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History Of Ancient India : Scientific Dating of Mahabharata

Thanks for being my guest. You are going to read an article written by By Dr S Balakrishna(saras_v@hotmail.com) on the dating of Mahabharata.

Dating Mahabharata - Two eclipses in thirteen days

By Dr S Balakrishna

Introduction
Mahabharatha
Eclipses
Some well dated eclipses from the past
Eclipses at the Kuruxethra
Analysis of eclipse tables
References
Conclusions
 

Abstract:

Mahabharata battle is considered by many to be a historical event. The epic states that a singularly ominous pair of eclipses occurred in thirteen days some time before the war. It also provides some astronomical planetary positions and retrograde motions at that time. Our article addresses the issue of whether "Thirteen day" eclipse pairs are possible. Eclipse pairs visible in Kuruxethra during 3300 BC to 700 BC period have been analyzed in great detail using modern astronomical software. Study shows that such 13-day eclipses pairs do occur occasionally. The article identifies some candidate dates for Mahabharata war.

Introduction:

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story from India (India is hence forth referred to as Bharata) in Sanskrit, considered by many to be a folklore type historical document.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 epic details politics of an old era covering many generations, with a climax in a major battle that occurred 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 of Bharateeya’s for many generations. The battle is said to have occurred before the transition of eons (rough translation of yuga) from Dwapara yuga eon to kali yuga eon.

Aryabhata, a famous early astronomer from Bharata with contributions to science made estimates of Kaliyuga start nearly 1500 years ago. His estimate of p, and the time of moon revolution 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) stated that 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 was 54 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 before start of saka count (either Shalivahana saka starting in 79 AD or Vikrama saka starting in 57 BC) [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 on Aryabhata’s/ Surya Siddhanta data base), and that Mahabharata battle occurred a few decades before that. Millennium year 2000 AD is Kali 5102.

Like Homer’s Iliad, another epic poetry from Greece, different scholars have expressed opinions varying between the story of Mahabharata being either total fiction or true record of historical facts. It took efforts by Schliemann, and others to show physical archeological evidence of existence of Troy in present day Turkey, and Homer’s poems having historical relevance.

Bharata has been continuously and relatively densely lived in for thousands of years and in Northern Bharata the archeological evidence is difficult to come by because of many 100’s of generations of people living in same area. Hence, it is usual to look for Puranic and vedic (written and oral recitation) evidence to substantiate the time periods. As is true of all such documents like bible stories, Scandinavian, Chinese, Japanese, Egyptian and other documented local folklore, the historical truths are likely to be anywhere between absolute truth to vivid imagination. An objective analysis can help in determining the likelihood of folklore being a historical fact or not.

Mahabharata:

Mahabharata epic story was written by, Vedavyaasa (or Krishna Dwaipaayana) after the Mahabharata battle. Vyaasa is also credited with codifying the existing branches of Vedas. It is perhaps the longest poem of its kind of such antiquity. The presently known oldest version of Mahabharata, based on its style, grammar and other feature was probably written down before the Gupta period. This Mahabharata text does not refer to any Zodiac’s or raashis (a western concept probably accommodated in to Jyotishya some time during 300BC to 200AD). The linguistic style of the oldest version of Mahabharata clearly cannot be the basis for determining if and when the events of Mahabharata occurred. It probably may have been rewritten/re-rendered many times as the mode of transference was by oral traditions is in the case of Vedic chandas prosody). This version has nearly 90,000 to 100,000 kavya poems dominantly with 32 syllable Anushtup chandas. There are 18 chapters called Parva.

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

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

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), Sun’s son (Shani) is near Bhaga-Poorva Phalguni (Denebola/chort), Shukra (Venus) is near Poorva Proshtapada (early Pisces), A white planet with smoky look has passed Jyeshta (Antares), Dhruva (Polaris) is wickedly bright, Both Sun and Moon are near Rohini (Aldebaran), A manly planet is between Chitra and Swati (Spica and later Virgo) and the red bodies planet is also near Shravana with Brishaspti(Jupiter) in a long 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 of shani and Brihaspati

.

Those two blazing planets Shani and Brihaspti having approached Vishaka (Zubenel genubi 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…..

This astronomical reference "thirteen day" eclipse pair appears to be a unique astronomical observation. One interpretation is that a lunar eclipse occurred first followed by a solar eclipse 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 an evening dark episode, on a clear day, which may have been a short solar eclipse occurring and concluding before sunset. This is detailed in Drona Parva. The war occurred over a period of 18 days in a place called Kuruxethra.

