I once read an article (in the nr. 10 2005 issue of NW&T, a Dutch science magazine) in which a connection was made between the precession of Mercury's orbit and the speed of gravity. It was written that when Mercury is closer to the sun it's "deeper in the spacetime pit" than when Mercury is further from the sun. This difference in "deepness" causes an extra length difference which is that big (because Mercury orbits the sun so close) that the speed of gravity plays a significant role.
My reply was that the gravity field of the sun is a static field and that this static field was the cause of the precession. For the little planet, it makes no difference if there is a length difference because the gravity is constant in time. And besides, this length difference is the thing that makes the orbit precess. The precession was (is) according to me a geodetic effect, which has nothing to do with the speed of gravity.