"If a large mass accelerates (for instance, by orbiting a second mass) it should create a gravitational wave that travels outward at the speed of light at least in theory. But, despite some early intriguing work by Joseph Weber, the consensus is that no one has yet directly detected these waves, let alone measured their speed.
"There is, however, good indirect evidence that an accelerating mass creates gravitational waves. This evidence consists of observations of the changing orbit of binary pulsars, pairs of neutron stars (collapsed stellar remnants) that are in very small, rapid orbits about each other. These pulsars spiral in toward one another in exactly the way predicted if they were emitting energy in the form of gravitational radiation.
"There is also good indirect evidence that gravity waves must travel at the speed of light. The fact that the force of gravity varies as the inverse of the square of the distance from a mass strongly indicates that the graviton (the particle exchanged by a pair of gravitationally attracting masses) must have zero mass. According to current physics theory, massless particles like gravitons must travel at the speed of lightjust like photons."