An article I read said we haven’t solved the three body problem and can’t predict the motion of 3 orbiting things in motion (2002 VE “Venus moon”) but we’ve been able to get the telescope to orbit just fine with itself the earth and the sun.. what’s the difference?
In: Physics
The key here is what is meant by “solved”. It’s been proved that there’s no general “closed-form” solution for the three-body problem. This means that, generally, there’s no mathematical formula we can use to give us the future positions of three bodies orbiting each other. But that’s not a problem at all for spacecraft because we can just use computers to simulate their motion to any degree of accuracy. This is a “numerical” solution as opposed to a “closed-form” one.
In practice, the limiting factor on the accuracy of our numerical solutions is in knowing the exact positions and velocities of the objects at some point in time. Small errors in the starting conditions of the simulation lead to larger and larger errors over time.
Anyway, the solar system has many more than three objects orbiting around so, even if we had a closed-form solution to the three-body problem, it wouldn’t give an exact solution. There’s still the problem of not knowing the exact starting conditions and then you have the other planets contributing tiny effects that build up over time. There are also small effects from sunlight and the solar wind. As you get closer to the earth, the fact that it bulges at the equator has a substantial effect and its magnetic field can have effects too.
The five, special-case solutions to the three-body problem discovered by Lagrange are often useful in planning orbits for spacecraft. It’s just like our knowing the two-body problem has solutions like circular and elliptical orbits. The two-body solutions aren’t exactly correct in the real world, because there are many more than two or three bodies, but they’re a close-enough approximation and they’re easy to understand.
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