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THE DATE OF MAHĀBHĀRATA WAR
ON ASTRONOMICAL REFERENCES IN THE MAHĀBHĀRATA – AN EXERCISE IN
ARCHAEOASTRONOMY*
Virendra N. Sharma
University of Wisconsin Fox Valley
1478 Midway Road
Menasha, WI 54952, USA *English version of a paper appeared in PUR}NA,Vol.XLVI., No. 2, pp.83-112, July 2004. Abstract
Mahābhārata, the great epic of India describes a legendary war which is believedto be based on actual events that took place anytime between 3500 and 500 B.C.
A number of astronomical references, portents of calamitous events, are reportedin the epic around the time of the war. In the archaeoastronomical exercise undertaken forthis paper, these astronomical references are critically examined. The exercise is basedon a number of assumptions. One, the astronomical reports in the epic belong to theearliest version of the epic; and two, that they are based on visual observations and noton astronomical computations. Three, that the domain distributions of the lunar mansionsof the Hindu astronomy, the nakatras, were different in the ancient times than they aretoday. With these assumptions,the paper reports that most of the planetary conditionsdescribed in the epic are satisfied around the date -3021 A.D.
ON ASTRONOMICAL REFERENCES IN THE MAHĀBHĀRATA - AN EXERCISE INARCHAEOASTRONOMY
Introduction
Mahābhārata, the great epic of India describes a legendary war between the royalcousins of Kuru dynasty, the Kauravas and Pāavas, in which warrior princes from all overthe subcontinent fought on one side or the other. It is widely believed that the narrationcenters around actual events that took place, some time between 3500 and 500 B.C. Theauthor of the epic is said to be a sage-- Veda Vyāsa–who according to the evidence of the epic itself, was a contemporary of andan eye witness of the events. However, the original version of Veda Vyāsa did not surviveunaltered for long, as it was continually enlarged and new stories added to it over thecenturies.1 The present form of the epic is supposed to have taken shape by 400 A.D.,and very little or nothing has been added to it since then.
A number of astronomical references, portents of calamitous events, are scatteredin the epic around the time of the war.2 Based on these references scholars have madenumerous efforts to date the time of the epic.3 However, most of these efforts have beenbefore the availability of modern computers.4 In this paper, the astronomical references ofthe epic are critically examined using computer programs and a possible date or dates ofthe events searched which will satisfy most of the astronomical references.5
Chronology of Events6
The chronology of the events related to the war is as follows. Having come out in
the open after one year of hiding, the Pāavas demanded their share of the kingdom fromKauravas, their cousins. The Kauravas refused declaring that the Pāavas had brokentheir agreement of staying incognito for one full year. The Pāavas claimed that they hadindeed stayed in hiding for one whole year according to their own reckoning. Peacemissions, one led by a Brahmin and the other led by Ka, were dispatched from thePanava's side to the court of the Kauravas; both of which failed. When peace overturesfailed, war preparations began in earnest on both sides. The armies of the twoantagonists assembled on the field of Kurukatra, and a terrible war followed which wasfought from sunup to sundown for 18 days. On the tenth day of the war, Bhīma, thegrand-sire of the Kauravas, and the first commander-in-chief of their side, was mortallywounded and had to withdraw from the fighting. He lived on, however, for another 58days and breathed his last after the next winter solstice. On the 16th day Kara, acelebrated Kaurava warrior, fell on the field, and finally on the 18th day a mace dual tookplace between Duryodhana, the leader of the Kauravas and Bhīma, one of the Pānavabrothers. The dual was witnessed by several people including, Balarāma, the olderbrother of Ka. Balarāma had gone on a pilgrimage a few weeks before the war and assuch did not participate in any of its battles. The astronomical events discussed in thispaper took place at the time of these episodes or before, within a span of two-three years.
Astronomical References7
Just before the Pāavas appeared in the open, Bhīma tells Duryodhana:
teā kālātirekea jyotiā ca vyatikramātpañcame pañcame vare dvau māsānupajāyatah
teāmabhyadhikā māsāh pañca dvādaśa ca kapāhtrayodaśānā varāāmiti me vartate matih
M.B. 4.47.3-4.
"...Because of their [heavenly bodies'] irregular (motions), and with passage oftime, every five years, two extra months are generated. On this basis, my [Bhīma's] viewis that thirteen years, five months and 12 days have elapsed for the Pāavas [since theywent to the forest]." Ka'a Peace Mission
The month, the nakatra and the season when Ka started on his peace mission tothe court of the Kauravas were as follows:
kaumude māsi revatya śaradante himāgamesphītasyasukhe kāle kalyah sattvavatā varah
M.B. 5.81.7
When ... (Ka started on his journey), the month was Kārtika, the nakatra Revatī,end of Śarada (fall) and beginning of Hemanta (winter).8 The crops were flourishing.
Dialogue of Ka and Kara before the war
At the court of the Kauravas, Ka met Kara a celebrated hero of the epic. Ka tellsKara:
saptamāccāpi divasādamāvāsyā bhaviyatisagrāma yojayettatra ta hyāhuh śakradevatām
M.B. 5.140.18
The seventh day from hence, it will be new moon, which the learned call the day ofIndra, let the war (or preparations for war) begin then.9
Replying to Ka, Kara pointed out bad omens in the sky related to the oncomingevents.
prājāpatya hi nakatra grahastīko mahādyutihśanaiścarah pīayati pīayanprāino'dhikamktvā cāgārako vakra jyehāyā madhusūdanaanurādhā prārthayate maitra saśamayannivanūna mahadbhaya ka kurūā samupasthitamviśeea hi vāreya chitrā pīayate grahahsomasya lakama vyāvatta rāhurarkamupeyatidivaścolkah patantyetāh sanirghātāh sakampanāh
M.B. 5.141.7-10
That fierce planet of great effulgence, Saturn is oppressing the nakatra Prajāpati,10in order to greatly afflict the creatures of the earth. The planet Mars, O slayer of Madhu,with its crooked (retrograde) motion in Jyehā, approaches Anurādhā indicating a greatslaughter of friends. Without doubt, O Ka, a terrible calamity approaches the Kurus whenspecially, O thou of Vī race, as a planet is afflicting Citrā. The spot on the lunar disc haschanged its position; and Rāhu approaches towards the sun.11 Meteors are falling fromthe sky with trembling motion and loud noise.
When the peace mission of Ka failed, the Pāava army started for the battle field ofKuruketra as indicated by the following verse.
rohieye gate śūre puyea madhusūdanahpāaveyanpurasktya yayāvabhimukhah kurūn
M.B. 9.34.14
After Balarāma had departed, Ka and Pāavas, (the same day) in Puya nakatra,started for Kuruketra. Vyāsa's Narration
Before the war began, the sage Vyāsa comes over to see the blind king Dhtarāra,the patriarch of the Kauravas and draws his attention to evil omens he had beenwitnessing on the earth and in the sky above, warning an impending doom of the king'sdynasty. In the same context, he describes a set of planetary positions in sky foretelling agreat calamity ahead for the warrior class of the country.
