Inspired by your answer, I imagine we might also consider the fact that m1 and m2 are not perfect rigid point masses. Each is a spring-connected set of points of mass - molecules and atoms with intermolecular forces - spread in a volume. The individual points of mass will exert different gravitation forces on each other and have time-delayed spring forces transmitted through the network of points. I guess we can ignore the speed of gravity when doing a rough approximation.