On the measurement for the speed of gravity

Newton’s law of gravity is a theory of instantaneous action at a distance. However, Einstein’s general relativity states that the speed of gravity equals the speed of light, which is finite. Therefore, it is a worthy problem to discuss if Newton’s law of gravity needs modification, when studying and observing the gravitational tidal. In this paper, it is shown that the Newton’s law of gravity is fully applicable in the framework of general relativity. Based on the post-Newtonian approximation, we find that the observable effect for the speed of gravity is irrelevant to the velocity of a moving source, but it is dependent on its acceleration. In general, the effect of the speed of gravity is so weak that today’s any astronomical observations, including the sun tidal observations, can not confirm that the gravitational field travels at the speed of light.