In general relativity, currently the best gravitational theory
we have, gravitation is propagated at the speed of light. We have
indirect evidence for the existence of gravitational waves, though not
yet any direct measurement of their speed.
Note 8 of the 2d ed of Eddington's _The Mathematical Theory of
Relativity_ has a comment which is germane. In discussing the emission
of energy from a spinning rod via gravitational radiation Eddington
says:
"If gravitation is not propagated instantaneously the lag may
cause tangential components of the force to occur, so that there will be
a couple presumably opposing the rotation. Laplace anticipated that if
gravitation were propagated with the speed of light this disturbing
couple would be large enough to be appreciable in astronomical systems,
and deduced from its absence that gravitation must have a much greater
speed. We know now that the first order effect which Laplace expected
is compensated; but the loss of energy (1) [the formula from general
relativity] is actually the residual Laplace effect of the third order
of small quantities, as determined by modern theory."
Shalom,
George
George L. Murphy
gmurphy@imperium.net
http://www.imperium.net/~gmurphy