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I am searching for an year which satisfies the following criteria.

Dates are in Gregorian calendar.

Criteria

  1. Year range 3800 BC to 500 BC
  2. Solar Eclipse of any kind between October 14 and October 22 inclusive.
  3. Lunar Eclipse of any kind between September 29 and October 9 inclusive.
  4. Eclipses visible from New Delhi, India, UTC/GMT +5:30 hours.

Optional Criteria
The gap between the two eclipses must be less than 14 days.

Challenge

The challenge mainly is because the dates are in Gregorian and not Julian which the online eclipse searchers(eg: moonblink) use. I could not find an eclipse searching tool which uses Gregorian calendar. The problem with converting Gregorian to Julian and then searching is that the date changes as the year changes and we end up with varying dates over thousands of years making it difficult to search. How to solve this?

Feasibility

If we solve that problem, each day of the year has approximately 20 eclipses between 3800 BC and 500 BC. So the eight days from Oct 14 to 22 would approximately have 160 eclipses. Then back to back eclipses with Lunar eclipse followed by Solar eclipse are rare, so approximately 10 to 15 eclipses will fit the back to back eclipse criteria. From which using the 'visible from New Delhi, India UTC/GMT +5:30' criteria can be used to narrow down to couple of eclipses. The optional criteria can also be used if applicable.

Edit: It seems I have wrongly estimated the number of eclipses fitting the criteria. The number of years satisfying the first three criteria seem to be around 120 to 140.

Context

This is an independent effort to date the Mahabharata War using Archeastronomy.

In Mahabharata war, Bhishma is said to have left his mortal body on Winter Solistice which is Dec 21 or Dec 22 Gregorian. Which was also the first quarter of waxing Moon of Hindu lunar month Magha. But this Winter solistice observation was observed through naked eye, so researchers like Dr. Manish Pandit have opined that it was 4 or 5 days after Solistice. So it could be from Dec 21 to Dec 27. We also know that there was a Lunar eclipse on Karthika Full Moon and a Solar eclipse on Karthika New Moon. Which is approximately 83 days and 68 days from observed winter solistice. This gives us Solar Eclipse of any kind between October 14 and October 22 and a Lunar Eclipse of any kind between September 29 and October 9. They had to be visible from New Delhi, India.

Edit 1: Conversion of date range from Gregorian to Julian

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    $\begingroup$ Moonblink says it's main source is eclipse.gsfc.nasa.gov/LEcat5/LEcatalog.html . The eclipses are listed there in Gregorian date format. Note NASA's comments on delta T (how the Earth's rotation varies), so you'll probably want to loosen you're "Visible from New Delhi" criteria. $\endgroup$
    – Greg Miller
    Jan 27, 2022 at 22:04
  • $\begingroup$ @GregMiller thanks, but Gregorian is only used for modern dates, not for BC dates. It says 'The Gregorian calendar is used for all dates from 1582 Oct 15 onwards. Before that date, the Julian calendar is used' 1582 is AD. $\endgroup$
    – Profile name
    Jan 28, 2022 at 1:30
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    $\begingroup$ That Gregorian / Julian convention is what Horizons uses. And the Fred Espenak eclipse catalogs "only" go back to 2000 BC. I suggest you use Julian day numbers and do your own proleptic Gregorian date conversion. $\endgroup$
    – PM 2Ring
    Jan 28, 2022 at 1:45
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    $\begingroup$ Dealing with Delta T will be a major issue for those early dates. The uncertainty in Delta T is large in 3800 BC. eclipse.gsfc.nasa.gov/LEcat5/uncertainty.html says that in year -4000, the uncertainty in Delta T is 16291 seconds (>4.5 hours) and the longitude uncertainty is 67.9°. $\endgroup$
    – PM 2Ring
    Jan 28, 2022 at 2:04
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    $\begingroup$ I found some Espenak / Meuss pages with earlier eclipses: TEN MILLENNIUM CATALOG OF LONG SOLAR ECLIPSES & Solar Eclipses of Saros 0 to 180. Of course, they use Julian calendar dates, but converting those dates to Gregorian is a lot easier than calculating eclipses. ;) $\endgroup$
    – PM 2Ring
    Jan 29, 2022 at 2:25

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