dating the mahabharatha

7/30/2019 Dating the Mahabharatha

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Dating the "Mahabharatha" by Dr S Balakrishna

Mahabharata is a great epic poetic story from India (India is hence forth referred to as

Bharata) in Sanskrit, considered by many to be a folklore type historical document. This epicdetails politics of an old era covering many generations, with a climax in a major battle thatoccurred in Northern part of the Bharata. Whether it is considered as historical fact or fiction,Mahabharata story and its moral ethos have had profound influence on millions ofBharateeyas for many generations. The battle is said to have occurred before the transitionof eons (rough translation ofyuga) from Dwapara yuga eon to kali yuga eon.

Aryabhata, a famous early astronomer from Bharata with contributions to science made

estimates ofKaliyuga start nearly 1500 years ago. His estimate of, and the time of moonrevolution around the earth are so accurate, that his works are being extensively researched.There is also evidence to suggest he used zero in his work. Aryabhata (476-550 AD) statedthat Kaliyuga started 3600 years ago, when he was 23 years old (in year 499 AD), making

the start as 3102 BC [Aryabhateeya ref-1].).

Surya Siddhanta [Ref 2], a document evolved from roughly same period, states that sun was54 degrees away from vernal equinox when Kaliyuga started on a new moon day,corresponding to February 17/18, 3102 BCJ, at Ujjain (75deg47minE 23deg 15 min N).

Varaha Mihira (circa 560 AD), another famous astronomer, stated that 2526 years beforestart ofsaka count (eitherShalivahana saka starting in 79 AD orVikrama saka starting in 57BC) [Brihat Samhita Ref-3] as per text below.

When saptarishis (ursa major) were near Magha Yudhistira was king 2526 years before saka time.

Presently, traditional sanatana dharma followers consider that Kaliyuga started at 3102 BC(based onAryabhatas/ Surya Siddhanta data base), and that Mahabharata battle occurred afew decades before that. Millennium year 2000 AD is Kali5102.Like Homers Iliad, anotherepic poetry from Greece, different scholars have expressed opinions varying between the

story ofMahabharata being either total fiction or true record of historical facts. It took effortsby Schliemann, and others to show physical archeological evidence of existence of Troy inpresent day Turkey, and Homers poems having historical relevance.

Bharata has been continuously and relatively densely lived in for thousands of years and inNorthern Bharata the archeological evidence is difficult to come by because of many 100s of


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generations of people living in same area. Hence, it is usual to look forPuranicand vedic(written and oral recitation) evidence to substantiate the time periods. As is true of all suchdocuments like bible stories, Scandinavian, Chinese, Japanese, Egyptian and other

documented local folklore, the historical truths are likely to be anywhere between absolutetruth to vivid imagination. An objective analysis can help in determining the likelihood offolklore being a historical fact or not.

Mahabharata epic story was written by, Vedavyaasa (orKrishna Dwaipaayana) after theMahabharata battle. Vyaasa is also credited with codifying the existing branches ofVedas. Itis perhaps the longest poem of its kind of such antiquity. The presently known oldest versionofMahabharata, based on its style, grammar and other feature was probably written downbefore the Gupta period. This Mahabharata text does not refer to any Zodiacs orraashis (a

western concept probably accommodated in to Jyotishya some time during 300BC to200AD). The linguistic style of the oldest version ofMahabharata clearly cannot be the basisfor determining if and when the events ofMahabharata occurred. It probably may have beenrewritten/re-rendered many times as the mode of transference was by oral traditions is in thecase ofVedicchandas prosody). This version has nearly 90,000 to 100,000 kavya poemsdominantly with 32 syllableAnushtup chandas. There are 18 chapters called Parva.

The presently known oldest Sanskrit version is available in many scripts of India (52alphabet scripts of Nagari, Bengali, Telugu, Kannada, Oriya, Gujarati, Punjabi and manyothers author may not be aware) during 18-19th centuries. They have been extensivelytransliterated, translated, analyzed and commented.

The Bhishma Parva and UdyogaParva (specific chapters ofMahabharata) provideconsiderable astronomical/astrological descriptions and omens as the Mahabharata war wasapproaching and during the war. It describes a period of draught, with many planetarypositions. An electronic version has is available courtesy of Bhandarakar Institution in Pune,India, which has been used below. A literal translation ofBhishma Parva III-12-18 is asfollows. Both Ref 4 and Ref 5 provide very similar texts as,


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A white planet has passed Chitra (Spica). A fierce looking comet has passed Pushya(Early cancer). Mars is near Magha (Regulus) and is in retrograde motion.Brihaspathi(Probably Jupiter) is near Shravana (Deneb AlGeidi in Capricorn), Sunsson (Shani) is near Bhaga-Poorva Phalguni (Denebola/chort), Shukra (Venus) isnear Poorva Proshtapada (early Pisces), A white planet with smoky look has passedJyeshta (Antares), Dhruva (Polaris) is wickedly bright, Both Sun and Moon are nearRohini (Aldebaran), A manly planet is between Chitra and Swati (Spica and laterVirgo) and the red bodies planet is also near Shravana with Brishaspti(Jupiter) in along retrograde motion etc

Some of the planetary position statements appear to be contradictions with precise meaning

of where they were is not fully clear as in the case ofshaniand Brihaspati


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Those two blazing planets Shani and Brihaspti having approached Vishaka (Zubenelgenubi in Linbra) have remained stationary (retrograde motion) for a whole year etc .