This document is basically concerned with analysis of all eclipses visible at Kuruxethra in North 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 about Buddha-Mahavira-Parshvanaatha time of about 700BC.

Analysis of the time between successive eclipses, specifically time between end of one and beginning 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 between eclipses when no clocks existed, has been addressed.

Eclipses

Lunar eclipse occurs when Earth’s shadow falls on the Moon. There are about 150 lunar eclipses per century. Lunar eclipses can occur only at full moon, and can be either total or partial. Further they can be umbral and or penumbral. Total lunar eclipses can last up to 2 hours, while partial lunar eclipses can last up to 4 hours. Any observer on dark face of earth can see when lunar eclipse when it occurs, but solar eclipses are not so. During period 3500BC to 700 BC, nearly 4350 lunar eclipses have probably occurred. A good fraction of these 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 Moon’s shadow falls on earth observer. About 240 solar eclipses occur every century. During period 3500BC to 700 BC, nearly 6960 Solar Eclipses have occurred. 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 size of one to two thousand miles falling on nearly 8000-mile diameter earth. Hence, solar eclipses can be seen in a limited range of longitude-latitude where the shadow falls.

Julian Day of Solar eclipse= 2449128.59+29.53058867n +/-0.25

where 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 6960 solar eclipses have occurred. We need to search amongst these for eclipse pairs visible in Kuruxethra, which occurred in 13 days. Though solar eclipses are more in number, from a given location like Kuruxethra, they are relatively fewer solar eclipses seen because of limited moon shadow size, while all the lunar eclipses are visible. Hence for an observer at a given 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 have occurred, we need more precise computation for determining Mahabharata eclipses.

Jean Meeus [Ref-7] provides numerical algorithms, which take in to account many periodic terms in Moon’s longitude, latitude, and distance from earth. His algorithms calculate light traverse time, Moon’s argument latitude, sun’s mean anomaly, Moon’s mean anomaly and mean distance of moon from its ascending node. He also corrects for eccentricity of earth’s orbit around Sun, which is decreasing with time. His algorithms have many parameters and dimensions, but one simple identity that can be used for estimating possibility of an eclipse is given below. [Ref-4]

k is an integer, 1 for New Moon & 0.5 for Full Moon

JDE corresponds to Julian Ephemeris Day. If F is near zero or 360 (or multiples) then an eclipse will occur near Moon’s ascending node. If F is near 180, then the eclipse takes place near descending node of Moon.

This class of computation can assist in determining a lunar/solar eclipse somewhere on earth. Subsequently the earth’s observer location has to be considered based on precise Time of Julian day. This class of calculations are embedded in many software code currently available 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 with considerable amount of trajectory work conducted in Moon and other scientific projects. High accuracy computer models and software have been developed. These are validated against databases from US Naval Observatory’s Interactive computer Ephemeris, and Jet Propulsion Laboratory in California. One such code is LodeStar Pro copy righted by Wayne C Annala in 1994. [Ref- 8]

Its accuracy has been stated as about 0.9 deg in moon position between 2000BC and 4000 BC. This would correspond to about 3-4 minutes time error in eclipse time uniformly if it is along 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 checking for historical eclipses of 1000-2500 BC from clay tablet records from Mesopotamia area. A large number of clay tablets with eclipse data has been available and has been a subject of analyses and study. These not only detail eclipses but also provide concurrent planetary position data.

Some well dated eclipses from past

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 Chronology Forum, Volume 3, by Wayne Mitchell was chosen.

The earliest records of astronomical eclipses and omens date to the Mesopotamian Dynasty of Agade,. But the most extensive collection of celestial observations was undertaken during the Kassite period and evolved into a series known as Enuma Anu Enlil(EAE). A number of Recorded tablets from that old era which details the chronology of various kings and their lives, are presently available in British Museum. The article JACF3 [ref 7], refers to a number of eclipses, which have been dated using retro calculations. The author analyzes a number of tablet data to arrive at periods over which kings were ruling. The dates also have been corrected to earth’s rotation rate variation due to mass-inertia changes of polar caps etc. The eight 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 Adaru eclipse, (Second Eclipse of Ur III) which marked the end of the reign of Ibbisin or the Eclipse of Ibbisin.

