Der Stern Von Bethlehem , 2009 2, Frankfurt Am Main (Verlag Der Häretischen Blätter)
Dieter Koch
Astronomical Dating of the Mahābhārata War
Version 1.01 Copyright © 2014 by Dieter Koch, Erlenbach, Switzerland
Translation from the German original by the author himself, currently not perfect, will be edited by a native English speaker.
(This version has important updates in the chapter “How Old are the Astronomical Concepts of the Mahābhārata Epic?”)
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Contents
Contents ...... 2 How Old are the Astronomical Concepts of the Mahābhārata Epic? .... 4 Astronomical Concepts from the Bronze Age? ...... 4 Vernal Point in the Lunar Mansion Kṛttikā ...... 11 Vernal Point in the Lunar Mansion Rohiṇī? ...... 28 Vernal Point in Bharaṇī and Aśvinī ...... 31 Precession of the Equinoxes in Ancient Indien Astronomy ...... 35 Of the Origin of the Lunar Mansions ...... 52 Conclusions ...... 53 A Super Conjunction ...... 55 “The seven planets flew together...” ...... 56 „... like the planets beset the Moon at the end of the age“ ...... 62 The “Gathering Together” of All Beings in their Origin...... 67 Phases and Types of Super Conjunctions ...... 74 The Super Conjunction of 1198 BCE ...... 77 Moon in Maghā? ...... 78 Another Super Conjunction at the Death of Kṛṣṇa?...... 81 The Traditional Kaliyuga Era ...... 92 The Clustering of Planets of 3102 BCE ...... 92 Revatī as Ecliptic Zero Point in Vedic Times? ...... 104 The Clustering of Planets of 3143 BCE ...... 109 The Seven Ṛṣis and Varāhamihira’s Kaliyuga Era ...... 119 Conjunction of the Seven Ṛṣis at the Beginning of Kaliyuga ...... 119 Seven Ṛṣis and Seven Planets ...... 126 Super Conjunctions at Intervals of 100 Years ...... 130 The Clustering of Planets of 2449 BCE ...... 135 New Moon, Full Moon, Eclipses ...... 137 New Moon in Jyeṣṭhā and Full Moon in the Month of Kārttika ...... 137 Super Conjunction with Eclipses 1198 BCE ...... 147 Solar and Lunar Eclipses at the Time of the Great War ...... 150 Problems concerning the Eclipses and the Calendar in 1198 BCE ...... 164 Eclipses on the 13th of the Fortnight ...... 170 Two Suns at the End of the Age ...... 191 Ketu, Dhūmaketu, and Comets ...... 196 Planetary Configurations ...... 202 Jupiter and Saturn in Viśākhā ...... 202 Saturn and Jupiter torment Rohiṇī ...... 205 Mars in Jyeṣṭhā/Anurādhā ...... 208 3 Alternative Approaches I ...... 211 And another celestial configuration ...... 219 Alternative Approaches II ...... 225 Duels and Conjunctions of Planets ...... 229 Do the five Pāṇḍavas stand for the five planets? ...... 237 Bhīṣma’s Death ...... 246 How Many Days from the Battle to Bhīṣma’s Death? ...... 246 Bhīṣma’s Death and the Super conjunction of 1198 BCE ...... 263 Alternative Approaches III ...... 264 Solar Eclipses Before and After the War ...... 277 Conclusions...... 279 Appendices ...... 281 A: Super Conjunctions with New Moon 4000 BCE to 2500 CE ...... 281 B: Super Conjunctions Without New Moon ...... 299 C: Cycles of Super Conjunctions ...... 314 D: Super Conjunctions that Fulfill some Criteria from Mahābhārata ...... 316 E: All Planets Near the Moon in the Morning Sky ...... 319 F: All Planets Near the Moon in the Evening Sky ...... 325 G: Total Solar Eclipses at Sunrise ...... 334 H: Total Solar Eclipses at Sunset ...... 336 I: Annular Solar Eclipses at Sunrise ...... 337 J: Annular Solar Eclipses at Sunset ...... 338 K: Total and Annular Eclipses Observable in Kurukṣetra ...... 339 L: Total and Annular Eclipses Observable in Dvārakā ...... 391 M: Two Eclipses in a Month in the New Moon Calendar ...... 441 N: Two Eclipses in a Month in the Full Moon Calendar ...... 467 Bibliography ...... 492 4
How Old are the Astronomical Concepts of the Mahābhārata Epic? Astronomical Concepts from the Bronze Age? Numerous astronomical and calendrical statements in ancient Indian texts raise the question whether these texts could not be dated on the basis of astronomical calculations. If, for example, a text says that an equinox or solstice is located in a particular lunar mansion, we cannot avoid the question for what period this statement was valid. Due to lunisolar precession, such statements can be true only for the duration of a couple of centuries. Thus we can calculate the period in which this astronomical doctrine must have emerged. Calculations of this kind are very simple and the results will not leave much room for doubt. Unfortunately, however, the dates obtained in this way are mostly totally at odds with dates that have been found on the basis of historical or linguistic considerations. For example, the astronomical and calendrical informations contained in the Mahābhārata Epic are based on a lunar mansions system that has its initial point at the lunar mansion Kṛttikā (the Pleiades). As we shall see, the reason seems to be that in ancient times the vernal equinox was located near the Pleiades and the full moon, when it took place on the autumnal equinox, also was seen near them. Now, the vernal