(This isn't a homework problem, just something I've been thinking about.) Suppose we have two planets isolated in space separated by a distance "D." They exert a gravitational force on each other which changes as they get closer. If we were in the accelerating reference frame of one of the planets, how would one determine the acceleration of the other planet? Of course the acceleration is not constant and would be dependent on their distance. Relative accelerations don't add like relative velocities in the Galilean transformations, correct? Can you satisfy my curiosity?