Then there is this clear reference to pair of eclipses occurring on 13th day as shown below.

Fourteenth day, Fifteenth day and in past sixteenth day, but I have never known the Amavasya(New Moon day) to occur on the thirteenth day. Lunar eclipse followed by solar eclipse on

thirteenth day is in a single month etc..


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This astronomical reference "thirteen day" eclipse pair appears to be a unique astronomicalobservation. One interpretation is that a lunar eclipse occurred first followed by a solareclipse on the 13th day after lunar eclipse. It also states that two eclipses occurred in one

lunar month.

Further, during the war Jayadhrata was killed during evening of 13th day of war in anevening dark episode, on a clear day, which may have been a short solar eclipse occurringand concluding before sunset. This is detailed in Drona Parva. The war occurred over aperiod of 18 days in a place called Kuruxethra.

This document is basically concerned with analysis of all eclipses visible at Kuruxethra inNorth Bharata (Location where Mahabharata war took place, located north of New Delhi,Longitude 76 deg 49 min East, Latitude 29 deg 59 Min North) from 3300 BC to aboutBuddha-Mahavira-Parshvanaatha time of about 700BC.

Analysis of the time between successive eclipses, specifically time between end of one andbeginning of other has been made, with a view to look at astronomical feasibility of back-to-back eclipses in 13 days using modern computer software.

Another major issue of how did observers of the period define and determine period betweeneclipses when no clocks existed, has been addressed.

Lunar eclipses occur when Earths shadow falls on the Moon. There are about 150 lunareclipses per century. Lunar eclipses can occur only at full moon, and can be either total orpartial. Further they can be umbral and or penumbral. Total lunar eclipses can last up to 2hours, while partial lunar eclipses can last up to 4 hours. Any observer on dark face of earthcan see when lunar eclipse when it occurs, but solar eclipses are not so. During period3500BC to 700 BC, nearly 4350 lunar eclipses have probably occurred. A good fraction ofthese would have been visible in Kuruxethra. Lunar eclipse can be roughly predicted by,[Ref-6].

Julian day of Lunar eclipse=2449128.59+29.53058867n +/-0.25

Where n is a half-integer. Lunar Eclipses occur when n (mod 223) is one of 0.5, 6.5, 12.5,23.5, 35.5, 41.5, 47.5, 53.5, 76.5, 82.5, 88.5, 94.5, 100.5, 123.5, 129.5, 135.5, 141.5, 158.5,164.5, 170.5, 176.5, 182.5, 188.5, 205.5, 211.5, or 217.5.

The sequence of eclipses repeats with a period of 223 months Saros Cycle.

Solar Eclipse occurs when Moons shadow falls on earth observer. About 240 solar eclipsesoccur every century. During period 3500BC to 700 BC, nearly 6960 Solar Eclipses haveoccurred. Solar eclipses take place during daylight hours and can occur only at new moon.Solar eclipses may be total or annular. Total solar eclipses can last up to about 8 minutes,and partial solar eclipses can last up to 115minutes. The shadow of moon has a limited sizeof one to two thousand miles falling on nearly 8000-mile diameter earth. Hence, solareclipses can be seen in a limited range of longitude-latitude where the shadow falls.
http://www.treasure-troves.com/astro/Moon.htmlhttp://www.treasure-troves.com/astro/FullMoon.htmlhttp://www.treasure-troves.com/astro/Moon.htmlhttp://www.treasure-troves.com/astro/FullMoon.html


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Julian Day of Solar eclipse= 2449128.59+29.53058867n +/-0.25where n is a full integer, and solar eclipses occur when n (mod 223) is one of 0, 6, 12, 18,24, 30, 36, 42, 47, 53, 59, 65, 71, 77, 83, 89, 88, 94, 100, 106, 112, 118, 124, 130, 135, 141,

147, 153, 159, 165, 171, 177, 182, 188, 194, 200, 206, 212, or 218.

During the period of our interest of 3500BC to 700 BC, nearly 4350 Lunar Eclipses and 6960solar eclipses have occurred. We need to search amongst these for eclipse pairs visible inKuruxethra, which occurred in 13 days. Though solar eclipses are more in number, from agiven location like Kuruxethra, they are relatively fewer solar eclipses seen because oflimited moon shadow size, while all the lunar eclipses are visible. Hence for an observer at agiven location, lunar eclipses appear to be more. We are more interested in eclipse pairs,occurring during consecutive new moon/ full moon period that could be seen at Kuruxethra.