jvalitārkendunaksa nirviśeadinakapamahorātra mayā daa tatkayāya bhaviyatialakyah prabhayā hīnah pauramāsī ca kārtikīmcandro'bhūdagnivaraca samavare nabhastale
M.B. 6.2.22-23
rohiī pīyannea sthito rājañśanaiścarahvyāvtta lakama somasya bhaviyati mahadbhayam
M.B. 6.2.32abhīks kampate bhumirarka rāhustathāgrasatśveto grahastatha citrā samatikramya tihati
ābhāva hi viśeea kurūā pratipaśyatidhūmaketurmahāghorah puyamākramya tihati
senayoraśiva ghora kariyati mahāgrahahmaghāsvagārako vakah śravae ca bahaspatih
bhaga nakatra sūryaputrea pīyateśukrah prohapade pūrve samāruhya viśāpateuttare tu parikramya sahitah pratyudīkate
śyāmo ghah prajvalitah sadhūmah sahapāvakahaindra tejasvi nakatra jyehāmākramya tihati
dhruvah prajvalito ghoramapasavya pravartatecitrāsvātyantare caiva dhihitah paruo grahah12
vakrānuvakra ktva ca śravae pāvakaprabhahbrahmarāśi samāvtya lohitāgo vyavasthitah
M.B. 6.3.11-17
ghahau tāmrāruaśikhau prajvalantāviva sthitausaptarīāmudārāā samavacchādya vai prabhām
svatsarasthāyinau ca grahau prajvalitāvubhauviśākhayoh samīpasthau bahaspatiśanaiścarau
kttikāsu grahastīvro nakatre prathame jvalanvapūyapaharanbhāsā dhūmaketuriva sthitahtriu pūrveu sarveu nakatreu viśāpatebudhah sapatateʼ bhīka janayansumahadbhayam
M.B. 6.3.24-27
Elaborating upon the evil omens he had seen in the heavens, Vyāsa says, " I haveobserved this all the time (these days) that the sun, the moon and the stars are all ablaze. All this forebodes (our) great ruin. On the full moon day of month of Kārtika the moon,having lost its splendor, turned red along with the sky and then became invisible.13 (These days) the planet Saturn oppresses Rohiī (Aldebaran or Antares). The sign of thedeer on the moon has moved from its usual place. Rāhu (Lunar node) constantly eclipsesthe sun. The white planet (Venus) after passing over the nakatra Citrā (Spica) staysthere 14... A fierce comet is afflicting the nakatra Puya. The fiery bodied (Mars) isretrograde in the star group Maghās and Jupiter in the nakatra Śravaa. The sun'soffspring (Saturn) is attacking the nakatra Bhagam (the moon).15 Venus ascendingtoward the nakatra Pūrva Bhādrapadā, shines brilliantly, and is wheeling towards thenakatra Uttara Bhādrapadā. The dark planet blazing like fire ... having attacked thenakatra Jyehā (Antares), stays there ...16 A fierce planet, Venus (?) has come betweenCitrā (Spica) and Svātī (Arcturus)17. Dhruva (the north star) shining fearfully has movedto south. The ruddy planet (Mars), having covered the constellation Brahmarāśi, ... with itsuneven motion, overpowers the nakatra ravaa.18 The two blazing planets, Jupiter andSaturn both, have stayed for one whole year near the nakatra Viśākhā. The planetMercury sets with a terrible appearance indicating fearful happenings ahead.
Vyāsa goes on to add:
caturdaśī pañcadaśī bhūtapūrvā ca oaśīmimā tu nābhijānāmi amāvāsyā trayodasīm
candrasūryāvubhau grastāvekamāse trayodaśīmaparvai grahāvetau prajāh sakapayiyatah
M.B. 6.3.28-29
An amāvasyā (new moon) [usually] falls on caturdaśī (14th day), pañcadaśī (15thday), and in the past [it has fallen] even on a oaśī (16th day) [after a full moon]. But this Ihave not known that an amāvasyā [can also] fall on a trayodaśī [an interval of 13 daysfrom a full moon], i.e., on an aparvan, [improper day]. The moon and the sun have beeneclipsed in one month at an interval of 13 days. These two celestial bodies [therefore] willdestroy the populace. The First Day of Battle
Sañjaya says:
meghāvanarudhamākāśataddina pratyapadyatadīpyamānāśca sapeturdivi sapta mahāgraāh19
M.B. 6.17.2 (footnote)
The sky was clouded over that day, and the seven great planets began to shine likefire in the sky.20
The Death of Kara
On the 16th day when Kara, the celebrated hero fell, the poet observes:
hate sma kare sarito na sravanti jagāma cāsta kaluo divākarahgrahaśca tiryagjvalitārkavaro yamasya putro'bhyudiyāya rājan
M.B. 8.68.47 .
sakānanāh sādricayāścakampuh pravivyathurbhūtagaāśca māria
bhaspatī rohiī saprapīya babhūva candrārkasamānavarah
M.B. 8.68.49Your majesty! [the king Dhtarāra] At the death of Kara, the rivers stopped flowing,
The sun turned dark and set (in the west). The son of Yama (Mercury), with its color offire, appeared (in the sky). The mountains with forests upon them began to tremble, andthe creatures of the world became (terribly) upset. Jupiter, shining like the sun and moon,arose oppressing the nakatra Rohiī. Balarāma's Observation
On the last day of the war, Balrāma, the elder brother of Ka, appeared and watchedthe mace battle between the last surviving Kaurava, Duryodhana and one of the Paavabrothers, Bhīma. Balarāma observed that
catvāriśadahānyadya dve ca me nihstasya vaipuyea saprayāto'smi śravae punarāgatahśiyayorvai gadāyudha draumkāmo'smi mādhava
M.B. 9.33.5
O Ka, I left (on pilgrimage) in nakatra Puya, 42 days ago and have now returned inthe nakatra Śravaa. I am desirous to watch the mace battle of my two disciples. Death of Duryodhana
Duryodhana received a mortal wound in the mace battle and fell. At that momentthe poet reports:
rāhuścāgrasadādityamaparvai viśāpatecakampe ca maākampa pthivī savanadrumā
M.B. 9.55.10The Rāhu, in spite of it being an aparvan (improper day), attacked the sun. The
earth with its trees and forests began to tremble. Bhīma's remarks before he passed away
Some 50 days after the last day of the war, Bhīma, the grand-sire of the Kauravas,who was still alive, observed:
diayā prapto'si kaunteya sahāmātyo yudhiharaparivtto hi bhagavānsahastrāśurdivākarah
aapañcāśata rātryah śayānasyādya me gatāhśareu niśitāgreu yathā varaśata tathā
māso'ya samanuprāpto māsah puyo yudhihiratribhāgaśeah pako'ya śuklo bhavitumarhati21
M.B. 13.153.26-28By good fortune, O son of Kuntī, Yudhihira!, you have come here with all your
councilors. The thousand-rayed lord, the sun, has resumed its northerly course. I havebeen lying on my bed of arrows here for 58 nights. Stretched on these sharp-pointedarrows I have felt this period to be as if it were a century. O Yudhihira, this auspiciousmonth has come. This is a bright paka, and three-fourth part of it [the month] is still to go(according to my reckoning).
The Astronomical Knowledge at the Time of Mahābhārata
Before any analysis of the astronomical data is attempted, it will be useful to reviewbriefly the astronomical knowledge of the M.B. age. To begin with, there are reasons tobelieve that at the time of the M.B., the Vedāga Jyotia was in use.22 For instance: It is therules of the Vedāga jyotia that Bhīma cites while counting the number of years thePāavas had spent in the forest, including their time in hiding.23
The day of an event, in the epic, is pointed out by describing the nakatra of thatday. However, we do not know the exact domain of a nakatra, as understood by theancients at the time of the epic.24 It is possible that the nakatras system was used merelyto indicate an approximate position of a heavenly body in the sky. We only know for
certain that the ecliptic was divided into 27 parts, each of which was identified by a singlestar, group of stars, or nakatra. It is also uncertain if all nakatras were 13°20′ wide each aswe know them today.
