This is a followup to the question Is there a simple formula to calculate eclipse timings that you have on your website. Though I read Mr. Pandian's answer, I am still interested in seeing the "tedious" formulae for these eclipse calculations for myself. There are several pieces of software that calculate the eclipse (rather than retrieving it from a server on the Internet), and knowing the calculations necessary would indeed be helpful, as I am creating a weather model and would like to have an inderstanding of what I'm actually up against.

Only in this way can I create the piece of software I am writing.

Eclipse calculations are a combination of orbital mechanics and the geometry of the various orbits. I have put a few equations and figures to illustrate this in this pdf document.

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