It's been spectacularly confirmed by observation, but theoretically, it couldn't have been any other way.
rKeep in mind that these are the only four parameters that are allowable in Newtonian gravitation. You can perform all sorts of calculations from this force law to derive, for example, elliptical planetary orbits around the Sun. But the equations only work if the gravitational force is instantaneous.... [+]
This would make orbits not only elliptical, but unstable. On the scale of a mere century, orbits would shift substantially. By 1805, Laplace had used observations of the Moon to demonstrate that the speed of Newtonian gravity must be 7 million times greater than the speed of light. Modern constraints are now 20 billion times the speed of light, which is great for Newton. But all of this placed a great burden on Einstein....
qualitatively, it isn't merely a sheet of fabric but all of space itself gets curved by the presence and properties of the matter and energy within the Universe. Note that spacetime can only be described if we include not only the position of the massive object, but where that mass is located throughout time. Both instantaneous location and the past history of where that object was located determine the forces experienced by objects moving through the Universe.
So that's the theoretical motivation for why the speed of gravity should equal the speed of light. If you want planetary orbits to be consistent with what we've seen, and to be consistent for all observers, you need a speed of gravity that equals, and to have your theory be relativistically invariant. There's another caveat, however. In General Relativity, the cancellation between the gravitational aberration and the velocity-dependent term is almost exact, but not quite.
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