The Date of Mahabharata War is a very challenging historical issue. A lot of research has been done on this and there is no consensus.
At best we may say that the date of Mahabharata War is likely to be around 2800 BC.
I have arrived at this date of Mahabharata War based on 7 sources ranging from science, archaeology to astronomy.
1. Date of Mahabharata War as per NASA - 2559 BC
Image Source: Space Answers
Dr. S. Balakrishna (NASA, USA) analyzed the event of two eclipses in (a span of) 13 days prior to Mahabharata using Lodestar Pro software and came up with 2559 BC.
Hence date of Mahabharata War as per NASA is 2559 BC.
2. Date of Mahabharata War from Riyazu S Salatin - 2865 BC
Image Source: Wikimedia Commons
The history book Riyazu-S-Salatin, by Ghulam Hussain Salim (~1785 C.E), is held in very high esteem by Muslims. Based on Riyazu-S-Salatin Date of Mahabharata War is 2865 BC.
I have done a detailed analysis in one of my previous articles "Date of Mahabharata War based on Riyazu s Salatin"
3. Date of Mahabharata War from Aihole Inscription - 3102 BC
Image Source: Wikimedia Commons
An inscription in the Jain Temple at Aihole prepared by one Chalukya King Pulakesin says that the temple was constructed in 3735 years, after the Mahabharata War and 556 years of Shaka (Saka) era in Kali era, that is in 634 AD.
Hence the date of Mahabharata War as per Aihole Inscription is 3102 BC.
4. Date of Mahabharata War as per Greek Records - 3360 BC
Image Source: Howell World History
The Greek Ambassador Megasthenes has recorded that 138 generations had passed between Krishna and Chandragupta Maurya (300 BC).
Taking 20 years per generation, 138 generations means that 2760 years have elapsed between date of Mahabharata War and Chandragupta Maurya.
Hence date of Mahabharata War as per Greek Records is 3360 BC.
5. Date of Mahabharata War as per Aryabhatta - 3102 BC
Image Source: Vedic Sciences
Aryabhatta was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy
He has written the following
"When the three yugas (satya yuga, treta yuga and dwapara yuga) have elapsed and 60 x 60 (3,600) years of kali yuag have already passed, I am now 23 years old.”
This comes to 3102 BC. Hence date of Mahabharata War as Aryabhatta is 3102 BC.
6. Date of Mahabharata War as per Archaeology - 1800 BC
Image Source: Unacknowledged
Dr. S.R. Rao based on archaeological evidence obtained from onshore and offshore excavations conducted in Dwaraka, Bet Dwarka and in the Kurukshetra region found 1900-1700 B.C. as acceptable.
7. Date of Mahabharata War from Astronomy - 3100 BC
Image Source: stories.illinoisstate.edu
In an event jointly organized by The Mythic Society, Indira Gandhi National Centre for the Arts - Southern Regional Centre and Sir Babasaheb (Umakanth Keshav) Apte Smarak Samithi Trust in 2003 called "Date of Kurukshetra War based on astronomical data", most agreed on 3100 BC as date of Mahabharata War based on astronomical analysis of Mahabharata and other texts.
Hence date of Mahabharata War as per astronomical references is 3100 BC.
Based on all this overwhelming evidence we can say that the date of the Mahabharata War is around 2800 BC.
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References and Additional Reading
The Vedic Foundation