# Back-predicting solar eclipses

I want to back-predict solar eclipses as part of a research project. My main goal is to obtain a list of all solar eclipses that took place over a tight grid (let's say of 100km by 100km) for the years 5000BC to 4000BC (just as an example).

Ideally, I'd like results to follow, more or less, the format here of https://eclipse.gsfc.nasa.gov/JSEX/JSEX-SA.html, but any library you can suggest will be fine. According to the previous reference, "The Besselian elements and values of ΔT used in Solar Eclipse Explorer are the same as those used by Five Millennium Canon of Solar Eclipses: -1999 to +3000. For the purposes of calculating eclipse circumstances from a given place, the growing uncertainty in the value of ΔT and the corresponding longitude become unacceptably large outside time period of -1499 to 3000 (1500 BCE to 3000 CE)." and hence I could not use their tool.

Since I will simply count how many eclipses could be seen at the center of each square on my grid for the 1000-year period, I can tolerate large inaccuracies in the timing of eclipses. Moreover, as long as errors are random, I can also afford missing some eclipses or having them missplaced.

Is there any resource I could use to compute eclipses as I described?

• Is the 5,000BC in your example the farthest back that you want to go? If not, then how far back? For example, DE431 covers years –13,200 to +17,191 (see here and here) so searching for eclipses and calculating their ground tracks based on that would be straightforward but it might take a while on a PC. A script using some geometry in python with Skyfield is all that's needed for example, plus some patience. The accuracy would be as good as DE431. – uhoh Jun 26 '17 at 16:25
• Thank you! I was thinking not going much further back in time, so -13200 sounds just perfect. I will check your references. Probably it will take a bit to run on my PC, but and I can certainly wait. – Keizer Jun 26 '17 at 17:35
• I was surprised that not even eclipse.gsfc.nasa.gov/SEcatmax/SEcatmax.html goes far back enough (only to 3999 BCE). The answer's not hard to calculate using CSPICE (naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/index.html) and I might give it a go (feel free to contact me directly if you want to program it and just need help), but the accuracy will be fairly poor-- finding the eclipses should be "easy", but finding where on Earth they occur might be more difficult. – user21 Jun 28 '17 at 17:45