Also see post 39:
LIGO: "Test general relativity's prediction that these [gravitational] waves propagate at the same speed as light, and that the graviton (the fundamental particle that accompanies these waves) has zero rest mass."
http://www.freerepublic.com/focus/chat/2491839/posts?page=39#39
The gravitational field effects are instantaneous for all practical purposes. If they weren’t the planets would have spiraled into the sun a long time ago. Newtonian physics works just fine for non relativistic acceleration.