equinox could be attributed to the Pleiades only between about 3000 and 1500 BCE, whereas current indology dates the final redaction of the Mahābhārata Epic to between 400 BCE and 400 CE. The underlying astronomical theory thus seems to be over 2000 years older than the text in which it is used. This raises the question of how this huge time gap can be explained. I do not intend to challenge the late dating of the Mahābhārata Epic and the other texts of the Vedic tradition as given by the scientific establishment. The problem should be taken seriously, though. While it is understandable that historians and indologists, who usually do not have deeper insight into astronomical and 5 calendrical issues, give less weight to archaeoastronomical arguments and even tend to disregard the whole issue, astronomical dating does weigh very heavy from the point of view of the “strict” sciences. It is therefore necessary to discuss the problem duly, as has also been pointed out by authors such as Tilak, Sengupta, Elst, and others. Let us first study a less extreme example, namely David Pingree’s statements concerning the dating of the Vedāṅgajyotiṣa, the oldest Indian astronomical treatise. According to the text, the solstices are located at the middle of Āśleṣā and the beginning of Dhaniṣṭhā. Now, while we do not know exactly where the initial points of the nakṣatras were assumed in ancient times, it is reasonable to assume the Lahiri ayanāṃśa as a good approximation, because then the reference stars of the nakṣatras, when projected on the ecliptic in polar projection, fall nicely into their respective nakṣatras. Based on this reasonable assumption, the text would have to be dated to about 1400 BCE. I shall explain this in more detail later. Now, Pingree writes: Lagadha (der Autor des Vedaṅgajyotiṣa; D.K.) has retained the Vedic list of twenty seven nakṣatras beginning with Kṛttikā, but treats them not as constellations but as measurements of arcs on the ecliptic of 13;20° each beginning with the vernal equinox. This adaption means, of course, that the actual position of the equinoctial and solsticial colures with respect to the fixed stars can not be used for dating the JV. 1 For, in another place he says: We simply do not know where Lagadha would have placed the beginning of the equal nakṣatra Dhaniṣṭhā with respect to the fixed stars... 2 Pingree then dates the text to about 400 BCE, on the basis of purely historical grounds, which are not very certain. Now the main stars of the lunar mansions Dhaniṣṭhā and Āśleṣā are quite far off the ecliptic, and in fact we do not know with certainty in which way or using what projection they were linked to their respective lunar mansions. However, the rough placement of the lunar mansions is indicated by other stars that are close to the ecliptic, e. g. by the
1 Pingree, Jyotihśāstra , p.10. His argumentation is also similar in: “The Meso potamian Origin of Early Indian Mathematical Astronomy”, p. 3; 10. 2 Pingree, “The Mesopotamian Origin of Early Indian Mathematical Astronomy”, p. 10. 6 Kṛttikās or Pleiades. Moreover, the text states that the axis of the solstices is placed at the beginning Dhaniṣṭhā and the middle of Āśleṣā, from which we must conclude that the system of 27 equal lunar mansions was used. If we take Pingree at his word, then Lagadha would have assumed the beginning of Dhaniṣṭhā at the winter solstice in 400 BCE, i. e. at tropical ecliptic longitude 270°. The lunar mansion Kṛttikā began 7 x 13°20’ = 93°20’ after Dhaniṣṭhā, thus at 270° + 93°20’ = 363°20’ = 3°20’ in tropical ecliptic longitude, and it ended at 16°40’. Now, in the year 400 BCE, the Pleiades (Alcyone) were at tropical longitude 26°40’, thus 10° after the end of Kṛttikā, near the end of the lunar mansion Rohiṇī. This is surely anything but plausible. The Pleiades must have been located at least within the lunar mansion Kṛttikā. For this to be the case, we need to go further back into the past by more than 700 years. The celestial observations that formed the basis of Vedaṅgajyotiṣa must therefore have been made before 1100 BC. Other arguments made by Pingree read as follows: ... nor do we know the accuracy with which he could have determined the sidereal longitude of the Sun at the winter solstice. Since a displacement of the beginning of the equal nakṣatra by some 10°, or an error of 10 days in computing the date of the winter solstice, or some combination of these two effects is all that is required to bring the date from the twelfth century to the fifth century B.C., we should not lend much weight to this chronological argument. 3 But it is plausible to assume that ancient Indian stargazers contented themselves with an inaccuracy of 10 days in determining the date of a solstice? While the direct observation of the solstices with day accuracy is difficult or actually impossible, there are also indirect means which provide far better accuracy than assumed by Pingree. E. g. one could just count 91 days from the equinoxes, which can be determined a lot easier by direct observation. Or one could observe for how many days the length of the noon shadow did not seem to change and then assume the solstice in the middle of that period. This method is described in Aitareyabrāhmāṇa 18:18. An explanation of the text has been given by Sengupta.4 To