Solar eclipses have been mentioned at several places in the epic by stating thatRāhu had swallowed the sun. It is doubtful, however, if the true nature of the solar eclipsehad been known then, because Rāhu, the lunar node, has been described in the epic notas a point on the ecliptic but a distinct body having finite dimensions.25
Analysis
We will attempt the analysis of the astronomical data elaborated earlier with the
Vyāsa's observation prior to the war as it is more elaborate. The planetary positionsindicated by Vyāsa are shrouded in poetic metaphors. In the following his description isrearranged in its bare essentials in a tabular form. Henceforth, this table will be called theVyāsa table. For this table, the words that a planet afflicts, overpowers, threatens,oppresses, devourers, and attacks a nakatra will be interpreted to mean a close proximityof a subject body with its object nakatra. Table 1. Vyāsa Table:
The planetary positions described or implied by Vyāsa in his conversation with theking Dhtarāra on the eve of the battle. The letter R in the table indicates a retrogrademotion. Body Location1. Moon a. near Kttikā (by inference)26
b. Near Saturn in Rohiī (Aldebaran or Antares)2. Dark planet a. Jyehā
(Rāhu27)3. Venus a. Between Pūrva Bhādrapadā and
Uttara Bhādrapadā, R.b. Citrā
4. Mars a. Maghā, R.b. Śravaa, R.
5. Saturn a. Rohiīb. near the moon (Bhagam)c. Stayed near Viśākhā for one year, R.
6. Jupiter a. Śravaab. Near Viśākhā for one year together with the planet Saturn, R.
7. A comet28 a. Puya8. Fierce planet (?) Between Citrā and Svātī
A close examination of the Vyāsa table indicates that it describes two types ofobservations for a given planet: one, a drawn out event in time, such as retrogrademotion, observed over several weeks or months and the other its location within a nakatraon a particular day before the war.29 For instance: the planet Saturn is described ashaving stayed near the nakatra Viśākhā for a year then observed at the nakatra Jyehā. The drawn out events of the Vyāsa table are summarized in the following table: Table 2. Drawn out events of the Vyāsa table a. Venus undergoing a retrograde motion between Pūrva Bhādrapadā and Uttara
Bhādrapadā.b. Mars undergoing a retrograde motion in Maghā, and also in Śravaa.c. Jupiter stays near the nakatra Viśākhā for a year along with the planet Saturn.
Undergoes a retrograde motion in the nakatra Śravaa.d. Saturn stays for one year near the nakatra Viśākhā.
Planetary Positions and Planets’ Retrograde Motions
VenusThere are two positions for Venus described in the Vyāsa table, one, in
the Bhādrapadās and the other near Citrā. Venus can be found inBhādrapadās (343°-10°) only from mid-January to mid- May (Gregorian), whereas, the war took place sometime in October-November, or during the seasons of Hemanta or Śiśira.30 Thus it isreasonable to assume that when the conversation of Vyāsa with Dharāra tookplace Venus was near Citrā and not in one of the Bhādrapadās.
Mars
In the Vyāsa table, there are two different positions of the planet Marsdescribed-one in the nakatra Maghā and then the other in Śravaa, and atboth of these locations the planet is reported to be undergoing a retrogrademotion.31 A third retrograde motion of the planet is described by Kara inJyehā, during his conversation with Ka a few weeks before Vyāsa’s dialogue with Dharāra. A retrograde motion of Mars takes place once every 780days. Any two consecutive retrograde motions of this planet normally occurin two adjacent nakatras. Therefore it is impossible to observe three separateretrograde motions of Mars in three widely separated nakatras in the sky in amatter of weeks before the war. For the analysis of the Vyāsa table, we willassume that only one retrograde motion of Mars was observed in one of thethree nakatras and that its final location was noted in either Maghā or Śravaa.
Planet Saturn and the nakatras Rohiī and Bhagam
The Vyāsa table describes the planet Saturn in the nakatra Rohiī. Inliterature two nakatras are identified by the name Rohiī: the star Aldebaran inthe constellation of Taurus and the star Antares in the constellation ofScorpio. The star Antares is also called the nakatra Jyehā in literature. Webelieve that it is the nakatra Jyehā which is referred to in the Vyāsa table. Theplanet Saturn having stayed near Viśākhā for a year will take only a fewmonths to reach the nakatra of Jyethā. Whereas, it will take 16-17 years toreach the star Aldebaran in Taurus from Viśākhā, which appears to be anunreasonable length of time.
In the mss. consulted by Bhandarkar, both bhāgyam and bhagam arefound in relation to the planet Saturn as pointed out earlier.32 The termbhāgym (fate) has no relevance here, and bhagam has several meanings toit. It means nakatra Uttara Phalgunī as well as the moon. However, theplanet Saturn will take at least 5 years to travel from Uttara Phalgunī nakatrato the nakatra Jyehā. Hence this interpretation does not seem reasonable. We interpreted, therefore, bhagam to be the moon. That is, the moon wasnear the planet Saturn or in Jyehā on the day when the alleged conversationbetween Dhtarāra and Vyāsa took place.
The Location of the SunVyāsa says that a few days before his meeting with the blind king, Dhtarāra,there was a full moon in Kttikā. A full moon in Kttikā, implies the Sun to be inAnurādhā, 180° apart. Fifteen days later, when the moon is in Jyehā, the Sunwill also move down to Jyehā the next nakatra east of Anurādhā
The solar eclipses:
Vyāsa talks about a solar eclipse just before the war and then anotherafter the death of Duryodhana. However, two solar eclipses at an interval ofone month observed from the same location are impossible. The epicdescribes many other solar eclipses in additions to the ones at the time of thewar, which all fell on improper days or "aparvai," i.e., not on an amāvasyā, or anew moon. The report of each and every one of these eclipses may not betaken seriously.33 In fact, the account of the eclipses may be the least reliableof all astronomical reports in the epic. Ancient authors all over the world had atendency to drag in an eclipse or two whenever fierce battles were fought orthe fortunes of dynasties changed hands.34 Further, the statement such as"Rāhu (the node of the moon) constantly eclipses the sun," indicates that thecause of a solar eclipse was not fully grasped by the author the epic. The Discarded Facts of Vyāsa Narration
In Vyāsa's narration as well as in Kara’s narration, there are statementsof purely imaginary nature that may be disregarded altogether. For instance,in the context of bad omens they add, "The sign of the deer on the moon hasmoved from its usual place; the star Dhruva (the north star) has shifted towardsouth."35The Dates Satisfying the Vyāsa Table
The location of planets in nakatras according to Vyāsa at the time of hisconversation with Dhtarāra must have been in either one of the following twodescribed in Table 3.
Table 3. The Planetary distributions in nakatras according to Vyāsa at
the time of his conversation with Dhtarāra.
Saturn Jupiter Mars Venus Mercury Sun 1. Jyehā ravaa ravaa Citrā open36 Jyehā
2. Jyehā ravaa Maghā Citrā open Jyehā
Methodology37
In order to find computer generated dates satisfying the planetary
distribution of Table 3, we limited the time frame between -4000 A.D. and500 A.C., and used the Julian calendar. The two time limits, we argued,adequately cover the possible period of the events of the epic. We did allour computations for the coordinates of modern Hastinapur (29;10 N,78;01E)38 In our calculations the longitudes of the planets were reduced toa fixed point on the ecliptic, the vernal equinoctial point of 1956 by applyinga correction for the precession.39 That is, the longitudes of the planets inour analysis are "nirayana longitudes."
Having found a set of dates satisfying the planetary distribution inTable 3, we next searched for the date or dates for which retrograde motionof the planets as enumerated in Table 2 applies. For this exercise, a periodof two to three years prior to the dates of Table 3, was arbitrarily chosen. We argued that any observation prior to a three-year limit would have little orno astrological significance to the author of the epic for the forthcomingevents, the impending war. Next we applied the "13-day paka" condition. Then we searched for the date when the moon was in the nakatra Mgaśirāas called for by the observation of Balarāma, after it had been observednear the planet Saturn in Jyehā by Vyāsa. From the date of the moon in thenakatrā Mgaśirā we checked if there was an uttarāyana, or the sun'snortherly motion after the winter solstice, 68 day later as implied by Bhīma. The possibilities of eclipses were searched next. After that the conditionselaborated by Kara in his conversation with Ka, and the appearance of theplanets after the death of Kara were applied to the date satisfying the Vyāsatable. Finally, the possible dates of conversation between Vyāsa andDharāra and other events were deduced.
