"It assumes gravity is an instantaneous force; which it is not."
Has that been determined experimentally? I admit that gravitational theory is not one of the areas I read in frequently. Where should I go to see something about this?
I've not been able to find anything specific (admittedly I didn't search very deeply), but Special Relativity implies that gravity, like everything else, is limited by the speed of light. According to general relativity, gravity propigates at lightspeed. It's hard to get a lot of solid information given that gravity is far less understood than other more well-established scientific theories, like evolution.