While the Saros cycle concept gives us a gross feeling for number of eclipses that may haveoccurred, we need more precise computation for determining Mahabharata eclipses.

Jean Meeus [Ref-7] provides numerical algorithms, which take in to account many periodicterms in Moons longitude, latitude, and distance from earth. His algorithms calculate lighttraverse time, Moons argument latitude, suns mean anomaly, Moons mean anomaly andmean distance of moon from its ascending node. He also corrects for eccentricity of earthsorbit around Sun, which is decreasing with time. His algorithms have many parameters anddimensions, but one simple identity that can be used for estimating possibility of an eclipse isgiven below. [Ref-4]

kis an integer, 1 for New Moon & 0.5 for Full Moon

JDE corresponds to Julian Ephemeris Day. IfFis near zero or 360 (or multiples) then aneclipse will occur near Moons ascending node. IfFis near 180, then the eclipse takes placenear descending node of Moon.

This class of computation can assist in determining a lunar/solar eclipse somewhere onearth. Subsequently the earths observer location has to be considered based on preciseTime of Julian day. This class of calculations are embedded in many software code currentlyavailable on market. Considerable validation is required

Eclipse evaluating computational software and its validation in present context

Astronomical calculations have been greatly improved since past 30 years, particularly withconsiderable amount of trajectory work conducted in Moon and other scientific projects. Highaccuracy computer models and software have been developed. These are validated against


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databases from US Naval Observatorys Interactive computer Ephemeris, and Jet PropulsionLaboratory in California. One such code is LodeStar Pro copy righted by Wayne C Annala in1994. [Ref- 8]

Its accuracy has been stated as about 0.9 deg in moon position between 2000BC and 4000BC. This would correspond to about 3-4 minutes time error in eclipse time uniformly if it isalong the ecliptic. If the error is orthogonal to ecliptic, eclipse will not occur.

Effort has been made to validate and develop confidence in the LodeStar Pro by checkingfor historical eclipses of 1000-2500 BC from clay tablet records from Mesopotamia area. Alarge number of clay tablets with eclipse data has been available and has been a subject ofanalyses and study. These not only detail eclipses but also provide concurrent planetaryposition data.

For checking the validity of the LodeStar Software, the data contained in the article "Ancient

Astronomical Observations" and "Near Eastern Chronology in Journal of Ancient ChronologyForum", Volume 3, by Wayne Mitchell was chosen.

The earliest records of astronomical eclipses and omens date to the Mesopotamian Dynastyof Agade,. But the most extensive collection of celestial observations was undertaken duringthe Kassite period and evolved into a series known as Enuma Anu Enlil(EAE). A number ofRecorded tablets from that old era which details the chronology of various kings and theirlives, are presently available in British Museum. The article JACF3 [ref 7], refers to a numberof eclipses, which have been dated using retro calculations. The author analyzes a numberof tablet data to arrive at periods over which kings were ruling. The dates also have beencorrected to earths rotation rate variation due to mass-inertia changes of polar caps etc. Theeight eclipses cover a period of 2053 BC down to 984 BC (sic from Ref[9]).

1. The Lunar eclipse on the 19th April 1793 BC identified as best candidate for the Adarueclipse, (Second Eclipse of Ur III) which marked the end of the reign of Ibbisin or the Eclipseof Ibbisin.


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2. The Lunar eclipse on 31 July 1835 BC, the Ur III Simanu eclipse (First Eclipse ofUr III),said to mark the end of the reign ofShulgi or the Eclipse of Ur III.


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3. The partial Lunar eclipse on the 25th April 2035 BC, identified to mark the end ofRimushor the Eclipse ofAgade.

4. The 'sequential' eclipses on the 27th March 1959 BCJ and the 16th March 1958 BCJidentified to mark the end ofSharkalisharri,. Note that these occur just before sunrise.


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5. The Solar eclipse of 30th April 984 BCJsets date ofMursili's Year 10 campaign.


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6. The Solar eclipse of 30th April 984 BCJsets date ofMursili's Year 10 campaign.


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7. The 26th April 1932 BCJ Lunar eclipse of partial 0.62 magnitude eclipse

As was stated before, the eclipse data has been exclusively taken from Ref 9. The Lodestarpro accurately predicts all these eclipse without an error, at longitude and latitude of about40 deg East, 34 deg North, near the Mesopotamia area. One mild exception that thesequential eclipses in 1959 and 1958 BC are shown to occur through sunrise. Also some ofthe dates change to next day at midnight after the beginning of eclipse.

This validation gives us some confidence that the LodeStar can be used to predict theeclipse periods of at least up to 2100 BC. We now take a further step and assume that it canbe extended to 3300 BC. Of course, this whole exercise of astronomical retro-calculation hassome degree of uncertain character. Let us proceed with assumption that the LodeStar Procan provide accurate eclipse data forKuruxethra in the period 3300 BC down to 700 BC.

