Astronomical dating of mahabharata
For kārtika paurṇimā, the sun can be anywhere from viśākha to jyeṣṭhā. 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
This is the month of māgha, the month to celebrate bhīṣma aṣṭamī etc.
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.
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.