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 three body problem is so difficult to solve not because it is impossible but because the calculations needed to do it accurately over a long period just pile up rapidly as the motions of each body (it’s not just three bodies, obv, it’s any system of 3 or more bodies) all affect each other. Your initial conditions, presumably at rest or in constant motion, are easy to compute. Once they move, it’s harder and harder to know with precision where things will be simply because the rules of gravitation and motion guiding them initially are all that dictate the motion at the outset, but as time passes, you have to continually factor how their influence on each other is affecting them. In terms of real bodies like the objects of the solar system, there’s also the issue that you’re not actually dealing with three bodies, or 8, or 9, or 100,000. To have extremely precise calculations, you’d need to account for the effects of all the objects in the solar system – the more bodies you can add in, the more precise the projections you can calculate.
Eclipses though are a separate thing from this. Eclipses can be predicted mathematically not through the three body problem (I mean, yes, it’s a three body problem) but through more straightforward math. The positions of the sun, moon and earth do not need to be known with the level of precision that is normally what you’re trying to get when you’re dealing with a three body problem situation. Predicting eclipses is ultimately about knowing when various paths on orbits that are already known will cross one another, and we can know that from observational data. The three body problem applies to predictions of positions of objects that are, like, “purely predictions” – you’re trying to work out mathematically where objects will be and to a precise degree. Once it was figured out formally that the earth was orbiting the sun and that the moon also orbits the earth, all of them in ellipse shapes, it was/is possible to work out eclipse predictions from observations of their real orbits over time and relatively straightforward math. You also don’t have to know exacting positions of the objects – like down to milimeter or whatever arbitrarily small metric you want to use – to predict an eclipse.
The issue with the three body problem is ultimately a calculation problem – it’s not that it’s formally impossible, it’s just that the burden of calculations you have to do spirals out of control quickly to do on paper, or even with a computer. The more objects you have to calculate, the more quickly the calculation burden spirals. In actual reality, it’s also impossible to actually know all the forces acting on the real objects whose positions you’re trying to predict with mathematically certainty into the future, and the less you know of those forces, the more quickly your prediction breaks down.
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