During the period of our interest, 3500BC to 700 BC, nearly 4350 Lunar Eclipses and 6960solar eclipses have occurred on earth. Of these nearly 673 solar and lunar eclipses occurredin pairs of time gap of about nominal 15 days corresponding to roughly half lunar month. Weneed to search amongst these 673 for an eclipse pair visible in Kuruxethra, which occurred

in "thirteen" days.

A very detailed scan of all the visible lunar and solar eclipses for every year from 3300BC to700 BC was made on the Lodestar software forKuruxethra location. These were sorted aspairs of eclipses occurring back to back in about 15 days. The aim was to identify sucheclipse pairs and for each determine contact time, maximum eclipse time and release time


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with the relevant sunrise time or sunset time. These are tabulated. Maximum eclipse timegap (end of one eclipse and beginning of next eclipse for naked eye observers) was found tobe about 379 hours while the minimum was about 332 hours. A plot of time gap between

back-to-back eclipses versus eclipse pair number is shown below. (This time corresponds tomaximum to maximum not end of one to beginning of next as in the future table).

The plot shows that during the period 3300BC to 700 BC, (Julian year corresponds to zero at4712 BC- an imaginary date- Our range corresponds to 1412 Julian year to 4012 JulianYear) nearly 672 pairs of eclipses occurred on earth, which in principle may have beenvisible at Kuruxethra. Amongst these nearly 32 pairs would be occurring for period less than14 days. Some of them were found to be weak penumbral eclipses of moon. Some solareclipses had such low obscurity as to raise the issue whether any body could see it.

The plot above shows time between maximum eclipse to next maximum eclipse, whichwould be considered as beginnings of Shukla pratipat and Krishna pratipat or vice versa.

A more detailed study of the 18 pairs (fourteen of 32 had very weak eclipses dominated bypenumbral eclipse) has been made with a view to precisely determine the initial visiblecontact of eclipse, the maximum eclipse and the release or end time.


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Definition of Day and issue of timing determination

It is easy for us, in present time, to precisely analyze the eclipse times based on a 24 hour

per day time clock. However many thousand years ago, such a time evaluation would clearlybe irrelevant. Hence the count of the day and time had to be based on clear, natural andunambiguous events such as sunset to sunset or sunrise to sun rise. Hence in all theanalyses, presented below, the time of relevant sun rise or sun set is indicated such that theeclipse beginning and end can be evaluated with reference to the sun rise or sun set. Inmodern day definition, the period from sunrise to next sunrise is never 24 hours except onequinox day. On all other days, the time will be either less than 24 hours (when day light timeis shrinking) and more than 24 hours (when day light time is increasing). For people ofancient times, sunset-to-sunset or sunrise-to-sunrise day definition would be a very logicalone

As will be illustrated, all the eclipses are shown to occur though sunset or sunrise, makingthe day count round off easy.

The table below shows eighteen pairs of eclipses, which can be analyzed further todetermine whether Mahabharata war and events could occur then.

Eighteen eclipse pairs visible at Kuruxethra occurring in less than or near 14 days

Events in red not visible due to sun rise(Lunar) or sun set(Solar)

Year BC Eclipse Julian day Initial con Max End Sunrise Sunset end/strt dt

3230 Solar Jan-24 15:38:57 17:00:08 18:09:23 17:42 13d23h4m

3230 Lunar Feb-07 17:13:28 18:08:27 19:03:26 17:51

3188 Solar May-07 06:34:01 07:19:57 08:09:09 05:56 14d0h24m

3188 Lunar April-23 01:43:27 02:48:32 05:36:40 06:10

3176 Solar Feb-25 12:11:18 14:03:50 15:42:21 18:04 14d0h25m

3176 Lunar Mar-11 16:07:59 17:25:29 18:42:59 18:13

3129 Solar Aug-11 18:53:48 19:48:04 20:38:54

19:22 13d20h20m

3129 Lunar Aug-25 16:58:50 18:21:36 19:44:21 19:17

3075 Solar Sep-13 18:23:49 19:22:35 20:17:05 19:03 13d22h00m


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3075 Lunar Sep-27 18:17:49 19:44:11 21:10:33 18:48

