Isn’t the 3 body problem (sun, Earth, Moon) very difficult to solve? How did humans predict future eclipses decades even centuries ago?
In: Planetary Science
The Sun, the Earth and the Moon is not really a three-body problem because of huge differences in mass between the bodies and in distances between the pairs.
Effectively, you have two separate two-body problem Sun vs (Earth+Moon) and Earth vs Moon; and you can solve them independently and then introduce small perturbations for each from the third body if necessary to achieve required precision.
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