     

  1. The Lunar eclipse on 31 July 1835 BC, the Ur III Simanu eclipse (First Eclipse of Ur III), said to mark the end of the reign of Shulgi or the Eclipse of Ur III.
  2. Total Lunar eclipse on 28th June 1908 BC which is identified as marking the victory of Utu-hegal, or the Eclipse of Gutium.
  3. The partial Lunar eclipse on the 25th April 2035 BC, identified to mark the end of Rimush or the Eclipse of Agade.
  4. The 'sequential' eclipses on the 27th March 1959 BCJ and the 16th March 1958 BCJ identified to mark the end of Sharkalisharri,. Note that these occur just before sunrise
  5. The Solar eclipse of 30th April 984 BCJsets date of Mursili's Year 10 campaign.
  6. The Partial Lunar eclipse of 13th April 2053 BC, with 0.63 magnitude eclipse
  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 Lodestar pro accurately predicts all these eclipse without an error, at longitude and latitude of about 40 deg East, 34 deg North, near the Mesopotamia area. One mild exception that the sequential eclipses in 1959 and 1958 BC are shown to occur through sunrise. Also some of the 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 the eclipse periods of at least up to 2100 BC. We now take a further step and assume that it can be extended to 3300 BC. Of course, this whole exercise of astronomical retro-calculation has some degree of uncertain character. Let us proceed with assumption that the LodeStar Pro can provide accurate eclipse data for Kuruxethra in the period 3300 BC down to 700 BC.

Eclipses at Kuruxethra

During the period of our interest, 3500BC to 700 BC, nearly 4350 Lunar Eclipses and 6960 solar eclipses have occurred on earth. Of these nearly 673 solar and lunar eclipses occurred in pairs of time gap of about nominal 15 days corresponding to roughly half lunar month. We need 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 to 700 BC was made on the Lodestar software for Kuruxethra location. These were sorted as pairs of eclipses occurring back to back in about 15 days. The aim was to identify such eclipse pairs and for each determine contact time, maximum eclipse time and release time with the relevant sunrise time or sunset time. These are tabulated. Maximum eclipse time gap (end of one eclipse and beginning of next eclipse for naked eye observers) was found to be 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 to maximum 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 at 4712 BC- an imaginary date- Our range corresponds to 1412 Julian year to 4012 Julian Year) nearly 672 pairs of eclipses occurred on earth, which in principle may have been visible at Kuruxethra. Amongst these nearly 32 pairs would be occurring for period less than 14 days. Some of them were found to be weak penumbral eclipses of moon. Some solar eclipses 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, which would 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 by penumbral eclipse) has been made with a view to precisely determine the initial visible contact of eclipse, the maximum eclipse and the release or end time.

 

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 clearly be irrelevant. Hence the count of the day and time had to be based on clear, natural and unambiguous events such as sunset to sunset or sunrise to sun rise. Hence in all the analyses, presented below, the time of relevant sun rise or sun set is indicated such that the eclipse beginning and end can be evaluated with reference to the sun rise or sun set. In modern day definition, the period from sunrise to next sunrise is never 24 hours except on equinox day. On all other days, the time will be either less than 24 hours (when day light time is shrinking) and more than 24 hours (when day light time is increasing). For people of ancient times, sunset-to-sunset or sunrise-to-sunrise day definition would be a very logical one

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

The table below shows eighteen pairs of eclipses, which can be analyzed further to determine 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

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

 

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

 

19:10

 

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

May–31

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 the middle, and these would form ideal candidates for consideration for Mahabharata war. The other nine sets have in them only one sunrise or sunset transition and hence are not so ideal. Only six of the pairs occur in the early morning sunrise time while the other twelve occur in the sunset time. After serious analysis of all the eclipses, six eclipse pairs from 3129 BCJ, 2599 BCJ, 2056 BCJ, 1853 BCJ, 1708 BCJ and 1397 BCJ clearly are the best candidates for Mahabharata war year from "thirteen day" eclipse pairs view point. The other twelve have low obscurity for solar eclipse, or have dominant penumbral lunar eclipse content 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 during relevant 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 eclipse before sunset. The light/day transition is clearly shown in all the eclipse, which would form the only method of determining that the eclipses occurred in less than fourteen days, which has to be called thirteen-day eclipses. In some typical cases (not all cases), motion of Sani and Brihaspati, Shukra in retrograde are illustrated for period around the eclipse pairs.

