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Eclipses, Solar and Lunar
Both solar and lunar eclipses dates, described in the MBH, have been tried to find out using the Lode Star Software. Generally 240 Solar and 150 Lunar eclipses occur in a century and during the period from 3300 BC to 700 BC nearly 6000 solar and 4000 lunar eclipses took place, though not all of them were visible from Kuru Kshetra, India. Out of them, 672 were eclipse pairs, or both Solar and Lunar eclipses within a Lunar month. There are mentions of solar eclipses at 8 places in MBH, out of which three of them are very important.
(1) The first solar eclipse is mentioned in the Sabhaa Parv.
(2) The second solar eclipse is mentioned in the Udyog Parv to which Karn tried to draw the attention of Krishn when He was returning from Hastinaapur.

(3) The third important solar eclipse has been mentioned in the Shalya Parv, that occurred along with two lunar eclipses within a month. Many believe that there was a total solar eclipse occurred on the 13th day of the War, which has been allegorically mentioned as covering the Sun by Krishn with His Sudarshan Chakra to facilitate Arjun to be able to kill Jayadrath.

(4) Three Eclipses Together - Another important mention of eclipses is the set of three eclipse occurred just prior to the MBH War, a very rare event of three eclipses occurring just within a lunar month took place: a lunar eclipse followed by a solar one and then another lunar eclipse. According to the text of MBH, the solar eclipse occurred just 13 days after the first lunar eclipse. S. Balakrishna of NASA, USA, has searched all eclipse pairs, a lunar eclipse followed by a solar eclipse after 13 days, that took place from 3300 BC to 700 BC, using the Lodestar pro-software. He found that nearly 672 eclipse pairs have occurred within the said period, out of which 27 pairs have been found to have less than 14 days time gap. And according to Balakrishna, the eclipse pair of 2559 is the best match with the description given in the text of MBH. But according to Kalyanaraman, the eclipses occurred in 3067 BC - the Lunar eclipse on 29th September at the asterism Krittikaa and the Solar eclipse on 14th October at the asterism Jyesthaa.

--One occurrence of a Solar Eclipse is mentioned at the asterism Jyesth and a Lunar eclipse at the asterism Krittikaa, just before the beginning of the War.

Nakshatra and Tithi
Many people say that Nakshatra were not known in MBH times, so they are not mentioned in it. But this is not so. Vyaas Jee has mentioned Nakshatra in it, and not only mentioned them in relation to time but in other senses also. If you want to see where the word has appeared, use the search method of your browser to search the word, such as "Hast" ---

The Udyog Parv of MBH narrates that, just before the War,
--Lord Krishn, on His final peace mission, went to Hastinaapur in the month of Kaarttik. He set out on the day when the Moon was at the asterism Revatee. On His way to Hastinaapur, Krishn took rest for a day at a place called Vrik Sthal, and on that day the Moon was at the asterism Bharanee.
--The day on which Duryodhan turned down each and every effort of Lord Krishn to make peace and made the war inevitable, the Moon was resting at the asterism Pushya.
--And the Lord left Hastinaapur with Karn, on the day when the Moon was yet to reach the asterism Uttaraa Phaalgunee. As mentioned above, Karn accompanied Him to some distance to see Him off and he then described to the Lord the positions of planets in the sky and expressed his apprehension that such a planetary configuration stood for very bad omen: such as large scale
loss of life and drenching of blood.
--Vyaas Jee narrated all these planetary positions in as many as sixteen verses as if someone was describing it only after visualizing them in the sky.
--It is also well known that during the War, Lord Balaraam went on a pilgrimage to holy places along the banks of the River Saraswatee and MBH describes the position of the Moon during the entire course of his pilgrimage. For example, He set out on the day when the Moon was at the asterism Pushya and returned on the day when the Moon was at the asterism Shravan.

(MBH, G-2-Childhood/2)
Here Vyaas Jee uses the name of "Hast" Nakshatra just to give a simile to Drone and five Paandav.

(G-3-Youth/2)
Thus the Paandav set to Baaranaavat on the 8th day of the month of Phaalgun when Rohinee star was in ascendant.

--Krishn, on His final peace mission, set out for Hastinapur when the Moon was at the asterism Revatee.
--Krishn arrived Hastinapur when the Moon was at the asterism Bharanee.
--The Full Moon and Lunar eclipse at Krittikaa occurred.
--The Solar eclipse occurred at Jyeshthaa.
--The comet Mahaaghor appeared at the asterism Pushya after Bheeshm had died.

Some Other Astronomical Information
--It also mentions the appearance of a comet at the asterism Pushya, on the 8th day of the bright half of the month of Maagh, when Bheeshm died. On that day the Moon was at the asterism Rohinee and it was the day of Winter Solstice.

--The day on which Ghatotkach, son of Bheem, died, the Moon appeared at the horizon at 2 am.

--The epic also mentions the occurrence of a very rare astronomical event that took place prior to the War: three eclipses, two lunar and a solar, within a lunar month of 27 days.

--There is also another continuing tradition in this country that says that the beginning of the present Kali Yug, Kurukshetra War, death of Lord Krishn and coronation of Emperor Yudhishthir were contemporary events.

--Famous astronomer Aaryabhatt in his celebrated work Aaryabhatiyam had accepted the said tradition and used the word Bharatapoorvam in the said work very often and scholars agree that he used the word to refer to such events that occurred before the MBH War. In 1991, Dr. D. Abhayankar and Dr Ballabh of the Osmania University calculated that the present Kali Yug began on 7th February, 3104 BC. But it is now well accepted by the both Eastern and the Western scholars that the present Kali Yug began on the midnight of 17th and 18th February, 3102 BC. And hence it can roughly be said that the Mahaabhaarat War took place nearly 5000 years ago from now.