Astronomical references from the text suggest that the Mahabharata war took place not earlier than 3200 BCE nor later than 1800 BCE.
Dr. B. N. Narahari Achar, is Professor Emeritus at the University of Memphis in the Physics Department. He earned his B,. Sc (Hons) degree from Mysore University and M. S. and Ph. D. degrees from the Pennsylvania State University. He taught at the Pennsylvania State University and Bucknell University before joining the University of Memphis. His primary research area is in the theory of Solids and recently in the application of Fractional Calculus to Physics. His other interest is in the ancient astronomy of India and applications of Planetarium software in its study. He has contributed to the determination of the Date of the Mahabharata war. He is currently working on tracing the history from Rigveda to Nandas through Mahabharata, Parikshit and Janamejaya. He has developed a new model for the structure of RigVeda.
This is the month of māgha, the month to celebrate bhīṣma aṣṭamī etc. It would not be inappropriate to ponder about the date of the events connected with the pitāmaha. One cannot fail to recognize the ingenuity of vyāsa in providing the information for finding the date of the war.
antare caiva saṃprāpte kalidvāparayorabhūt |
samantapañcake yuddhaṃ kurupāṇḍava senayoḥ || ( MB 1.2.9)
“The war between the Kaurava and Pandava armies took place at samantapancaka at the sandhi between Dvapara and Kaliyugas.”
This is all the epic says about the date of the war. It took place during the transition from Dvapara to Kali yugas. Nowhere does it say when Dvapara ended or when Kali started. It leaves the exact date unspecified. It specifies that kṛṣṇa exited from this world thirty-six years after the war, but leaves the exact date unspecified. This much information is enough for the collective memory of Bharatiyas to celebrate Gita Jayanti, kṛṣṇa Jayanti etc.
kaumude māsi revatyāṃ śaradante himāgame |
sphītasasya sukhe kāle kalyāḥ sattvavatāṃ varaḥ || (MB 5.81.7)
“In the month of Kartika, on the day of Revati after the passing away of sharad ṛtu and in the dewy season, and at a time when the earth had an abundance of crops on it that foremost of men of prowess (set forth for Hastinapura)”.
This is an absolutely clear reference to seasons when kṛṣṇa sets out for his peace mission.
Here Vyāsa provides the information for determining the limits for the date of the war which can be done in the following way. kṛṣṇa reaches Hastinapura on kārtika paurṇimā and it is the end of sharad ṛtu. For kārtika paurṇimā, the moon can be anywhere from bharaṇī to rohiṇī. For it to be in the autumn season (sharad ṛtu) the sun must be near or just beyond Autumnal Equinox (AE). For the paurṇimā moon, the sun must be exactly 180 degrees from the moon. For kārtika paurṇimā, the sun can be anywhere from viśākha to jyeṣṭhā. So the AE can be from viśākha to jyeṣṭhā. This can happen between 1800 BCE and 3200 BCE. Thus kṛṣṇa’s peace mission, involving kārtika paurṇimā at the end of sharad ṛtu, can happen only between 1800 BCE and 3200 BCE. No date much earlier than 3200 BCE (such as 5561 BCE) or much later than 1800 BCE (such as 1478 BCE) is possible as the connection between kārtika paurṇimā and end of sharad ṛtu will be lost.
saptamāccāpi divasāt amāvāsyā bhaviṣyati |
sangrāmaṃ yojayet tatra tāmhyāhuḥ śakradevatām ||MB( 5.140.18)
“Seven days from now falls the New Moon day, with Indra as the Deity for the nakshatra of the day. (i.e., jyeshtha nakshatra). Let things be readied for the war starting on that day.”
After the peace talks fail, kṛṣṇa rides with karṇa and has a long conversation with him. At the end of that conversation, kṛṣṇa sends this message to bhīṣma droṇa and kṛpa with karṇa. Here is the most important reference about the amāvāsyā at jyeshtha nakshatra. Karṇa tells kṛṣṇa
somasya lakṣma vyāvṛttaṃ rāhurarkamupeṣyati || MB(5. 141. 10)
“The moon lost its luster and rāhu is approaching the Sun.”