When the computer program was run, considering the modernnakatra-domain distribution, given in the Appendix, we immediately ran intoa difficulty; as no date could be found within the time frame of -4000 A.D.and 500 A.C. that would satisfy the planetary spread of Table 3. Wesuspected that perhaps the domains of the nakatras at the time of theMahābhārata had been different than the modern ones. However, since anumber of nakatras had been identified by prominent stars in the days of theMahābhārata as they are today, their domains in the M.B. days could nothave been much different than the modern.40 At best the domain of anakatra might have shifted to its left or to its right by one nakatra span, sayabout 130, since the days of M.B.
Therefore we searched for the set of dates satisfying Table 3arbitrarily within ±20° from the mid-point of the modern nakatra domains. The span of a nakatra is taken as 130:20'. For instance: the domain ofMaghā was taken to be anywhere between 130°-170°.41
Trial 1
For this trial, we searched the dates for which the planetarylongitudes were within the range given in the table. The search wasconfined for the period -4000 A.D. and +500 A.C. as pointed out earlier.
Table 4. A planetary distribution in nakatras
nakatra LongitudeSun (open)42 180° ± 180°Mercury (open) 180° ± 180°Venus Citrā ± 13° 205° ± 20°Mars ravaa ± 13° 310° ± 20°Jupiter ravaa ± 13° 310° ± 20°Saturn Jyehā ± 13° 260° ± 20°
The following set of dates satisfied the above conditions. They
appear to repeat somewhat every 617 years except between -2784 A.D. and-3021 A.D.; and -1550 A.D. and -1016 A.D.
Table 5. Dates satisfying the planetary configuration of Table 4.
Year Period1. -3638 A.D.( Julian)43 Oct. 24 - Nov. 1
2. -3021 Oct. 13 - Nov. 33. -2784 Oct. 11 - Oct. 204. -2167 Sept. 29 - Oct. 315. -1930 Sept. 25 - Oct. 46. -1550 Oct. 25 - Nov. 37. -1313 Sept. 14 - Oct. 148. -1016 Oct. 19 - Nov. 109. -459 Aug. 26 - Sept. 9 10. -399 Oct. 16 - Nov. 1911. -162 Oct. 2 - Oct. 2512. 218 A.C. Oct. 19 - Nov. 813. 455 Oct. 4 - Oct. 28
A typical set of dates satisfying the conditions of the Table 4 is given inTable 6.
Table 6. Set of Days in -3021 A.D. satisfying the planetary configurationof Table 4.
Date Sun Mercury Venus Mars Jupiter SaturnOct. 13 247° ± 1° 257° ± 1° 215° ± 1° 291° ± 1° 305° ± 1° 257° ± 1°
14 248 259 215 291 305 25715 249 260 215 292 306 25716 250 262 215 293 306 25717 251 263 216 294 306 25718 252 265 216 295 306 25719 253 266 216 295 306 25720 254 268 217 296 306 25821 255 269 217 297 307 25822 256 271 218 298 307 25823 257 272 218 298 307 25824 258 274 219 299 307 25825 259 275 219 300 307 25826 260 277 220 301 308 25827 261 278 220 302 308 25828 262 280 221 302 308 25829 263 281 221 303 308 25930 264 283 222 304 308 25931 265 284 223 305 309 259
Nov. 1 266 285 223 305 309 259 2 267 287 224 306 309 259 3 268 288 225 307 309 259
Jupiter and Saturn Near Viśākhā
We interpreted the statement of Vyāsa that "Jupiter and Saturn, afterapproaching the nakatra Viśākhā had become stationary for one year" tomean that they were observed between the star Spica (Citrā) on the westand the nakatra Anurādhā on the east of Viśākhā, or between 203° and240°. This region of space is rather devoid of bright stars. The two verybright planets in this region would be very conspicuous. The slowmovement of the two planets coupled with their retrograde motions musthave made them appear stationary in this region for a long time, say for ayear.
We searched for a simultaneous presence of the two planets in a timeperiod of 2-4 years prior to the dates in Table 5. We found that this conditionwas satisfied more or less for just about every date of the table. Forexample, for -3021 A.D. date, the two planets stayed together from October25, -3025 A.D. until January 15, -3023 A.D. between 203° and 240°.
Retrograde Motion of Planets
With the assumption that the domain distribution nakatras in the M.B.days might have been different than it is today, as pointed out earlier, weconsidered the retrograde motion of the planets within a region of ±20° fromthe midpoint of the object nakatra.
Retrograde Motion of Venus
Vyāsa reports a retrograde motion of the planet Venus within thenakatras Uttara Bhādrapadā and Pūrva Bhādrapadā.44 This condition issatisfied for five dates of Table 5. Venus retrogrades within ±13° of the two
Bhādrapadās for the dates: -3638 A.D., -3021 A.D., -1930 A.D., -1313 A.D.,and -162 A.D. For instance, For the date -3021 A.D. the retrograde motionbegins 10° east of Uttara Bhādrapadā, in Revatī, and ends within UttaraBhādrapadā. Venus undergoes a second retrograde motion betweenAugust 30 and Oct.10, -3021 A.D. in Svātī. The motion ends 4° from thestar Citrā.45 However, Vyāsa does not mention this retrograde motion.
Retrograde Motion of Mars
For its final location in Śravaa, Mars is supposed to undergo aretrograde motion in nakatra or the star group Maghās (143°-157°). Marsretrogrades by about 16°-20° every 780 days or 2.17 yr. while going aroundthe sun. We found that for the date, -3638 A.D. its retrograde motion takesplace within and around Maghā. For -3021 A.D., the retrograde motion ofthe planet begins on December 24, -3022 A.D. at 184° in Hastā, 27° to theeast of Maghā. It ends at 166° in Pūrva Phalgunī about 9° to the east ofMaghā.46 For the date -2784 A.D. it takes place at distance of 15° also tothe east of Maghā. For all other dates in Table 5, it is no closer than 48° tothe nakatra Maghā.
Retrograde Motion of Jupiter
According to the Vyāsa table, Jupiter undergoes a retrograde motionin the nakatra Śravaa. Jupiter retrogrades every 399 days or 1.1 yr. whilejourneying around the sun. We found that except for the date 218 A.C., theplanet underwent a retrograde motion within ±11° of the nakatra Śravaa. For the date 218 A.C., its retrograde motion approached within 15° to theeast of the nakatra Śravaa, and for the date -3021 A.D., the planetunderwent a retrograde motion between April, 19, -3021 A.D. and August 9,-3021 A.D., from 307° in Śravaa .to 297°, a distance 6° west of Śravaa. The Thirteen Day Paka
In his description of inauspicious omens before the war, Vyāsa pointsout a thirteen day paka. A lunar month is divided into two pakas, dark andbright. A dark paka begins after the full moon and ends at the next newmoon, and the bright paka following a new moon ends at the following fullmoon. As the sun and moon travel with varying speeds, the length of a pakacan be anywhere between 14 to 17 days. The average length of a paka,however, is 15 days. According to the Siddhānta Hindu Jyotia, a 13 daypaka is possible, in principle at least, because of this varying speed of thesun and the moon.47
We did not find any 13-day paka around the dates of Table 5,according to the Siddhānta Hindu Jyotia. It is not known how amāvasyā(new moon) and the pūrimā (full moon) were calculated in the days of theMahābhārata. We suspect that in the M.B. days, the "astrologers" reliedprimarily on their visual observations to ascertain a new moon or a fullmoon. It is rather easy to decide when the moon is new as there is no lightin it that night. However, in the case of a full moon it is difficult to judgewhen the moon is 100% illuminated. A simple criterion can eliminate theuncertainty, however, whether the day had been indeed a full moon. Thecriterion is to watch the rise time of the moon in relation to the setting of thesun. If the moon rises just before the sunset, the day is a full moon or apūrimā, and if it rises just after the sunset, the day is one-day-past the fullmoon or past the pūrimā.48 Using this criterion, we found four dates inTable 4 for which there were a 13-day paka "prior to the war" as called for byVyāsa.
