[douglas]

One of the most basic assumptions of relativity is that all inertial reference frames are equally valid. Simply choose your inertial reference frame to be one where the sun is motionless, and you can trivially show that the speed of gravity makes virtually no difference to the influence of the sun on any of its planets. Working out how this is compensated for in other reference frames is a bit more work, but the conclusion is guaranteed unless relativity is wrong.

For the speed of gravity to have a significant effect on gravitational interactions, both masses must be large enough to have significant effects on each other so that both have significant acceleration and no inertial reference frame exists where either body is reasonably close to at rest.