“The fact that gravitational damping is measured at all is a strong indication that the propagation speed of gravity is not infinite. If the calculational framework of general relativity is accepted, the damping can be used to calculate the speed, and the actual measurement confirms that the speed of gravity is equal to the speed of light to within 1%.” -Steve Carlip
According to General Relativity, the speed of gravity must be equal to the speed of light. Since gravitational radiation is massless, it therefore must propagate at c, or the speed of light in a vacuum. But given that the Earth orbits the Sun, if it were attracted to the Sun’s position some 8 minutes ago instead of its present position, the planetary orbits would disagree with what we observe!
What, then, is the resolution to this? It turns out that in relativity itself, what we experience as gravitation is also dependent on both speed and changes in the gravitational field, both of which play a role. From observations of binary pulsars, a gravitationally lensed quasar and, most recently, direct gravitational waves themselves, we can constrain the speed of gravity to be very close to the speed of light, with remarkable precision.