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
Back before we had an idea of Newtonian gravity, we just assumed all of the orbits were on rails and could not change. This would drift over time, but not fast enough to notice for hundreds of years.
If you just treat everything as a two body problem between the planet and Sun (and between the Moon and Earth), you get a pretty accurate model, but things start to drift over time. Even then, that’s not even the best we can do with just Newton. This won’t drift for tens of thousands of years.
Even with an N-body system, you can apply Newton’s laws and make very accurate predictions. The problem is if you are even slightly wrong about the initial conditions, you start to drift over time, and the results can’t end up looking very different. That’s why the 3-body problem is so hard, because we can’t tell what it’s going to do after a small change in initial conditions. This won’t drift for millions of years, but we have no idea what it’s going to do when it drifts without more accurate measurements.
Once we had general relativity, Einstein was able to calculate the orbit of the Moon within a centimeter. A prediction we weren’t able to confirm until we landed on the Moon. You don’t need predictions that advanced to predict an eclipse.
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