For example, we found that for -3021 A.D., the paka betweenSeptember 27, -3021 (new moon) and October 10 (full moon), had 13 daysto it. On the night of September 27 there was no light in the moon, and onOctober 11, the moon rose 3 minutes after the sunset at Hastinapur. ThusOctober 11 could be technically called the day after pūrimā, and October10, the pūrimā or a full moon.49'50 The paka therefore had 13 days. Similarly the pakas between October 16, -2784 A.D. (new moon) andOctober 29 (full moon); September 14 and 27 and October 14 and 27, -1313A.D.; September 27 and October 11, 455 A.C. all had 13 days.
The Moon on the First Day of Battle and Solstice thereafter
The date of the first day of the war is calculated from a statement ofBalarāma. On the eighteenth day of the war, Balarāma who had justreturned from a pilgrimage, observed that the nakatra on the day of hisreturn was Śravaa (310°±7°). Calculating backward from Śravaa, the moonon the first day of the war, 17 days earlier, then must have been in Mgaśiras(83°±7°). Further, in his conversation with the blind king, Vyāsa reports thatthe moon on the day of his conversation was near Saturn in Jyehā. First, wecalculated the dates for which the moon would be in the nakatra Jyehā, for
the set of Table 5. Then we determined the dates for which the moon wouldbe in the nakatra Mgaśiras next, a few days later. Having calculated thedates of the first day of the war for the set of Table 5, we calculated next thenumber of days to the forthcoming winter solstice from these dates.
Bhīma, a celebrated hero of the epic, was mortally wounded on thetenth day of the war as mentioned earlier. He lived on for another 58 daysand passed away just after the winter solstice, when the sun had resumedits northward journey or underwent uttarāyana. Thus according to the epic,the journey of the sun to north or the uttarāyana was observed 68 days afterthe first day of the war, or when the moon was in Mgaśiras.
The first day of battle and solstice thereafter, for the dates of Table5, are summarized in the following Table.
Table 7. The First Day of the Battle and the Next Winter Solstice
Date First day of Battle: Winter Solstice No. of Days ( Moon in Mgaśirā ± 7°) since the first
day of war until the solstice
-3638 A.D. Nov. 19 ± 1 day Jan. 17, -3637 A.D. 59 ± 1 day
-3021 Nov. 9 Jan. 13, -3021 65
-2784 Oct. 29 Jan. 10, -2783 71
-2167 Oct. 19 Jan. 6, -2166 77
-1930 Oct. 12 Jan. 5, -1929 86
-1550 Nov. 7 Jan. 2, -1549 57
-1313 Oct. 29 Jan. 1, -1312 64
-1016 Nov. 13 Dec. 29, -1016 47
-459 Sept. 12 Dec. 26, -459 106
-399 Nov. 2 Dec. 25, -399 54
-162 Oct. 24 Dec. 24, -162 62
218 A.C. Oct. 23 Dec. 21, 218 A.C. 59
455 Oct. 15 Dec. 20, 455 67
As pointed out, Bhīma breathed his last after the northern motion of
the sun, the uttarāyana, had been observed. A naked eye observer will
notice a shift in the position of the sun from its solstitial position only when it
has moved by at least one arc-minute. One arc-minute is considered to be
the resolving power of an average eye. Near a solstice, it takes the sun
about three days to move nearly one arc-minute. Thus uttarāyana, or the
northerly journey of the sun should have been observed after three or more
days only, after the winter solstice. With this reasoning, three dates in the
above table, namely, -3021 A.D., -1313 A.D. and 455 A.C. are the only ones
that satisfy the condition that there was uttarāyana of the sun 68 days after
the first day of the Mahābhārata battle.51
The Paka at the Time of Solstice
Bhīma, just before his death, observes, "the paka at the time must be
the bright one (śukla), and three parts of it [the present month] were still
remaining."52 However, for the three dates, for which the solstice condition
is satisfied, the paka turns out to be dark (ka) and not bright (śukla).
Further, for the date -3021 A.D., nearly three-fourth of the month (Phālguna),
about 22 days, remain, as called for, when uttarāyana or the northerly
motion of the sun is observed.53 For the other two dates, -1313 A.D. and
455 A.C., it is 20 days, and 16 days that remain in the month respectively.
Lunar and Solar Eclipse at an Interval of 13 Days
Vyāsa describes a lunar eclipse followed by a solar eclipse 13 days
later. Considering the minimum length of a modern day paka to be 13.8
days and the maximum duration of lunar and solar eclipses to be 6 hours
and 4 hours respectively, it can be shown that a lunar eclipse followed by a
solar eclipse at an interval of 13 days is not possible. A pair of eclipses in
which the solar eclipse occurs first and a lunar eclipse less than full 14 days
later is possible. However, we did not find any such pair of eclipses for the
set of dates in Table 5.5455 The date of -3021 A.D. for which most of the
conditions in Table 8 are satisfied had three eclipses in succession.56
(Double check this reference) It is not clear if all these were visible at the
location of Hastinapur. These dates are given in the following table.
Table 8. The Eclipses in -3021 A.D.
a. October 27, Partial Solar eclipse
b. November 10 Total Lunar eclipse
c. November 25 Partial Solar eclipse
Trial 2
Next we considered the planetary combination for which the planet
Mars’ final location is in the nakatra Maghā, after it had undergone a
retrograde motion earlier in the nakatra Śravaa. The planetary positions for
this search are as follows.
Table 9. Planetary combinations 2.
planet nakatra longitude
Sun open 180°±180°
Mercury open57 180°±180°
Venus Citrā 205°±20°
Mars Maghā 150°±20°
Jupiter Śravaa 310°±20°
Saturn Jyehā 260°±20°
The set of dates satisfying these conditions are as follows.
Table 10. Set of dates satisfying conditions of Table 9.
-3934 A.D. July 3 - July 28
-3637 Aug. 8 - Aug. 23
-2783 July 21 - Aug. 10
-2725 Oct. 17 - Oct. 27
-2606 Aug. 11 - Aug. 16
-2108 Oct. 8 - Nov. 7
-1929 July 18 - July 28
-1752 July 24 - Aug. 3
-1491 Oct. 19 - Oct. 24
-1254 Oct. 15 - Oct. 25
-957 Oct. 16 - Nov. 15
-340 Sept. 8 - Nov. 21
-103 Oct. 8 - Nov. 2
Retrograde Motion
In the set of Table 10, there were no dates satisfying the retrograde
motion of Mars in Śravaa and Venus in Bhādrapadās. The retrograde
motion of Jupiter in Śravaa is satisfied for nearly all the dates, except one.
The details are as follows:
Retrograde Motion of Mars in Śravaa
Mars should have undergone a retrograde motion in Śravaa, if its
final position is in the nakatra Maghā. However, we found that retrograde
motion of Mars does not take place in or near Śravaa for this set of dates.
Mars approaches within 17° of Śravaa for the date -1752 A.D. only, and for
the other dates its retrograde motion takes places even farther than that.
Retrograde Motion of Venus in Uttara and Pūrva Bhādrapadās.
For the date -1254 A.D., the retrograde motion of Venus comes as
close as 35° to Uttara Bhādrapadā. For all other dates it is much farther
than that.
Retrograde Motion of Jupiter in Śravaa
Jupiter undergoes a retrograde motion in Śravaa for all dates except
-3637 A.D. for which it takes place in Dhanihā-Śatābhiaja, at a distance of
15° from Śravaa.
Retrograde Motion of Mars in Jyehā according to Kara
For our exercise we have chosen Śravaa or Maghā, as the final
destination of Mars. During his conversation with Ka, Kara points out Mars
retrograding in Jyehā. With its final location in Śravaa, Mars undergoes a
retrograde motion for the date -1550 A.D. only of Table 5. With its final
location in Maghā, on the other hand, Mars does not undergo a retrograde
motion in Jyehā for the dates of the Table 10,. However, for the date -1929
A.D. of Table 10, retrograding in Viśākhā, the planet comes as close as 20°
to the west of Jyehā.