3 Pingree, “The Mesopotamian Origin of Early Indian Mathematical Astronomy”, p. 10. 4 Sengupta, Ancient Indian Chronology , S. 155ff. 7 assume an inaccuracy of +/–10 days is in fact anything but plausible, especially since we can be sure that the observations were repeated at every opportunity, i. e. every year, and major errors would have been corrected. Let us not forget that the Vedic calendar, which inserted leap months every two to three years, was completely dependent on astronomical observations. And let us not forget that the exact determination of the cardinal points of the year was of great significance for Vedic ritual. Rather we have to ask the question of how the position of the Sun in the lunar mansions was determined for a given date. Observations of lunar eclipses must no doubt have played an important part here, because they allowed to determine the position of the Sun with an accuracy of roughly one degree, which corresponds to two lunar diameters. In any case, Pingree’s answer to the problem is too simple.5 It therefore seems that the Vedāṅgajyotiṣa is actually based on astronomical observations that were made in the late 2nd millennium BCE. This does not necessarily mean that the text was composed in the same epoch. The composition may have been preceded by centuries of oral tradition. Besides, it is possible that the author did not make any observations of his own and did not review the tradition, which had become outdated, because his only goal was preserving an ancient tradition unchanged. Considering the extremely conservative mentality of Hindu traditions, this is by no means improbable. Hence, the final redactions of the two extant recensions of the text may in fact have taken place in 400 BCE or even later. This explanation is not new. E. g. Max Müller already said:
5 Witzel does not really seem to understand the problem either when he says: “Further, lagaDha puts the winter solstice on the new moon of mAgha at the heliacal rising of dhaniSThA, which post dates the establishment of the calendrical scheme with amAnta months.” (Witzel, “Autochthonous Aryans?...”, §30) Whatever may be the intended meaning of this statement, there is no mention of heliacal rising (“rising before the Sun” or the like) of Dhaniṣṭhā (β Delphini) in the Vedāṅgajyotiṣa. Besides, if the heliacal rising of that star had coincided with the winter solstice, then the text would have to be dated to 2000 BCE. 8 ... we may fairly grant to Colebrooke and others, that there was a real tradition which fixed these important points as they are fixed in the Jyotisha ; nay, we may believe that for sacrificial purposes these points were still supposed to be in the same position even at a time when, by the laws of nature, they had considerably receded from it. 6 And Thibaut: For it is neither possible to derive from the given data, with any degree of accuracy, the time when the original observation was made ; nor, even if that could be done, would the result prove anything regarding the period when the works in question were composed, since it is quite clear that the place of the solstices having once been ascertained was adhered to and stated in works composed many centuries after it had ceased to be true. 7 Even more glaring is the time gap between the historical dating of the Mahābhārata Epic and the astronomical age of some astronomical concepts used in it. Even though the final redaction of the epic was made only after 400 BCE, it will be shown in the next few chapters that it uses a list of nakṣatras that begins with Kṛttikā, which must be even 2000 years older. Indeed, this discrepancy can be explained only by the extreme conservatism of Indian spiritual culture. This conservatism can be illustrated by a side glance to the methods used in current Indian astrology. Here, the list of the lunar mansions does not start with Kṛttikā, but with Aśvinī. The reason is given by the fact be that all astrological and astronomical texts of late antiquity assume the equinoxes and solstices at the initial points of Aries, Cancer, Libra and Capricorn, where the initial point of Aries coincides with the initial point of Aśvinī and the vernal point. Now, the vernal equinox has since moved further. It has crossed Revatī and is currently located in the lunar mansion Uttarabhādrā. However, traditional Indian astrologers and calendar makers do not care and do not even think about reforming their system. Caught in their conservatism, they celebrate the winter solstice, the “northward course” of the sun ( uttarāyaṇam ), still on the date when the sun enters sidereal Capricorn (uttarāyaṇam = makarasaṃkrāntiḥ), and thus not on the 21st December, as they should, but only in mid January.
