Newton’s theory viewed gravity as instantaneous while Einstein’s theory viewed it as traveling at the speed of light.
I believe in 2003, or thereabouts, it was announced by a physicist here at the University of Missouri (go Tigers!) that the speed of gravity had finally been measured and it was consistent with Einstein’s theory. However, his methodology and conclusions are still controversial.
Okay, I just Googled it. His name is Sergei Kopeiken. Here’s an article you can read that pretty much encompasses the debate:
http://www.space.com/scienceastronomy/gravity_speed_030116.html
And, here is Kopeiken’s rebuttal:
http://xxx.lanl.gov/PS_cache/astro-ph/pdf/0311/0311063v6.pdf
It’s a great read when you have some time.
Cheers
The situation is fairly simple: Newton was right, Einstein and Kopeikin are wrong. Those experiments which Van Flandern described are simple and unambiguous. If there were any delay to the propagation of gravity, our solar system would have flown apart after the first few centuries and we’d not be having this discussion.