Date -3021 A.D.: Kara's Observation
For the date -3021 A.D., for which most of the conditions of the Vyāsa
table are met, we looked for the date when the conversation of Kara with Ka
must have taken place. We found that the conversation must have taken
place around September 20. The planetary configurations for September 20
are as follows:
Table 11. The Planetary Configuration According to
Kara58
Planet Longitude Nakatra Dist. from the Expected Nakatra
Expected
Mars 271° Jyehā 8° to the east of JyehāMercury 219° Svātī 9° to the east of Citrā
(A planet)59
Saturn 252° Jyehā 11° east of β,δ,π Scorpii, the stars of or Prajāpati Prajāpati60
Seven days later, on the 27th of September, there was a new moon
as Kara points out and the nakatra that day turns out to be Viśākhā which
was ruled by Indra as called for by the observation of Kara.61
Planets at the time of Kara's Death
The epic says that at the time of Kara's death, the planet Mercury
appeared in the sky and the planet Jupiter threatened the nakatra Rohiī.
However, our analysis does not support this.62 Mercury will be a morning
star on November 25, the 16th day of the war, when Kara fell. Besides, it
will be only 7° from the sun and with 5% illumination, too difficult to be seen
in the morning twilight. Jupiter, on the other hand, will be in Śravaa then,
nearly 60° from Rohiī and thus can hardly be called threatening the nakatra
Rohiī.
Rāhu in the Vyāsa Table
In the Vyāsa Table we have identified the "dark planet" as Rāhu. For
the date October 27, -3021 A.D., the lunar node, Rāhu falls at 275°, or 12°
to the east of Jyehā.
The Nakatras shifted 6° - 10° and the planets
A close examination of the planetary distribution according to the
tables of Vyāsa and Kara reveals that many planets lie just outside the
present day Nakatra domains given in the Appendix. However, if the
Nakatras are shifted by 6° - 10°, primarily to the east, the planetary positions
fall within the expected Nakatras. This fact suggests that when the epic was
written, the domain distribution of the Nakatras had been different than it is
today in the cannons of Hindu astronomy.
Table 12 below elaborates this fact.
Table 12. The Nakatras shifted 6° - 10° and the planets.
Planet Date Longitude Nakatra shifted Table
to east by 10°
Mercury Sept. 20, -3021 A.D. 219° Citrā (207°- 220°) Kara
Venus Oct. 27, -3021 A.D. 220°63 Citrā (207°- 220°) Vyāsa
R. Motion of Jan. 22 to P. Bhādrapadā -
Venus March 9, -3022 A.D. 19° - 3° U. Bhādrapadā Vyāsa
(353° - 20°)
===================================================================
Planet Date Longitude Nakatra shifted Table
(-3021 A.D.) to east by 8°
Mars Sept. 20 270° Jyehā (258°- 271°) Kara
Saturn Oct. 27 258° Jyehā (258°- 271°) Vyāsa
Rāhu Oct. 27 275°64 Jyehā (258°- 271°) Vyāsa
========================================================
=========
Planet Date Longitude Nakatra shifted Table
(-3021 A.D.) to west by 6°
Mars Oct. 27 302° Śravaa (297°-311°) Vyāsa
Jupiter Oct. 27 308° Śravaa (297°-311°) Vyāsa
R. Motion of April 9 to
Jupiter Aug.9 307° - 297° Śravaa (297°-
311°)
V
y
ā
s
a
Maghās and Prajāpati
According to Vyāsa, before the war, between Dec. 24, -3022 A.D. and
March 10, -3021 A.D., Mars undergoes a retrograde motion from 184° to
166°, in the star group Maghās. It is not known what stars were included in
the asterism Maghās during the M.B.days. If the asterism included stars
within 184° and 166°, somewhat 9° or more to the east of the naktra Maghā
(143° - 157°), the Vyāsa condition is satisfied. Similarly, if Prajāpati
included stars 11° east of β,δ,π Scorpii, the observation of Kara is also
satisfied.
Fierce planet
Vyāsa says, "A fierce planet has come between Citrā and Svātī."
The model points to Venus to be this "fierce planet" as according to Table
12, Venus falls exactly between the naktras Citrā and Svātī.
Critique of the Exercise
The model developed in this paper shows that most of the conditions
specified in the epic are met by the date -3021 A.D. However, a number of
questions may be raised about this date.
Jupiter and Saturn
According to the model developed in this archaeoastronomical
exercise, Jupiter and Saturn stay together for nearly a year around Viśākhā,
as required by the statement of Vyāsa, between October 25, -3025 A.D.
and January 15 -3223 A.D., full 2 ¾ years before his meeting with the blind
king Dhtarāra in October -3021 A.D. A question may be raised, "Why
something that happened nearly three years earlier is considered
astrologically important by Vyāsa?" The model has no answer to the
question.
The Second Retrograde Motion of Venus
The second retrograde motion of Venus takes place just prior to the
war, between August 30 and October 10, -3021 A.D., but Vyāsa makes no
mention of it during his conversation with the blind king.
The Paka at the Time of Winter Solstice
According to our model, the war started on November 9, -3021 A.D.
when the moon was in nakatra Mgaśiras, and full. Sixty days later, at the
time of the solstice, the paka then will be dark and not "bright" as pointd out
by Bhīma before he passed away.65
Constellation Brahmarāśi
The model does not identify the constellation Brahmarāśi in the Vyāsa table.
Conclusion
The archaeological exercise undertaken for this paper is based on a
number of assumptions. One, the astronomical reports in the epic belong to
the earliest version of the epic; and two, that they are based on visual
observations and not on astronomical computations. Three, that the domain
distributions of the lunar mansions of the Hindu astronomy, the nakatras,
were different in the ancient times than they are today.
Nakatra Domains
The second assumption above is supported to some extent by the planetary
events for the date -3021 A.D. for which most of the planetary conditions
described in the epic are satisfied.66 For this date, the reported retrograde
motions of the planets Venus, Mars, and Jupiter as reported by Vyāsa
(Table 4), and the positions of the planets, Mars, Mercury or Venus, and
Saturn as reported by Kara (Table 11), all fall 8°-12° to the east of the
modern domains. This suggests that the domain boundaries of the
nakatras, when the epic was written, were 8° - 10° to the east of their
present nakatra boundaries as reproduced in the Appendix. Thus if the
domains of the nakatras are shifted to the east by about 8° - 10°, all the
planets fall within their prescribed nakatras. The nakatra Śravaa appears to
be an exception to this rule, however. The final location of Mars and the
retrograde motion of Jupiter is to the west of Śravaa by 1° and 6°
respectively. This suggests that the domain of nakatra Śravaa could have
been a few degrees to the west of what it is today. Similarly, the star group
Maghās could have included stars of two Phalgunīs somewhat 9° to the east
of modern nakatra of Maghā.
The War and the Date -3021 A.D.
According to this exercise, most of the planetary configuration
described in epic before the war match for the year -3021 A.D.,
suggesting, therefore, that the war started on November 9, and ended 17
days later on November 26, -3021 A.D. (Julian) .67
Did the war really took place in -3021 A.D., the date for which most of the
conditions of the epic are satisfied? Unfortunately, the analysis of the paper
cannot answer this question with certainty. All one can say, with some
degree of certainty, is that in October of -3021 A.D., the configuration of the
planets in the sky had been the same as in Table 6 and that this
configuration of planets matches with the Vyāsa table. The answer
regarding the war, in a way, hinges on the time when the epic was written. If
the events of the epic, particularly the ones regarding the planets, were
observed and jotted down by a contemporary author, such as Vyāsa, as
asserted by the epic, the analysis has considerable merit. On the other
hand, if Vyāsa was not a contemporary witness of events, but someone like
Homer, who generations after the events, compiled and elaborated oral
traditions and bardic tales into an elaborate poem, the analysis of the paper
is no more than an interesting exercise in archaeoastronomy, and the date
of -3021 A.D. just a coincidence.