2950 Solar July-14 05:18:57 06:19:18 07:26:37 05:11

13d23h23m

2950 Lunar June-30 03:20:34 04:38:12 05:55:49 05:11

2907 Solar Mar-22 16:50:51 17:45:03 18:35:00 18:20 13d21h51m

2907 Lunar Mar-08 17:16:57 18:09:26 19:01:54 18:13

2775 Solar July-29 17:38:17 18:16:03 18:51:29 19:23 13d21h49m

2775 Lunar Aug-12 16:40:20 18:24:42 20:09:05 19:21

2559 Solar July-11 03:50:53 04:36:27 05:24:36 05:12 13d20h8m

2559 Lunar June-27 03:29:54 05:13:45 06:57:36 05:07

2290 Solar Jul-08 05:31:14 06:13:35 06:59:23 05:12 13d21h55m

2290 Lunar Jul-22 04:53:25 06:30:33 08:07:42 05:16

2056 Solar Nov-25 16:50:19 17:52:24 18:48:02 17:38 13d21h40m

2056 Lunar Dec-09 16:27:47 18:12:55 19:58:05 17:32

1853 Solar Dec-30 15:47:28 17:00:02 18:03:38 17:29 13d22h14m

1853 Lunar Jan-13 16:17:56 17:24:16 18:30:37 17:36

1708 Solar Mar-27 04:55:14 05:47:28 06:44:15 06:37 13d20h18m

1708 Lunar Apr-10 03:02:36 04:46:36 06:30:55 06:19

1666 Solar Jul-08 17:11:19 18:09:13 19:01:38 19:21 13d21h24m

1666 Lunar Jun-24 17:02:50 18:25:12 19:47:34 19:15

1397 Solar Jul-04 19:00:34 19:36:54 20:11:34 19:21 13d21h30m

1397 Lunar Jul-18 17:41:38 19:34:00 21:26:30 19:23


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1343 Solar Aug-06 17:54:01 18:16:12 18:37:33 19:18 13d20h45m

1343 Lunar Aug-20 15:23:21 17:18:13 19:13:05

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1235 Solar Oct-10 18:09:04 18:24:43 18:39:51 18:14 13d20h50m

1235 Lunar Oct-24 15:29:22 17:22:33 19:15:44 17:59

790 Solar Jun-14 05:27:40 05:54:19 06:22:08 05:15 13d20h59m

790 Lunar May31 04:38:07 06:33:30 08:28:52 05:20

Location of Kuruxethra 76deg49 min East, 29deg 59min North

Amongst the eighteen pairs of eclipses, nine pairs have sunrise or sunset occurring in themiddle, and these would form ideal candidates for consideration for Mahabharata war. Theother nine sets have in them only one sunrise or sunset transition and hence are not soideal. Only six of the pairs occur in the early morning sunrise time while the other twelveoccur in the sunset time. After serious analysis of all the eclipses, six eclipse pairs from 3129BCJ, 2599 BCJ, 2056 BCJ, 1853 BCJ, 1708 BCJ and 1397 BCJ clearly are the bestcandidates for Mahabharata war year from "thirteen day" eclipse pairs view point. The othertwelve have low obscurity for solar eclipse, or have dominant penumbral lunar eclipsecontent and hence do not constitute strong candidates for the Mahabharata war

In the following pages, these six eclipse pairs are illustrated using Lodestar Pro views duringrelevant sunset/sunrise periods. Each picture shows eclipses in various phases, the

observability dependent on, in case of lunar eclipse after sunset, and in case of solar eclipsebefore sunset. The light/day transition is clearly shown in all the eclipse, which would formthe only method of determining that the eclipses occurred in less than fourteen days, whichhas to be called thirteen-day eclipses. In some typical cases (not all cases), motion of Saniand Brihaspati, Shukra in retrograde are illustrated for period around the eclipse pairs.

Solar-Lunar eclipse pair from Julian year 3129BC

x


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Fourteen days later at the same time


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The figures above show the pictures of night sky for a pair of Solar-Lunar eclipses, end oflunar eclipse being only 13 days and 20 hours before start of a solar eclipse. Any observerwould have easily concluded that the eclipses occurred in less than 14 days because ofsunset/moonrise occurring in middle of both the eclipses. On Julian August 11 afternoon, asolar eclipse begins at 6:54 before sunset and it is still on going at sunset at 7:14. Fourteendays later (On Julian August 25) in the evening at sunset a lunar eclipse is already occurring

suggesting it started on the 13th day after the previous eclipse! Clearly the end of lunar andstart of solar eclipses were less than 14 days or occurred in 13 days. This could beconcluded without the benefit of modern clocks.

The dates of this eclipse pair are Julian 3129 and Julian month of August. In ancientBharata, since the full moon occurred on Proshtapada in Meena, the month would beconsidered as Bhadrapada. Normally, this is the monsoon rainy season in North India.However, there are many occasions when monsoon fails. The epic states that draught likeconditions existed. Even during normal monsoon the sky is occasionally clear for theeclipses to have been witnessed.

The two planets Jupiter, and Saturn are in motion (vakri) and these do occur during 3129

JBC as illustrated below. Motion of Angaraka or Mars is normal.


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Items in red show retograde or Vakri motion


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Graha(Planet) 3129BCJ Mahabharata text

Brihaspati(Jupiter) U.Ashada/Shravana Shravana-Vishakha

Sani(Saturn) Revati Shravana-Vishakha

Angaraka(Mars) U.Ashada/Shravana Magha

Shukra(Venus) U Phalguni Poorva Bhadrapada

Ravi (Sun Solar) U Phalguni Rohini

The location of the planets at the time of eclipse pair is shown in table above. Clearly, onlyBrihaspati, and Shukra are the planets at the location indicated in the Mahabharata text.

