These computer models that predict solar eclipses (or reveal solar eclipses that have happened in history): how far back in time can they go? To the beginnings of the Earth and Moon as we know them? How far forward can they predict? Until the end of the Universe as we know it?
Well sure they can predict that far, but they lose accuracy the further they go. For one thing, the sun will probably go red giant and swallow up the Earth long before the end of the universe, so predictions beyond that are meaningless.
But more importantly the orbits are not long-term completely stable, and they cannot solve the general three-body (let alone n-body) problem analytically even for Newton’s model (let alone General Relativity). So all calculations are numerical which leads to rounding error if nothing else. There there’s changing orbits to deal with. The moon is receding from the earth , for example and the day is getting longer which affects where on earth you see the solar eclipse.
The calculations are accurate enough to be verified by the historical data we have but that’s only a few thousand years.
The ephemeris DE431 (published 2013) covers the years -13,200 to +17,191. One question is, if you are merely interested in solar eclipses on Earth, how accurate do you need to be, and how much further could you reasonably push it in that case?
You don’t need data from thousands of years into the future to know at what point the model would cease to be accurate enough. The models are all based on data, and the data all have error bars, and the error bars should all be known. So you run the model once, with all of the best values for the data. Then you add random noise to all of the observations, according to the known error bars, and use those values as input for the model, and run it again. Repeat many times. If you do this a thousand times and every single run out of that thousand predicts an eclipse on such-and-such a date, then you know that the model is good that far out. If most of the runs predict an eclipse, but a few say there won’t be, then you know that you’re getting to the limits of your model. And when you get to the point where the different runs all say completely different things, you know your model is no good at all at that point.
Also the moon is getting further away while the sun is gradually growing larger, so eventually there will be no total solar eclipses.
DPRK’s link talks about all the things that go into calculating past and future eclipses … fairly extensive list I might add … I wouldn’t have thought the liquid nature of the Moon’s innards would make that much difference …