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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....

There is an electrically charged sphere with a significant electrical charge, and in which the mass and radius are such that the gravitational acceleration from the sphere is negligible. Also any tidal forces on the sphere are negligible and the sphere is in a near inertial if not an inertial refere...

How would I find the force law that describes the force between a point and an infinite straight line g(r), given the force law between two points is f(r)? I have found that simply multiplying f(r) by r only produces the force law g(r) when f(r) is an inverse, or reciprocal law, but if f(r) is somet...

Also these are the excel files I used for these simulations

I also simulated orbital motion using the Natural Log Law
Finally I simulated orbital motion using the Natural Log Law at extremely close range

I also simulated orbital motion using the Exponential Decay Law or Inverse Exponential Law

I also simulated orbital motion using the Exponential Law

I also simulated orbital motion using the secant law