Abstract

Mahabharata war 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. Using modern astronomical software, our article shows that a number of Thirteen day eclipse pairs were visible in Kurukshethra. Article suggests some candidate dates for Mahabharata war.

Introduction

Mahabharata is a great epic, and is one of the pillars of present day Hinduism. The Mahabharata story and its moral ethos have had profound influence on millions over many generations. Mahabharata war is said to have occurred before the transition of Dwapara Yuga to Kali Yuga.  Dating the Mahabharata war and start of Kaliyuga has been elusive and going on for many centuries.

Aryabhata, is a famous early astronomer with contributions to science, whose estimate of p, and the time of moon revolution around the earth are so accurate, that his works are being extensively researched. Aryabhata (476-550 AD) stated that Kaliyuga started 3600 years before, when he was 23 years old, making the start as 3102 BC [Aryabhateeya ref-1]). It would date Mahabharata war to around circa 3130-3140 BCJ.

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 15min 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].

When Saptarishis (ursa major) was near Magha Yudhistira was king 2526 years before Saka time

Presently, traditional Sanatana Dharma followers consider that Kaliyuga started at 3102 BCJ, when Sri Krishna passed away, and that Mahabharata war occurred in 3138 BCJ. 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) astronomical 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 war. 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 features 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 as in the case of Vedic chandas prosody. The known oldest version has nearly 90,000 to 100,000 poems dominantly with 32 syllables Anushtup chandas, in 18 chapters called Parva's [ref-4 and 5].

The Bhishma Parva and Udyoga Parva (specific chapters of Mahabharata) provide considerable astronomical/astrological descriptions and omens as the Mahabharata war was approaching. It describes a period of draught, with many planetary positions. 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 lunar month etc...

This reference to Thirteen day eclipse pair appears to be a unique astronomical observation.

Mahabharata text also refers to retrograde motions of planets prior to war and provides their location with reference to 27/28 Vedic star locations. Mahabharata Drona Parva also refers to Jayadhratha's killing during a dark episode on 13th day of the war, which some consider as another short solar eclipse.

This document is basically concerned with analysis of all eclipses visible at Kurukshethra (Location where Mahabharata war took place, 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 astronomical 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. During period 3500BC to 700 BC, nearly 4350 lunar eclipses have probably occurred. A good fraction of these would have been visible in Kurukshethra [ref-6]. 

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 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 few thousand miles falling on nearly 8000-mile diameter earth. Hence, solar eclipses can be seen only in a limited range of longitude-latitude where the shadow falls. Elsewhere, even though sun is visible, eclipse will not be seen.

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- 7]. The Lodestar Pro was checked for historical eclipses of 1000-2500 BC from clay tablet records of Mesopotamia area presently available with British Museum. Wayne Mitchell has analyzed this data [Ref-8]. Lodestar Pro provided excellent match with ref-8.

Eclipses at Kurukshethra

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 eclipse pairs visible in Kurukshethra, 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 Kurukshethra location. These are tabulated and plotted. 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 Kurukshethra. Amongst these, nearly 32 pairs would be occurring for period less than 14 days. Many of these were found to be weak penumbral eclipses of moon, and solar eclipses had such low obscurity as to raise the issue whether any body could see them. Six pairs of 'thirteen day' eclipses could be seen unambiguously. 

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 would be the logical definition of a day. Using this definition, it is possible to determine whether an eclipse pair occurred in 'Thirteen days'.

Kurukshethra eclipses and some planetary retrograde motions

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

Six eclipse pairs visible at Kurukshethra 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/start date

Location of Kurukshethra 76 deg 49 min East, 29 deg 59 min North

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. There are others that have low obscurity for solar eclipse, or have dominant penumbral lunar eclipse content and hence do not constitute strong candidates for the Mahabharata war.

One typical eclipse pair of the six is illustrated using Lodestar Pro views of the relevant sunset/sunrise periods. 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. Planets Sani (Saturn) and Brihaspati (Jupiter), Shukra (Venus) in retrograde motion are illustrated for period around the eclipse pairs.

Solar-Lunar eclipse pair from Julian year 3129 BC

Fourteen days later at same time

Let us now look at how any observer can study these eclipses and conclude that the pair occurred in 'Thirteen days'. The figures above show the pictures of day/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 August 11 afternoon, a solar eclipse begins 20 minuets before sunset and it is still on going at sunset. Fourteen days later (On Julian August 25) in the evening at sunset a lunar eclipse is already occurring. It clearly suggests that eclipse started on the 13th day after the previous eclipse! Obviously the end of lunar and start of solar eclipses were less than 14 days period, 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, 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 retrograde or Vakri motion

1. Aryabhateeya by Brahmagupta, S.Shukla,New Delhi, INSA 1976
2. Surya Siddhanta: Translation of an Ancient Indian Astronomical Text.
   Translation by Bapudeva, Varanasi, 1860.
3. Varahamihira's Brihat Samhita- M Ramakrishna Bhat, Motilal Banarasidas Publications, 1981
4. Ramashesha Shastry Bhagavata Mahapurana,
   10th skanda, Upodghata (in Kannada script), 1930
5. John Smith web page - Mahabharata Text checked by Bhandarakar Oriental Research Institute
6. Eric Weisstien, World Of Astronomy web page
7. Wayne Annala, Lodestar Pro Manual, 1994
8. Wayne Mitchell
      Ancient Astronomical Observations and Near Eastern Chronology
      Journal of Ancient Chronology Forum, Volume3