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 is much more massive than the Earth, and the Earth is much more massive than the Moon. Gravity is a force proportional to mass, so in this setup, the Sun dominates the equations of motion, while the Moon’s effects are somewhat negligible, allowing for approximate solutions. It is true that the exact solution would be chaotic over very long time periods, but the differences on human timescales are rather small and wouldn’t be easily detected by ordinary observation.
Thus, eclipses could be predicted by assuming the Earth orbits around the Sun in a circle, and the Moon orbits around the Earth in a circle, which produce regular patterns depending on the angles of those orbits. Better approximations could be made by using elliptical orbits instead of circular orbits.
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