Acknowledgements
The author wishes to thank Anjani K. Mehra for his encouragement,
and discussions he had with him. The computer program for the analysis of
the Vyāsa table was written by Bill Bolten. The author appreciates his
assistance.
APPENDIX
The first points and the mid-point of the nakatras according to modern
classification, are as follows.68
naktra First Point Mid-point
1. Aśvinī 23;15 29;552. Bharaī 36;35 43;153. Kttikā 49;55 56;354. Rohiī 63;15 56;355. Mgaśiras 76;35 83;156. Ārdrā 89;55 96;357. Punarvasu 103;15 109;558. Puya 116;35 123;159. Āśleā 129;55 136;3510. Maghā 143;15 149;5511. Pūrva Phalgunī 156;35 163;1512. Uttara Phalgunī 169;55 176;3513. Hasta 183;15 189;5514. Citrā 196;35 203;1515. Svātī 209;55 216;3516. Viśākhā 223;15 229;5917. Anurādhā 236;35 243;1518. Jyehā (Rohiī) 249;55 256;3519. Mūla 263;15 269;5520. Pūrva Āāhā 276;35 283;1521. Uttara Āāhā 289;55 296;3522. Śravaa 303;15 309;5523. Dhanihā 316;35 323;1524. Śatabhiaj 329;55 336;3525. Pūrva Bhādrapadā 343;15 349;5526. Uttara Bhādrapadā 357;35 3;1527. Revatī 9;55 16;35
END NOTES 1. The epic itself reports its three successive narrators, namely, Vyāsa, Vaiśampāyana,
and Ugraśrava. We will assume for the analysis of this paper that the astronomical
events reported in the Mahābhārata belong to the original version of Vyāsa and not
added later on with other stories.
2. It is sometimes said that the omens described in the epic Mahābhārata have been
directly borrowed from the Babylonian astrology. However, we did not find any
resemblance between the Babylonian omens and the Mahābhārata omens. See R.
Campbell Thompson, The Reports of the Magicians and Astrologers of Nineveh
and Babylon in British Museum, Vol. 1, London, Luzac & Co., (1900).
3. A summary of views regarding the dating of the epic is given by Gupta, S.P., and
Ramchandran, K.C., Mahabharata Myth and Reality Differing Views, Delhi, (1976).
4. For example see Vedavyas, E., Astronomical Dating of the Mahabharata War, Delhi
(1986).
5. The computer programs used for this research were: 1. modified version of Planetary
Programs & Tables -4000 to +2800, Pierre Bretagnon/Jean-Louis Simon,
Winllmann-
Bell Inc., Richmond, (1986). 2. LoadStar Plus, Zephyr Services, Pittsburgh, (1990).
3. CalMaster 2000, Zephyr Services, Pittsburgh, (1991).
6. For a brief story of the epic see Narsinhan, Chakravarthi V., Mahābhārata, Columbia
Univ. Press, (1965).
7. This paper is based primarily on the following editions of the epic:
1. The Mahābhārata, ed. Sukthankar, S. Vishnu et al, publ. by Bhandarkar Oriental
Research Institute, Pune, (1942-1966). This reference will be called Bhandarkar in
this paper.
2. The Mahābhārata, ed. Satavalekar, Sreepad V., Paradi, (1972).
3. The Mahābhārata, Eng. tr. by Roy, Pratap C., Calcutta.
Mahābhārata will be abbreviated as M.B. from now on.
8. See the Appendix for modern designantion of nakatras within the zodiac.
9. Here "begnning of the war" should be intepreted as "the beginning of the preparations
for the war" and not necessarily engaging in the first battle of the war.
10. A vast region of space spanning from the stars β,δ,π Scorpii of Anurādhā (237°- 250°)
to the star α-Virginis, or Spica, of nakatra Citrā (197°-210°), was known as
Prajāpati in ancient India. Allen, Richard Hinckley, Star Names, Their Lore and
Meaning, p. 181, Dover Publications Inc., New York, (1963).
11. One of the lunar nodes is called Rāhu in Hindu astronomy.
12. An emended version given in the Bhandarkar edition of the M.B. is as follows:
"rohiimpīayatyevamubhau ca śaśibhāskarau" Bhandarkar, M.B., 6.3.16, p. 14,
(foot notes).
"The moon and the sun both are afflicting the nakatra Rohiī."
13. The description indicates a lunar eclipse. In the month of Kārtika, the moon at full is in
the nakatra Kttikā.
14. A number of translators have interpreted "white planet" as Ketu, one of the nodes of
the Moon's orbit. For example see Roy, Pratap Chandra, M.B. Vol. 4, Udyoga
Parvan, Calcutta, Op. Cit. However, the accepted meaning of "white planet" is
Venus. Besides, Ketu is not mentioned anywhere as such in the Mahābhārata
chapters of interest for this paper.
15. We have taken "bhagam" to mean the Moon. In a number of mss. consulted by
Bhandarkar, "bhagam" is replaced by "bhāgyam" which a number of translators
interpret as the nakatra Pūrva Phalgunī. See Satavalekar, M.B. 6.3.14, Op. Cit.
However, we have not accepted this interpretation as will be explained later.
16. In certain retention of the M.B. the "dark planet" (śyāmo graha) is given as the "white
planet" (śveto graha) See Bhandarkar, M.B. 6.3,15. We have rejected this
interpretation as "white planet," Venus has already been indicated near the nakatra
Citrā. 17. It is not clear what is meant by "fierce planet." Its most likely meaning is Venus.18. It is not clear what is meant by Brahmarāśi here.
19. In a number of mss. "meghāvanarudhamākāśaa" is replaced by "maghāviayagah
somah," Bhandarkar, M.B. 6.17.2. We have rejected "maghāviayagah somah," i.e.,
"the moon was in the nakatra Maghā." Instead we have taken the interpretation
"meghāvanarudhamākāśataddina" that "the sky was clouded over that day" found
in one of the Bhandarkar mss.
20. The seven planets include Sun and the Moon and the five well known planets.
21. In a number of mss. the first line of this verse has the following version:
"māgho'ya samanuprāpto māsah puyo yudhihira"
"The auspicious month of Māgha has arrived, O Yudhihira." This version does not
agree with the analysis of this paper. See Bhandarkar, M.B. 13.153.28. The
second part of the verse is found in nearly all the mss. consulted by Bhandarkar.
Ibid.
22. Vedāga Jyotia of Lagadha, in its k and Yajus Recensions, Sastry, Kuppanna T.S.; ed.
Sarma, K.V.; New Delhi, (1985).
23. Ibid, p. 65.
24. Pingree, David and Morrissey, Patrick, "On the Identification of the Yogatārās of the
Indian Nakatras," J. Hist. Ast., Vol. XX, pp. 99-119, (1989).
25. Rāhu, the lunar node, has a diameter of 12,000 yojanas (approx. 16,000 Km)
according to the M.B. and is not a geometrical point. Compared to Rāhu the
diameter of the Sun is merely 10,000 yojanas (approx. 14,000 Km). M.B. 6.13.40-
43.26. See footnote 13.27. We have interpreted "dark planet" as Rāhu, because it is an invisible object,28. Because a comet in the sky can appear at any time, it is of not much help to the
analysis of this paper.
29. An interpretation differing from this paper is given by the author in Sharma, Virendra
Nath, "Model of Planetary Configurations in the Mahābhārata: An Exercise in
Archaeoast ro no my," Archaeoastronomy, pp. 88-98, Vol. IX, Numbers 1-4,
January-December, 1986. The paper elaborates upon an interpretation that the
Vyāsa table is a result of dialogues between Vyāsa and Dhtarāra at three different
times.
