[edit] this reminds me of something I read about how NASA doesn't predict solar eclipses by trying to keep an exact model of the solar system, but rather uses pattern matching algorithms.
We struggle to predict the exact path of asteroids because of measurement errors, not because computing is slow. Minuscule changes to the initial condition manifest as massive differences in the outcome.
>> In summary, it is clear ancient people could predict timings for lunar eclipses and partial solar eclipses, but there is no convincing evidence of people predicting the times and locations of total solar eclipses.
>> Today, we don’t rely on calculating the orbits of the whole Solar System to predict eclipses. For example, NASA uses a highly advanced form of an ancient technique – pattern recognition. Using some 38,000 repeating mathematical terms, NASA can predict both solar and lunar eclipses for 1,000 years into the future. Beyond that, the Moon’s wobble and Earth’s changing rotation make eclipse prediction less accurate.
[0] https://www.astronomy.com/observing/humans-have-been-predict...
