Answer Sure, when he assumes this: "Gerber proposed that the speed of gravity was the same as light and this might account for the missing precession." At the time (before special Relativity in 1905) the speed of light was not generally known to be a constant and the same for all inertial reference frames. So his supposition at the time was premature. A fascinating one, but if taken to its fullest conclusion (doesn't change the math shown at all) basically re-creates General Relativity. So in essence, this little blurb proves relativity by recreating Einstein's result before relativity was known. It's not inconsistent, Einstein's field equations involve the speed of light and predict that gravitation propagates at that speed. If Newtonian mechanics, which assume that gravity moves at infinite speed, was completely true then we'd still have this 43 arc second problem. Since relativity assumes the speed of light, what you pointed to above is consistent with it and not inconsistent.
Relativity is right. GPS works fantastically well and would be many kilometers off if it was wrong. The reference you pointed to is consistent with relativity and not inconsistent. It's actually a proof that relativity is right, which was just waiting for relativity to come along as the proper theoretical framework to put it under.
I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.
I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.
Education/Credentials Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.