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
Almost all the comments are wrong. It has nothing to do with relative mass ratios. Classical 3 body problems were for a massless 3rd body, you can also predict very well the dynamics of triple star systems no matter what mass ratios are there
The moon is massive, it is the biggest moon in the solar system in relative terms (for a planet)
You can predict eclipses because the moon is so close to Earth you can approximate the gravity from the sun as some constant force plus linear tidal force.
The nice thing is that all the complex effects (relativity, quadrupole moment, tidal forces) just rotate the moon’s orbit. It rotates in one way every 8.85 years and in the other 18.6 years. You can empirically measure those without making complex calculations. This was even used to verify the theory of gravity.
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