The so-called 'speed of gravity' has been the source of some controversy over the years. The anti-relativity school maintains that the speed of gravity must be infinite, i.e., that gravity acts instantaneously over any distance. Relativists, on the other hand, maintain that no influence propagates faster than the speed of light and that gravity is no exception.
We know that gravity keeps the Moon in a stable orbit around Earth, despite the fact that Earth is moving around the Sun at the enormous speed of 30 km per second. What is more, the Moon and Earth are actually both orbiting around their common center of mass, also called their barycenter.
So what happens to the gravitational field in this scenario? It is reasonable to expect that the gravitational field must be varying continuously at every point in a barycentric coordinate system. According to Newton's theory of gravity, these variations in the gravitational field must occur simultaneously over the whole field.
Relativity says that any variation in the gravitational field will propagate at the speed of light. Find out how this 'conflict' is resolved in The Speed of Gravity.