[dmm]

Kimball -
You can't use Newtonian physics equations when describing relativistic situations (speed close to light speed, c). (Newton was a genius but one person can't discover everything.) You have to use general relativity equations, which are very complicated, involving stuff like tensors (which are like vectors but much worse). From those equations, it is believed that the force of gravity travels at the speed of light. The problem with observing this is that large hunks of matter tend to move at low speeds, so the gravitational field always seems to just "be there", unmoving, instantaneous. So you wind up looking for subtleties like the perihelion of Mercury being slightly different from that predicted by Newtonian theory. Big whoop. However, it is believed that one could detect gravity waves emitted from huge masses undergoing stupendous changes (for example, a supernova), and that these waves would move at the speed of light. There are several on-going experiments to detect gravity waves.

By the way, Einstein didn't get it totally right either. It is believed that general relativity is also incomplete, because it is incompatible with quantum mechanics. What I mean is, that when one attempts to "quantize" general relativity and to describe the gravitational force in terms of "gravitons" (analogous to photons), the whole thing falls apart. To his credit, Einstein knew this and it really bugged him. He spent the latter third of his life trying unsuccessfully to fix it (when he wasn't expressing his doubts about quantum mechanics).