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 so much bigger than the Earth and Moon (and all the other planets) that, to a very good approximation, the Sun may as well be unaffected by the gravity of its planets. The Earth is also quite a bit bigger than the Moon, but the difference isn’t as great, so the Moon’s effect is more noticeable.
To put it in perspective, the Sun contains 99.8% of the mass of the entire Solar System. All the planets may as well be a rounding error. ~~As far as we’re concerned, the Sun is standing still, completely unaffected by the planets (even if *technically* it is a little bit).~~ Some planets do have a noticeable effect on the Sun, but basically there are enough huge size differences that almost any calculation we would want to do simplifies to a two-body problem.
The three-body problem is mainly difficult when all three bodies are close enough in size that they all have a significant effect on each other.
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