30. Ka went on his peace mission in the month of Kārtika (Fall season). Secondly, when
Balarāma proceeded for his pilgrimage, 24 days before the start of the war the Sun
was in the nakatra Anurādhā (237°-250°). Third, the Sun's northward journey, the
uttarāyana, took place 68 days after the commencement of the war. All these three
independent facts indicate that the conversation of Vyāsa with Dhtarāra took place
sometime in October (Gregorian), and not sometime between January and May
(Gregorian).
31. It should be pointed out that in earlier literature, such as Taittirīyasahitā and
Atharvaveda, Maghā nakatra is Maghās, a plural signifying a group of several stars
together. Pingree, David and Morrissey, Patrick, Op. Cit.
32. Bhandarkar, M.B. 6.3.14.
33. For instance, when the Pāavas were going to the forest after Yudhihira had lost the
gambling duel, there was an eclipse.
"rāhuragrasadādityamaparvai viśāmpate"
"The Rāhu attacked the Sun on an `improper day'." M.B. 2.71. 26
34. The reliability of eclipse reports in the ancient literature has been discussed by Robert
Newton. See Newton, R., Ancient Astronomical Observations and the
Accelerations of the Earth and Moon, pp. 43-47, Baltimore, (1971).
35. The statement regarding the star Dhruva could be of a later period as in prehistoric
times there was no star that could be called a pole-star as the Polaris is these
days. Around 2600 B.C. the star Thuban in constellation Draco, was close enough
to be called the Pole star. Around 1000 B.C. the star Thuban would have been 23°
away from the pole. In 1500 B.C. it must have been 16° and in 2000 B.C. about
9°. Further, the shift of the pole of the earth being so slow, (taking 26,000 for one
complete circle, or nearly 72 years for 1° shift) that it is impossible that someone
would notice its shift within a period of few months before the war.
36. Since no clear position of the planet Mercury has been indicated, we have considered
its position "open" for this combination.37. An interpretation differing from this paper is given by the author in Sharma, Virendra
Nath, "Model of Planetary Configurations in the Mahābhārata: An Exercise in
Archaeoastronomy," Archaeoastronomy, pp. 88-98, Vol. IX, Numbers 1-4, January-
December, 1986. The paper elaborates upon an interpretation that the Vyāsa tableis a
result of dialogues between Vyāsa and Dhtarāra at three different times.
38. It is surmised that the city of Hastinapur described in the M.B. must not have been
very far from the modern town by the same name.
39. Because the nakatras do not shift with precession, their longitude has been calculated
from a fixed point on the ecliptic. This fixed point is taken as the vernal equinoctial
point of 285 A.D. The tropical longitude of this initial point has been adopted as
23;15;11 for the 21st March, 1956. The Indian Astronomical Ephemeris, (publ.
yearly), p. 413., Delhi, (1981). See the Appendix.
40. For example, the nakatra Citrā is named after a star by the same name (α-Virginis).
41. Through out this paper, the nakatra domains reported are modern as given in the
Appendix unless specified otherwise.42. In order to consider broader possiblities of the dates, we have taken the position of the
Sun as open, rather than in the nakatra Jyehā.43. We will use A.D. through out this paper instead of B.C. Between B.C. and -A.D., the
difference is of one year. For example: 11 B.C. equals -10 A.D.
44. Venus undergoes a retrograde motion every 584 days or 1.6 yr roughly for about three
months covering a distance of nearly 15°-16°.
45. It is tempting to speculate that Venus is the "parua graha," or the "fierce planet"
threatening the nakatra Citrā (Spica) as remarked by Vyāsa. However, it should be
pointed out that we have not seen Venus being described as a fierce planet in
literature. 46. See Ref. 31.47. The tithi of a day, according to the Siddhānta Hindu Jyotia, is calculated at the time of
sunrise from the longitudinal difference of the Moon and the Sun. The number of
tithis elapsed by a day equal to the complete digits of the fraction: (longitude of the
moon-
longitude of the sun)/12. However, no tithis, other than amāvasyā (new moon) and
pūrimā (full moon) are mentioned in the epic at the time of the war. It seems that in
the days of the Mahābhārata, people relied primarily on visual observation rather
than on observing longitudes of the Sun and the Moon with instruments.48. This agrees with the Siddhānta Jyotia reckoning of pūrimā, i.e., if the moon rose after
sunset, its longitude difference with the sun will be greater than 1800, and thus theday
will be a day after pūrimā.49. At midnight of October 10-11, the moon was in the nakatra Kttikā and 99% illuminated.
50. It is debatable if this criterion was indeed used by the M.B. people.
51. The "Julian Day Numbers" at noon, Universal Time for the three dates are: -3021 A.D.
(617950), -1313 A.D. (1241786), and 455 A.C. (1887534).
52. This statement is found in all mss. collected for the Bhandarkar edition of the M.B.
53. The month considered here is pūrimānta or ends on a full moon.
54. We used several programs for our search of eclipses:
1. a. LodeStar Plus, b. CalMaster 2000, c. SunTraker, d. EclipseMaster Plus, e.
EclipseComplete, all publ. Zephyr Services, Pittsburgh, U.S.A.
2. Canon of Lunar Eclipses: 1500 B.C. - A.D. 3000, Bao-Lin Liu and Alan D. Fiala,
by Willman and Bell, Richmond.
3. Kudlek, M., Univ. of Hamburg, Germany., private communication.
It should be pointed out that results of eclipse programs matched quite well
up to 800 B.C. Beyond that, their accuracy deteriorates and differences of
about one to two hours in timing of events around 2000 B.C. are found
between different programs. The difficulty lies in the fact there are no data
available to verify the results of various programs beyond 800 B.C.
55. Mehra et al calculated the solar and lunar eclipses taking place in northern India
between 3500 B.C. and 20 A.D. They looked for the conditions that will give a rare
paka of 13 days flanked by solar and lunar eclipses. They found only 3 dates
which satisfied the desired conditions: -168 A.D., -2291 A.D., and -2920 A.D.
Mehra, Anjani K., and Sharma, Virendra Nath, "Ancient Indian Chronologies and
Solar and Lunar Eclipse Calculations," Paper read at the International Symposium,
"Ancient Indian Chronology," Jan. 5-6, Hyderabad, (1994).
56. These eclipses were predicted by the program CalMaster 2000, Op. Cit, and not
repeated by any other program. According to the Lunar Tables and Programs, the
sun and moon missed by 51′, on October 27, -3021 A.D., which is within the
accuracy of the program of ±1° for that far in the past.
57. In order to find for all possible positions of Mercury, its coordinates are taken "open" in
this search.
58. This table will be called " Kara Table" from henceforth.59. We have interpreted "a planet" to mean Mercury here.60. See Ref. 10 for Prajāpati. It is possible that some sections of the nakatra Jyehā were
also included in the constellation Prajāpati.
61. Refer Allen, p. 175, Op. Cit.
62. The verse containing the statement that "Jupiter threatened Rohii" could be of a later
addition to the epic.63. It is noteworthy that Venus, interpreted as "fierce planet" lies on the boundary of Citrā
and Svātī, as called for by the Vyāsa table.64. The longitude of Rāhu, 275° on October 27, -3021 A.D. is a calculated value.
Since Rāhu is an invisible object, someone, relying purely on visual observation,can
only guess its location. Thus its location 4° beyond Jyehā (258°- 271°) ispermissible. 65. It should be pointed out that some scholars have doubted that Bhīma of the epic wasa
a real person. Saha, M.N., "The Age of the Mahābhārata," Science and Culture, pp.482-
488, March 1939.66. This date agrees with the traditional date of the Mahābhārata events.67. The Julian day number corresponding to November 9, -3021 A.D. (Julian) is 617950.68. For the purpose of calculating nakatras, the vernal equinoctial point of 285 A.D. has
been adopted as the origin, for the measurements of longitudes. The precise
position of this point has been adopted as 23° 15′ 00″ for 21st March, 1956. The
Indian Astronomical Ephemeris, p. 413, Delhi, (1981).