Solar-Lunar eclipse pair from Julian year 3129BC

 

 

Fourteen days later at same time

The figures above show the pictures of night sky for a pair of Solar-Lunar eclipses, end of lunar eclipse being only 13 days and 20 hours before start of a solar eclipse. Any observer would have easily concluded that the eclipses occurred in less than 14 days because of sunrise occurring in middle of both the eclipses. On Julian August 11 afternoon, a solar eclipse begins at 6:54 before sunset and it is still on going at sunset at 7:14. Fourteen days 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 and start of solar eclipses were less than 14 days or occurred in 13 days. This could be concluded without the benefit of modern clocks.

The dates of this eclipse pair are Julian 3129 and Julian month of August. In ancient Bharata, since the full moon occurred on Proshtapada in Meena, the month would be considered 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 like conditions existed. Even during normal monsoon the sky is occasionally clear for the eclipses 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.

 

Items in red show retograde or Vakri motion

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, only Brihaspati, 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 of Mahabharata war. The eclipses occur some time before the actual war, and there is a suggestion that another solar eclipse occurred in the evening during war, the Jayadhratha episode. However, no eclipse was found in December period, before the winter solstice or uttara ayana.

Lunar-Solar eclipse pair from Julian year 2599 BC

 

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

Lunar eclipse continues after sunrise ending at 6:57AM

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 of lunar eclipse being only 13 days and 20 hours before start of a solar eclipse. On Julian June 27,2559 BC morning, the lunar eclipse, which started at night, is not complete. Fourteen days later (On Julian July 11,2559) in the morning at sunrise the solar eclipse is already occurring and is almost over suggesting it started on the 13th day after the previous lunar eclipse. Clearly, even to the observers then, the end of lunar and start of solar eclipses were less 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 noted somewhere in the Mahabharata text, is to be explored. Also, there is a near Venus occultation during solar eclipse. The near Venus occultation occurring is to be looked for in Mahabharata text.

The dates of this eclipse pair are Julian 2559 and Julian months of June and July. In ancient Bharata, since the full moon occurred on Shravana nakshathra in Makara, 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) and these do occur during 2559 JBC as illustrated below.

 

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

May to September 2559 May to September 2559

Saturn(Shani)in retrograde motion in December 2559

 

Items in red show retograde or Vakri motion

Graha(Planet)

2599BCJ

Mahabharata text

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 positions at the time of eclipse pair. But Brihaspati is near the indicated location as per Mahabharata text

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 Pushya lunar month nearly six months after the short eclipse pair. It occurred shortly before sunset as illustrated below.

 

Clearly this episode can provide an explanation for events prior to Jayadhratha’s death. The Lunar month then was Pushya and sun is still at 19.5 degrees south in Dakshina Ayana. He still has to move to 23.5 degrees (thirty six days away) to reach Uttara Ayana (which occurs on 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 Mahabharata war year.

Solar-Lunar eclipse pair from Julian year 2056 BCJ

 

This pair of eclipses also is a viable pair for Mahabharata date. The eclipse pairs occur in Margashira/pushya lunar months as is evident from above picture. As before, naked eye observers can make out the fact that end of solar eclipse and beginning of lunar eclipse are less than 14 days apart.

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

Items in red show retograde or Vakri motion

Graha(Planet)

2056BCJ

Mahabharata text

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

 

 

This eclipse pair occurs in month of Magha as the full moon is near Magha nakshathra. This is a bit too late for Mahabharata war as the sun is very near winter solstice already at 24 degrees) or uttara ayana.

Items in red show retograde or Vakri motion

Graha(Planet)

1853BCJ

Mahabharata text

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 Sani and Brihaspati are in retrograde motion, but all planets are at positions, which do not agree with Mahabharata text.

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

Lunar-Solar eclipse pair from Julian year 1708 BCJ

 

Items in red show retograde or Vakri motion

Graha(Planet)

1708BCJ

Mahabharata text

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 Mahabharata text. However, the planets Brihaspati and Sani are in retrograde motion. The eclipse pair occurs just after the beginning of Uttara Ayana in winter, and the fact that there was a draught 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

 

 

Items in red show retograde or Vakri motion

Graha(Planet)

1397BCJ

Mahabharata text

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 our search.