6 Müller, On Ancient Hindu Astronomy and Chronology , p. 21. 7 Thibaut, The Pañchasiddhântikâ. The Astronomical Work of Varâha Mihira , S. xlix. 9 The majority of Hindu scholars does not care about the problem. There are people who are aware of it, though, and seek a reform of the system. In the Report of the Calendar Reform Committee of 1955 it is noted that such a reform is desirable for the future: This recommendation (des Lahiri Ayanāṃśa; D.K.) is to be regarded only as a measure of compromise, so that we avoid a violent break with the established custom. But it does not make our present seasons in the various months as they were in the days of Varahamihira or Kalidasa. It is hoped that at not a distant date, further reforms for locating the lunar and solar festivals in the seasons in which they were originally observed will be adopted. 8 A similar recommendation was already made by SB Dikshit in 1896.9 However, such proposals have been ignored, because the conservative forces are too strong. Some individuals still tirelessly fight for a reform but are susceptible to fierce attacks. E. g. Pandit AK Kaul, moderator of the Hindu Calendar Internet Forum, advertises a tropical calendar published by Darshaney Lokesh and TV Sivaraman.10 Kaul writes:
8 Report of the Calendar Reform Committee , p. 5. 9 Dikshit, Bharatiya Jyotish Sastra , Part II, p. 576: “I have given all the reasons for using Sayana Panchagas for astrology as well as rituals etc. If because of any reasons whatsoever and in spite of the fact that Sayana Panchanga is the one recommended by all our shastras, it is difficult to convince the general public of a gap of 23 days between a sayana sankranti and a nirayana Grahalaghava/Surya Sidhanta Sankranti, then we may start using a fictitious Ayanamsha opposite the Star Chitra, instead of from the end of Revati division because in the latter case, there will be a difference of three days even then between Grahalaghava and Revati Sankrantis, which the general public may not like. The difference be tween the starting point of 180° opposite Chitra and that of Grahalaghava San krantis will be hardly a few hours which the general public will not understand. As such, it is the path of least resistance and may be adopted if at all nirayana panchangas are a necessary evil.” 10 Darshaney Lokesh, ी मोहन कृ त आष त थ प क , (Sri Mohan Krity Aarsh Tithi Patrak, in Hindi), http://www.reformedsanathancalendar.in/SMKATP_internet%20Edition.pdf . There is also an English and Tamil version of the same calendar: T. V. Sivaraman, Reformed Sanathan Calendar , http://www.reformedsanathancalendar.in ; as PDF under: http://www.reformedsanathancalendar.in/sanathancalendar2014.pdf . Main page: http://www.reformedsanathancalendar.in . 10 Uttarayana is nothing but Winter Solstice and it was the start of the same Tapah month that was known as Makar Sankranti later as per the puranas. We must therefore realign our calendar immediately to the seasons if we want the real Vedic dharma to flourish really. 11 The discussion between reformers and traditionalits is extremely emotional, often even offensive. An objective discussion of the problem does not take place. So, coming back to our topic, if nowadays’ traditionalists so violently oppose a correction of their outdated teachings, why should not the same have taken place in ancient times? Why should texts from the 4th century BCE not include astronomical concepts from the 3rd millennium BCE? A good example of this phenomenon is given by chapter 2.8 of the Viṣṇupurāṇa. Experts agree that this work was compiled in post Hellenistic times. In VP 2.8.28ff., it says that the solstices are at the initial points of Capricorn and Cancer and the equinoxes at the initial points of Aries and Libra, and this statement clearly stems from post Hellenistic times, from the first half of the 1st millennium CE. However, a bit further below in the very same chapter, in VP 2.8.76 79 (quoted below on p. 25f.), it says that when the Sun is in the third quarter of Viśākhā and the full moon in the first quarter of Kṛttikā, then that is the autumnal equinox. This statement is only valid for the 2nd millennium BCE. Thus, there is obviously very old and very young material mixed together in this text. Very old astronomical observations, as must be underlying here, not only precede the written sources by thousands of years, but in several cases even go back to a time prior to the Aryan immigration into India. Thus, we have to conclude that the Vedic astronomical tradition was either introduced into India by the Aryans, when they came from Andronovo, or otherwise its origins might be in the Indus culture. I think that both solutions are possible. A considerable heritage from the Indus Civilisation must have been incorporated in the Vedic culture. Hence, I consider it quite possible that, in this matter, we are looking back through a window into the spiritual world of Harappa and Mohenjo daro.