Hence this date of 3129 BCJ is a serious candidate for consideration ofMahabharata war.The eclipses occur some time before the actual war, and there is a suggestion that anothersolar eclipse occurred in the evening during war, the Jayadhratha episode. However, noeclipse was found in December period, before the winter solstice oruttara ayana.

Lunar-Solar eclipse pair from Julian year 2599 BC


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June 27,2559 BCJ Start of Lunar eclipse 3:29AM Lunar eclipse total before sunrise 5:06AM


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Lunar eclipse continues after sunrise ending at 6:57AM


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July 9,2559 BCJ Solar eclipse max at 4:36 AM before Solar eclipse continues through Sunrise 5:12 Am

Sunrise Occurs near Magha or Regulus

Solar eclipse ends at 5:24 AM, 12 minutes after sunrise

The figures above show the pictures of night sky for a pair of Solar-Lunar eclipses, end oflunar eclipse being only 13 days and 20 hours before start of a solar eclipse. On Julian June27,2559 BC morning, the lunar eclipse, which started at night, is not complete. Fourteendays later (On Julian July 11,2559) in the morning at sunrise the solar eclipse is alreadyoccurring and is almost over suggesting it started on the 13th day after the previous lunareclipse. Clearly, even to the observers then, the end of lunar and start of solar eclipses wereless than 14 days or occurred in 13 days. The figures show that during lunar eclipse,occultation with Jupiter was also going on, a very rare event. Whether this has been notedsomewhere in the Mahabharata text, is to be explored. Also, there is a near Venusoccultation during solar eclipse. The near Venus occultation occurring is to be looked for inMahabharata text.The dates of this eclipse pair are Julian 2559 and Julian months of Juneand July. In ancient Bharata, since the full moon occurred on Shravana nakshathra inMakara, the month would be considered as Shravana. Normally, this is the monsoon rainy

season in North India. Mahabharata text does refer to draught like situation in the text.

The three planets Jupiter, Saturn & mars are said to be in retrograde motion (vakri) andthese do occur during 2559 JBC as illustrated below.


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Jupiter (Brihaspati) in retrograde motion (vakri) Mars(angaraka) in retrograde motion(vakri)


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May to September 2559 May to September 2559

Saturn(Shani)in retrograde motion in December 2559



Brihaspati(Jupiter) Shravana Shravana-Vishakha

Sani(Saturn) P Phalguni Shravana-Vishakha

Angaraka(Mars) Shravana/Danista Magha

Shukra(Venus) Magha Poorva Bhadrapada

Ravi (Sun Solar) Magha Rohini

Clearly, the Planet positions from Mahabharata text do not totally match the planet positionsat the time of eclipse pair. But Brihaspatiis near the indicated location as perMahabharata

text


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The ominous 13-day eclipse occurs in month Shravana. Some months later, during the war,which occurred before the winter solstice, it is said that Jayadhratha was killed when Sri

Krishna covered the sun for a short time just before the sunset. This could be looked upon

as a solar eclipse. A study of year 2559 shows that another solar eclipse did occur in Pushyalunar month nearly six months after the short eclipse pair. It occurred shortly before sunset

as illustrated below.


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Clearly this episode can provide an explanation for events prior to Jayadhrathas death. TheLunar month then was Pushya and sun is still at 19.5 degrees south in Dakshina Ayana. Hestill has to move to 23.5 degrees (thirty six days away) to reach Uttara Ayana (which occurson Jan 10, 2558 BCJ) at which time war was over and Bhishma passed away.

Hence 2559 eclipse pair can be considered to be fairly serious candidate for Mahabharatawar year.

Solar-Lunar eclipse pair from Julian year 2056 BCJ


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This pair of eclipses also is a viable pair for Mahabharata date. The eclipse pairs occur inMargashira/pushya lunar months as is evident from above picture. As before, naked eye


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observers can make out the fact that end of solar eclipse and beginning of lunar eclipse are lessthan 14 days apart.

The table below provides the trajectories of five naked eye planets. The motions ofBrihaspatiandSaniare retrograde as suggested by Mahabharata text, but the locations are not at the proper

nakshathras.



Brihaspati(Jupiter) Pushya Shravana-Vishakha

Sani(Saturn) Chithra Shravana-Vishakha

Angaraka(Mars) Swati Magha

Shukra(Venus) Jyeshta/Moola Poorva Bhadrapada

Ravi(Sun Solar) P Ashada/Shravana Rohini

Hence this pair of "thirteen day " eclipses does meet the Mahabharata period requirements.

Solar-Lunar eclipse pair from Julian year 1853 BCJ


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This eclipse pair occurs in month ofMagha as the full moon is nearMagha nakshathra. Thisis a bit too late for Mahabharata war as the sun is very near winter solstice already at 24

degrees) oruttara ayana.



Brihaspati(Jupiter) P.Phalguni Shravana-Vishakha

Sani(Saturn) Magha Shravana-Vishakha

Angaraka(Mars) Swati/Vishaka Magha

Shukra(Venus) U Ashada Poorva Bhadrapada

Ravi (Sun Solar) Shravana Rohini

Two planets Saniand Brihaspatiare in retrograde motion, but all planets are at positions,which do not agree with Mahabharata text.


