Two Body Problem for different Force Laws

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AlternateGravity
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Joined: Thu May 15, 2014 5:45 pm

Two Body Problem for different Force Laws

Post by AlternateGravity » Tue Jul 30, 2019 1:26 pm

I understand that the two body problem is solvable, for any two bodies using the inverse square law, and it is also solvable for the reciprocal law. I understand that the three body problem is not in general solvable, although there are some special cases of the three body problem that are solvable. I notice as well that the inverse square law, and the reciprocal law are the only force laws, in which all bounded orbits are also closed orbits for a two body system. I was wondering if the two body problem is solvable for force laws other than the force laws 1/r^2, and r, or if the two body problem is only solvable for the force laws 1/r^2, and r. For instance could I simply plug in some initial conditions, and a time into an equation corresponding to a force law f(r), in which f(r)=/=1/r^2, and f(r)=/=r, and calculate the position and velocities of two bodies for any force law without using a simulation?
Gravitons would be my favorite particle as their existence could prove extra dimensions.

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