nodes –ascending, 27, 28, 73, 74 –descending, 27, 28, 73, 74, 77 –line of, 28, 77 North point, 20, 32, 167

O Oldham, C. F., 141 Oldham, R. D., 141 Opposition –of moon, 27, 47, 63, 66, 74, 100 Orbit, 12, 13, 21, 27, 33, 40, 41, 45, 50, 72–74, 78, 80, 81, 135 Orbital plane, 12, 73, 77 Orion, 35, 115, 118, 119, 127

P Paksha –Ardharatrika, 58 ¯ –Arya, 58 –Brahma, 58

Index –krishna, 48 –shukla, 48, 103 –Soura, 58 Palaeochannel, 141, 142, 145, 146, 154 Palaeoclimatology, 88 Pamir, 89, 91–93 P¯anch¯al, 157 Panini, 94 Par¯asara Samhita, 56, 57 Pargiter, E. E., 96, 106, 151, 152 Parikshit, 84, 97, 104–106, 152, 185, 189 Parva, 52, 54, 55, 100 Penumbra, 74, 78 Perihelion, 13, 21, 41, 72, 75, 80–84, 135 Phase –of moon, 8, 47, 52, 53, 99 Playfair, Lord, 44, 87 Pleistocene, 2 Polaris, 25, 38, 112 Pole –celestial, 16, 18, 20, 25, 37–39, 62, 67, 85, 100, 112, 125, 167, 171 –ecliptic, 19, 62, 63, 82, 112, 171 –north, 15, 16, 18, 20, 25, 35, 37, 38, 62, 67, 82, 112, 171 Pole star, 25, 37, 38, 50, 67, 112, 113 Positional astronomy, vii, viii, 2, 3, 11, 25, 26, 65, 163 Praj¯apati-Rohini, 115, 127 Precession of the equinox, viii, 2, 8, 23, 25, 32, 33, 35, 37, 39, 52, 58, 61, 84, 85, 88, 102, 150, 161, 170, 171 –effects of, vii, 8, 25, 61, 171, 172 –period of, 52, 61, 84, 102 –retrograde, 23, 25 Pur¯ana –Brahm¯anda, 1 –V¯ayu, 1, 52, 84, 89, 90, 103–105 Purnam¯as¯a, 47 Purnim¯anta system, 13, 48, 54 Pyramids –alignment error, 2, 37 –of Giza, 35

R R¯ahu, 50, 189 R¯ak¯a, 48 Rakhigarhi, 158 R¯ama, 97, 106, 153, 183 R¯am¯ayana, 6, 106, 149, 150 Ramyaka, 90 Rana, N. C., 135

Index

197

Rao, S. R., 106, 148, 157 Rashi, 50, 56 Retrograde, 23, 25, 56, 74, 77, 81 Right ascension, 18–20, 62, 100, 114, 119, 124, 125, 127, 168, 173, 174 Rigveda, 5, 6, 45–47, 49, 50, 109–111, 114– 118, 121–125, 127, 128, 130–132, 139–142, 152, 153, 158, 159

–major, 33 –minor, 33 Star –alignment, 7, 8, 115, 132 Stonehenge, 33, 35, 161 Sule, A., 85 Sveta-Bar¯aha Kalpa, 96 Sweta, 90

S Sahni, D. R., 154 Samhit¯a, 57, 109, 110 Sanskrit, 4, 6, 44, 94, 97, 110, 154 Saptarshi –cycle, 84, 86, 103, 104 –mandal, 62, 85 Sarkar, A., 143, 144, 156 Saros cycle, 28 Satapatha Brahmana, 51, 110, 123, 131, 132 Saturn, 12, 45, 57, 60 S¯ayana, 26, 58, 72, 110 Sea level –changing, 147 Secular changes, 21, 61 Sengupta, P. C., 3, 44, 98, 103, 104, 111, 114, 116–118, 121–123, 127, 129–133 Setubandhan, 150 Shatadru, 141, 144 Siddh¯anta –Siromani, 60 –Surya, 60 Simsum¯ara, 113 Sindhu-Sarasvati, 93, 95, 106, 111, 152, 157, 158, 161 Sinibali, 48 Solar eclipse –annular, 2, 7, 38–40, 61, 72–75, 77, 79, 128 –total, vii, 2, 7, 22, 38–40, 61, 72–75, 77, 79, 128, 130, 136 Solstice –summer, 30, 32, 33, 35, 49, 52, 54, 63, 65, 66, 81–83, 115, 121, 122, 130, 131, 134, 170, 177 –winter, 17, 30, 32, 49, 52, 54, 63, 66, 81– 84, 99–103, 105, 114, 115, 118, 122, 130, 133, 134, 170, 177 Spast¯adhik¯ara, 58 Spence, K., 35, 37 Spherical triangle, 77, 78 Sringav¯an, 90, 91 Standstill of moon

T Taittiriya Samhit¯a, 48, 51, 110, 131 T¯andya Br¯ahmana, 128, 131, 132 Thuban, 25, 37, 38, 50, 112, 113 Tilak, B. G., 44, 52, 111, 118, 127 Time reckoning –in presiddh¯antic astronomy, 47 Time units, 55 Tithi, 48, 52–56, 60, 101 Transit, 35, 37, 38, 44, 67

U Umbra –in flexion point, 75 Upanishad, 109, 110 Uttar¯ayan, 17, 49, 54, 103 Uttar Kuru, 91

V Vajra, 157 Var¯aha Kalpa, 89 Varsha, 90 V¯ayu Pur¯an, 1, 52, 84, 89, 90, 103–105 Veda, 52, 88–90, 92, 109–112, 115, 116, 124, 136, 153 Vedee, 91 Venus, 12, 44–46, 50, 56, 60, 150 Vin¯asana, 100, 105 Visuvant, 129–131

W Whitney, W. D., 116, 124, 130

Y Yamuna, 141, 142, 144 Year –lunar, 48, 49, 53 –tropical solar, 49, 53, 54, 130 Yudhisthira, 103, 104 Yuga

198 –5-years, 53, 56, 58, 115 –Chatur, 52 –Daiva, 52 –M¯anusha, 52 Yuga system, 52, 56

Index Z Zarathustrian, 91, 92 Zend Avesta, 88, 89 Zenith, 20, 67, 69 Zodiac, viii, 45, 56, 57, 114, 134, 179