He refers to the lunar eclipse that had already taken place on kārtika paurṇimā, and the solar eclipse that is going to happen on the next amāvāsyā at jyeshtha nakshatra.
prājapatyaṃ hi nakṣatraṃ grahastīkṣṇo mahādyutiḥ |
śanaiścaraḥ pīḍayati pīḍayan prāṇinodhikam || MB(5.141.7)
kṛtvā ca aṅgārako vakraṃ jyeṣṭhāyāṃ madhusūdana |
anūrādhāṃ prarthayate maitraṃ saṃśamanayanniva || MB(5.141.8)
“The noxious and much lustrous graha Saturn, which always afflicts people severely, is afflicting the nakshatra presided by prajapati.”
“Mars has performed a retrograde near Antares, oh, madhusudana, and appears to be praying for anuradha ‘s friendship, as if to pacify it.”
Here vyāsa provides the information for determining the exact date of the war. The planetary configurations are
- Saturn near Aldeberan
- retrograde motion of Mars just before reaching Antares.
- a lunar eclipse with the moon near Pleiades and
- a solar eclipse Antares which follows the lunar eclipse.
A search is made for the years in which there is a conjunction of Saturn with Aldebaran between 3500 BCE and 500 CE. As Saturn takes an average of 29.5 years to go around the sun once, the event also repeats with the same period. There are 137 such conjunctions during the interval of 4000 years specified above.
A second search is then made for those years from among these 137 dates when Mars is retrograde before reaching Antares. Since the retrograde motion of Mars repeats with the same period as its synodic period (1.88 years), a spread of two years on either side of each of the dates was considered in the search. The search reduced the set to just seventeen: 3271 BCE, 3067 BCE, 2830 BCE, 2625 BCE, 2388 BCE, 2183 BCE, 1946 BCE, 1741 BCE, 1503 BCE, 1299 BCE, 1061 BCE, 857 BCE, 620 BCE, 415 BCE, 28 CE, 233 CE and 470 CE. These are the dates when Saturn was near Aldebaran and Mars executed a retrograde motion before reaching Antares. There are no other dates in the range 3500 BCE-500 BCE when these two events occur in the same year.
The third search is then made for those years in which there is a lunar eclipse near Pleiades. This reduces the set from 137 to just two, 3067 BCE and 2183 BCE. In both of these years, the lunar eclipse on kārtika paurṇimā is followed by a solar eclipse at jyeshtha nakshatra. Changing the order of search, i.e., searching for those years in which a solar eclipse at jyeshtha first and then search for dates with a lunar eclipse on kārtika paurṇimā did not alter the results.
Of the two solutions for the date of the war, 2183 BCE has to be rejected, for it requires the war to be started on an amāvāsyā, but this contradicts the description of the war on the fourteenth day when it continues into the night and is halted only when the moon rises in the wee hours of the morning. Thus a unique date emerges.
Thus vyāsa provides the information for determining the exact date of the war as well as for determining the limiting dates within the epic and in the udyoga parva. All other astronomical references must be interpreted appropriately so as not to violate the rules of interpretation. Any extraneous data such as the beginning of Kaliyuga in 3102 BCE (the so-called Aryabhata tradition) or that Kaliyuga started with the passing away of Krishna in 3102 BCE (the so-called Bhagavata tradition) and war happened 36 years before that date all lead to inconsistencies. Inconsistencies also result in linking winter solstice in Dhanishtha and the date of the war.
 In Ramayana (II. 70.12) a similar phrase occurs when Bharata is summoned to go to Ayodhya after Rama has been banished to the forest: “yujyatāṃ cāpi te rathaḥ” |“ Let your Chariot be readied”.