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Thus this pair of eclipses though meeting the "Thirteen day" requirement, occurs very nearthe solstice to be serious candidate forMahabharata.

Lunar-Solar eclipse pair from Julian year 1708 BCJ


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Brihaspati(Jupiter) Swati Shravana-Vishakha

Sani(Saturn) Punarvasu Shravana-Vishakha

Angaraka(Mars) Rohini Magha

Shukra(Venus) Krittika Poorva Bhadrapada

Ravi (Sun Solar) Bharani Rohini

The locations of the planets during the eclipse pair are totally different from the Mahabharatatext. However, the planets Brihaspatiand Saniare in retrograde motion. The eclipse pair

occurs just after the beginning ofUttara Ayana in winter, and the fact that there was adraught cannot be seriously considered. Hence this date is rather a weak candidate for the

Mahabharata eclipse pair.

Lunar-Solar eclipse pair from Julian year 1397 BCJ


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Brihaspati(Jupiter) Shravana Shravana-Vishakha

Sani(Saturn) U Ashada Shravana-Vishakha

Angaraka(Mars) Chithra Magha

Shukra(Venus) Punarvasu Poorva Bhadrapada

Ravi (Sun Solar) Aaslesha Rohini

This is the last eclipse pair that meets the "thirteen day" period requirement in oursearch.The season is right. The two retrograde planets Brihaspatiand Saniare very near

declared positions. There is no solar eclipse in the period prior to Uttara Ayana. This eclipsepair is a good candidate forMahabharata war.

This new date is very different and more recent than the traditional dates byAryabhata,Surya Siddhanta, Varaha Mihira

Beginning ofKaliyuga

The SuryaSiddhanta based data declare that the Kaliyuga started on the new moon day(Amavasya/Pratipat) when sun was 5 degrees away from vernal equinox (Ref 2). This datehas been estimated as February 18, 3102 BCJ. There is also a suggestion that there was a

solar eclipse at Ujjain. The picture below shows the view and sun and moon at that time.


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The Lodestar pro view of sky on that day shows that there was no eclipse at Ujjain (75 deg47 min E and 25 deg 15 min N) at Amavasya, but sun was 54 degrees away from vernalequinox. (3 hours 36 minutes from equinox- @15 deg/hour this works out to exactly 54

degrees).

This document has demonstrated that two eclipses can occur within about 332 hours, whichis less than 14 days. Hence the Mahabharata statement that such eclipse did occurominously before the war is clearly possible. Such events did occur in 3129 BCJ, 2559 BCJand few other dates. These were clearly visible through sunset and sunrise making the useof modern clocks irrelevant. Any observer could make out that the eclipses occurred in lessthan 14 days and hence two eclipses in "thirteen days" had happened. While these occurred,two major planets Shani and Brihaspati were in retrograde motion. Retrograde motion ofplanets occurs frequently enough, but these occurring, when 13-day eclipses are alsooccurring is unique. It tends to support the Mahabharata story.

The first and oldest eclipse pair from 3229 BC is unique. Aryabhata estimated that Kaliyuga

started in 3102 BC. So does Surya Siddhanta. These fit the Puranic description that SriKrishna passed away in 3102 BCJ, which is 27 years after the war. Our study confirms thatKaliyuga could have started in 3102 BCJ. Unlike the 2559 pair, there is no visible solareclipse during the Mahabharata time frame, which would occur. Still this date is a very gooddate for Mahabharata war.


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The second date 2559 BCJ is also unique in that Varaha mihira stated that 2526 before startof saka, Yudhishtira was the ruling king. There is some confusion about saka, whether it wasVikrama (57 BC) or Shalivahana(79 AD). If it was Vikrama it would make Yudhistira as king

in 2583 BCJ which is before Mahabharata War. Yudhistira was also king for a short timebefore war, before he lost it in a game of dice to Sakuni/Duryodhana. This date is also anexcellent candidate for Mahabharata war.

The third candidate is eclipse pair from 2056 BCJ. It occurs in Margashira/pushya months,the lunar eclipse occurring when moon is between Punarvasu/pushya nakshathra, and wouldbe right in the middle of war. Hence is not a very serious candidate for Mahabharata war.

The fourth candidate is eclipse pair from 1853 BCJ. It occurs in month of Magha very nearthe winter solstice or Uttara Ayana. It is not a very good candidate for Mahabharata War

The fifth candidate of eclipse pairs occurred in 1708 BCJ. This eclipse pair occurs in month

of Phalguna, just after Uttara Ayana and is a bad candidate.

The last candidate of eclipse pair occurs in 1397 in the month of Bhadrapada. It is areasonably good candidate for Mahabharata war. Again, there was no solar eclipse duringthe period prior to Uttara Ayana.