11 http://groups.yahoo.com/group/hinducalendar/ 11 Now, when our sources contain so old astronomical doctrines and when this fact is explained by the extreme conservatism of Hindu traditions, then it should also be clear that even though it is possible to give a date by which the old list of lunar mansions that begins with Kṛttikā must have emerged, this does not help us much to date of the Mahābhārata war. At best, it provides us a terminum post quem for the emergence of astronomical methods that were used at the time of the Mahābhārata war. However, this term will be quite worthless because it could be very far away from the actual events. The vernal equinox could have been attributed to Kṛttikā sometime after 3000 BCE, and to Rohiṇī before that. The time window for Kṛttikā as equinoctial lunar mansion could perhaps have lasted until 1500 BCE. But since the Kṛttikā tradition continued to live well beyond its astronomical expiration date untill Late Antiquity, we do not have a useful terminus ante quem either. The war could even have occurred as early as the first half of the 3rd millennium BCE or as late as 800 BCE, as has been suggested by BB Lal.12
Vernal Point in the Lunar Mansion Kṛttikā The list of nakṣatras, as we know it today and as we find it in astronomical works of the post Hellenistic period, begins with Aśvinī . However, in lists given in the Purāṇas, the Mahābhārata, and in Brāhmaṇa texts, Kṛttikā appears in the first place (e. g. MBh 13.63(64).5ff.) Also it seems that Kṛttikā, as well as Maghā, which is in square to Kṛttikā, are of exceptional importance. Kṛttikā is more frequently mentioned than any other lunar mansion, the obvious reason being that in ancient times the vernal equinox was in Kṛttikā and the summer solstice in Maghā. 13 The vernal point was near the Pleiades in about 2340 BCE. Taking into account the positions of neighbouring nakṣatra stars, i. e. Bharaṇī and Rohiṇī, one could say that the vernal equinox could be attributed to the Pleiades between 2500 BCE and 1800 BCE. However, as we shall see, there is evidence that, on the basis of a different point of view,
12 B. B. Lal, “Mahabharata and Archaeology”, p. 52ff. 13 e. g. Dikshit, Bharatiya Jyotish Sastra , p. 129; Sengupta in: Burgess, The Sûrya Siddhânta , p. xxxv ff.; Kuppanna Sastry in: Sarma, K. V. (ed.), Vedāṅga Jyotiṣa of Lagadha... , p. 12. 12 the vernal point was associated with the Pleiades already in 2900 BCE. This explanation, that the great importance of Kṛttikā has to do with the position of the vernal equinox in ancient times, is not acceptable to Hindu traditionalists because, among other reasons, it defines a terminus post quem for the Mahābhārata war that contradicts their views. Traditionalists believe that Kṛṣṇa died in the so called Kaliyuga year 3102 BCE and the war took place 36 years earlier in 3138 BCE. Besides, they do not admit that the equinoxes and solstices played an important role in Vedic religion because then they would feel forced to reform their sidereal calendar and make it tropical. E. g., Kota Venkatachelam denies any connection between Kṛttikā and the spring equinox in ancient texts. He believes that the Vedic calendar functioned completely independently of the equinoxes and solstices. In today’s Indian calendars this is indeed the case. As has been said already, the winter solstice (uttarāyaṇam ) is celebrated in mid January, at the ingress of the Sun into sidereal Capricorn, regardless of the actual date of the solstice, although this practice contradicts the very concept of the uttarāyaṇa, which means the “northward course” of the Sun. Concerning the Kṛttikā nakṣatra list, Venkatachelam says: ... that the Krittikas are given the first place among the Nakshatras in the Karma