Is the Newtonian gravitational potential $-\frac{GMm}{R}$ just an approximation?

Question

Is $-\frac{GMm}{R}$ just an approximation? I believe that it is since we assume that one of the mass is at rest when deriving it.

Answer 1

So when we use this Potential we tend to use it in cases whereon mass is much larger than another so any movement from gravity is negligible, like with us on earth we are pulling back on the earth as the earth pulls on us so we give it a minuscule change in momentum so in our reference frame negligible movement so can just be seen as being at rest. This applies to all masses in a Newtonian framework no matter the velocity.