I know the moon does. I know it is because tidal forces fall off as 1/r3. But why? Mathematically, I mean.
F = GMm/r2
The Attempt at a Solution
Did you try a search on Tidal Force? Even the Wikipedia article on Tidal Force shows a short derivation (granted it's for the locations lying along the line joining the centers of the two interacting bodies, but it avoids the vector math required for the more general solution for points located anywhere on the surface of the smaller body).I should have been more specific. How do you get from F = GMm/r2 to an equation for tides that has a 1/r3 in it?
Tides result because of the variation of the force of gravity. Points on the side of the earth near to the moon are more strongly attracted than points on the far side.I should have been more specific. How do you get from F = GMm/r2 to an equation for tides that has a 1/r3 in it?