The season is right. The two retrograde planets Brihaspati and Sani are very near declared positions. There is no solar eclipse in the period prior to Uttara Ayana. This eclipse pair is a good candidate for Mahabharata war.

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

Beginning of Kaliyuga

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 date has 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.

The Lodestar pro view of sky on that day shows that there was no eclipse at Ujjain (75 deg 47 min E and 25 deg 15 min N) at Amavasya, but sun was 54 degrees away from vernal equinox. (3 hours 36 minutes from equinox- @15 deg/hour this works out to exactly 54 degrees).

Analysis of the Eclipse tables.

This document has demonstrated that two eclipses can occur within about 332 hours, which is less than 14 days. Hence the Mahabharata statement that such eclipse did occur ominously before the war is clearly possible. Such events did occur in 3229 BCJ, 2559 BCJ and few other dates. These were clearly visible through sunset and sunrise making the use of modern clocks irrelevant. Any observer could make out that the eclipses occurred in less than 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 of planets occurs frequently enough, but these occurring, when 13-day eclipses are also occurring 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 Sri Krishna passed away in 3102 BCJ, which is 27 years after the war. Our study confirms that Kaliyuga could have started in 3102 BCJ. Unlike the 2559 pair, there is no visible solar eclipse during the Mahabharata time frame, which would occur. Still this date is a very good date for Mahabharata war.

The second date 2559 BCJ is also unique in that Varaha mihira stated that 2526 before start of saka, Yudhishtira was the ruling king. There is some confusion about saka, whether it was Vikrama (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 time before war, before he lost it in a game of dice to Sakuni/Duryodhana. This date is also an excellent 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 would be 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 near the 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 a reasonably good candidate for Mahabharata war. Again, there was no solar eclipse during the period prior to Uttara Ayana.

 

Conclusions

The aim of this work was to analyze the unique statement that Mahabharata war took place when an ominous pair of eclipses occurred in "Thirteen days". Initially, Mahabharata texts, contemporarily accepted as most authentic were reviewed and relevant data about Mahabharata 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 Mesopotamia valley during the period 2100 BCJ down to 900 BCJ, with best- known contemporary research data.

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

The third issue was, what was the definition of a day, and how was the determination that eclipses occurred in "thirteen days" made, has been addressed. Day was taken to be the time 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 from 3000 to 5000 years ago could identify accurately a "thirteen-day "eclipse pair.

Fourthly, eighteen pairs of possible ‘Thirteen day eclipses" were extensively analyzed. Six pairs 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 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 from Gupta period were credible dates for Mahabharata war. It would appear that 3129 BCJ is a first 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 occurred and observers could easily identify the duration using sunset/sunrise transitions. 3129 BCJ and 2559 BCJ dates appear to be very viable dates for Mahabharata war as are a few others. This study provides modern scientific support one critical astronomical statement made 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. Two articles in Ref 11 and 12 provide background in this area for those who do not have this information.

Acknowledgements

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

References

  1. Aryabhateeya by Brahmagupta,
  2. K.S.Shukla,New Delhi, INSA 1976

  3. SURYA SIDDHANTA : Translation of an Ancient Indian Astronomical Text. Translation by BAPU DEVA, BENARES, 1860.
  4. Varahamihira’s Brihat Samhita- M Ramakrishna Bhat,
  5. Motilala Banarasidas Publications, 1981

  6. Ramashesha Shastry
  7. Bhagavata Mahapurana, 10th skanda,Upodghata (in Kannada script), 1930

  8. John Smith
  9. Mahabharata Text checked by Bhandarakar Oriental Research Institute

    Courtesy http://www.bombay.oriental.cam.ac.uk/john/mahabharata/statement.html

  10. Eric Weisstien
  11. World Of Astronomy

    Courtesy http://www.scienceworld.wolfram.com/astronomy/SarosCycle.html

  12. Jean Meaus
  13. Astronomical Algorithms, Willman Bell Inc Publications, 1991

  14. Wayne Annala, Lodestar Pro Manual, 1994
  15. Wayne Mitchell
  16. Ancient Astronomical Observations and Near Eastern Chronology

    Journal of Ancient Chronology Forum, Volume3

  17. Courtesy http://www.baraha.com
  18. S.Balakrishna
  19. Names of stars from period of Vedas

  20. S.Balakrishna

Comparison of Names of stars-Comparison with R.H Allen’s…


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