I take it this question is derived from its current Wikipedia entry on the subject, which contains the following line:
Attempts to date the events using methods of archaeoastronomy have
produced, depending on which passages are chosen and how they are
interpreted, estimates ranging from the late 4th to the mid-2nd
millennium BCE
The footnote linked to for this passage currently reads as follows:
Gupta and Ramachandran (1976), p.246, who summarize as follows:
"Astronomical calculations favor 15th century BCE as the date of the
war while the Puranic data place it in the 10th/9th century BCE.
Archaeological evidence points towards the latter."
This reference is listed in their sources as:
Gupta, S.P. and Ramachandran, K.S. (ed.). Mahabharata: myth and
reality. Agam Prakashan, New Delhi 1976.
Unfortunately, that's where the trail goes cold for me. The book doesn't appear to be listed with Amazon or Goodreads, even though 2 other later works by this same pair are listed there. Presumably if someone could dig a copy of this book up, they could turn to page 246, and then trace any references/footnotes given there to the parties in question.
There's also a WP page specifically on Archaeoastronomy and Vedic chronology, but it doesn't mention the exact 200 year band you are looking for. Considering errors with this method appear to be in the multiple thousands of years, getting one that close by pure luck seems unlikely. The closest I see in there is 1660 BCE by Subhash Kak.
I can't help but add a bit of historical analysis here. Specifically the dating technique discussed is little more than science-flavored nonsense. Any technique of historical dating that has variances of 3,000 years or more has all the predictive power of a Magic 8 Ball. In other words, its worthless. You might as well just pick a date you like, and save yourself and everyone else a lot of work.
When actual historians take a crack at dating the setting of the work, using their normal textual analysis techniques, it appears to be set in Iron Age India, which we know from archeology means about 1300 - 200 BCE*. If it was any earlier than that, then they weren't actually using the iron weaponry the epic says they were. If we are looking for a culture that matches the one depicted, then our best bet is the Kuru kingdom of 1200 - 500 BCE. That's of course assuming it has any kind of solid basis in history at all.
* - The first iron smelting find anywhere in the area was around 1800BCE. So there's an 1800 number for you, I guess.