The aim of this work was to analyze the unique statement that Mahabharata war took placewhen an ominous pair of eclipses occurred in "Thirteen days". Initially, Mahabharata texts,contemporarily accepted as most authentic were reviewed and relevant data aboutMahabharata and astronomical planetary observations have been presented.

Firstly, this document looked at modern astronomical software with all known corrections,and validated its performance using the clay tablet eclipse information from the Mesopotamiavalley during the period 2100 BCJ down to 900 BCJ, with best- known contemporaryresearch data.

Secondly, a search of all eclipses during the period 3300 BCJ to 700 BCJ visible atKuruxethra, where Mahabharata war took place was made. Amongst nearly 672 possibleeclipse pairs, the time from end of one to beginning of next eclipse was found to varybetween 13.8 days to 15.8 days. Eighteen naked eye visible eclipse pairs with less than 336hours (14days) of time gap were found.

The third issue was, what was the definition of a day, and how was the determination thateclipses occurred in "thirteen days" made, has been addressed. Day was taken to be thetime between either successive sunrise or successive sunset. This is particularly important

when clocks did not exist. Using this method, it was easy to demonstrate that observers from3000 to 5000 years ago could identify accurately a "thirteen-day "eclipse pair.

Fourthly, eighteen pairs of possible Thirteen day eclipses" were extensively analyzed. Sixpairs amongst these, found to be good candidates for Mahabharata, have been illustrated,showing how any observer could conclude that the eclipse pairs occurred in less than 14


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days or in "thirteen days". The locations of Jupiter, Saturn, Mars, Venus, Sun and Moon,during the eclipses were identified with reference to Bharateeya 27 star locations.

Finally, it is found that two dates suggested by Indian authors Aryabhata, Varaha Mihira fromGupta period were credible dates for Mahabharata war. It would appear that 3129 BCJ is afirst candidate for Mahabharata war followed by 2559 BCJ. Four other dates viz., 2056 BCJ,1853 BCJ, 1708 BCJ and 1397 BCJ are other candidates which qualify as " Thirteen day"eclipse pairs.

In conclusion, this article has tried to address the basic issue, whether " Thirteen day"eclipse pairs are astronomically possible. The conclusion is that such eclipses have occurredand observers could easily identify the duration using sunset/sunrise transitions. 3129 BCJand 2559 BCJ dates appear to be very viable dates for Mahabharata war as are a fewothers. This study provides modern scientific support one critical astronomical statementmade in Mahabharata text that "thirteen day" eclipse pair occurred Kuruxethra.

Some related material about Vedic star astronomical locations

The Bharateeya 27/28 daily Star system is a lunar day count used in Vedic Bharata. Twoarticles in Ref 11 and 12 provide background in this area for those who do not have thisinformation.

Acknowledgements

The Internet web and search engines have been a great boon in providing rare materialonline, particularly conversion of Devanagari script to English and vice versa. Reference 5was of great help in finding such basic Mahabharata material, confirmed in Ref 4. Ref 10

provided a method of converting between scripts.

1.Aryabhateeya by BrahmaguptaK.S.Shukla,New Delhi, INSA 1976

2. SURYA SIDDHANTATranslation of an Ancient Indian Astronomical Text. Translation by BAPU DEVA, BENARES,1860.

3. Varahamihiras Brihat Samhita- M Ramakrishna BhatMotilala Banarasidas Publications, 1981

4. Ramashesha Shastry

Bhagavata Mahapurana, 10th skanda,Upodghata (in Kannada script), 1930

5. John SmithMahabharata Text checked by Bhandarakar Oriental Research InstituteCourtesy http://www.bombay.oriental.cam.ac.uk/john/mahabharata/statement.html
http://www.bombay.oriental.cam.ac.uk/john/mahabharata/statement.htmlhttp://www.bombay.oriental.cam.ac.uk/john/mahabharata/statement.html


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6. Eric WeisstienWorld Of AstronomyCourtesy http://www.scienceworld.wolfram.com/astronomy/SarosCycle.html

7. Jean MeausAstronomical Algorithms, Willman Bell Inc Publications, 1991Wayne Annala, Lodestar Pro Manual, 1994

8. Wayne Annala, Lodestar Pro Manual, 1994

9. Wayne MitchellAncient Astronomical Observations and Near Eastern ChronologyJournal of Ancient Chronology Forum, Volume3

10. Courtesy http://www.baraha.com

11. S.BalakrishnaNames of stars from period of Vedas

12. S.BalakrishnaComparison of Vedic period star name identities from R. H. Allens "Star names- Their lore &meaning" of circa 1899
http://www.scienceworld.wolfram.com/astronomy/SarosCycle.htmlhttp://www.vedicastronomy.net/stars.htmhttp://www.vedicastronomy.net/compare.htmhttp://www.vedicastronomy.net/compare.htmhttp://www.scienceworld.wolfram.com/astronomy/SarosCycle.htmlhttp://www.vedicastronomy.net/stars.htmhttp://www.vedicastronomy.net/compare.htmhttp://www.vedicastronomy.net/compare.htm

dating the mahabharatha

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