“Through very careful tests, it has been observed that the Earth is attracted to where the sun is, not where it was eight minutes ago. The simplest explanation for this is that the speed of gravity is effectively instantaneous.”
McChuck, I don’t know where you got this bizarre idea, but it’s wrong. The theory of gravity (The General Theory of Relativity) has gravitational influences traveling at the speed of light. Didn’t you hear about the recent direct detection of gravitational waves? They traveled from the source to us at light speed.
Lee – As I wrote above, waves (including gravity waves) are limited to light speed. The effect we call gravity is not. This has been exhaustively tested, and can be observed by noticing that the moon is in a stable orbit around the earth, which would not be possible if gravity operated at the speed of light. (If it did, the moon would orbit a spot 40,000 km behind the earth-moon center of gravity.) If gravity operated in waves limited to the speed of light, it would be red and blue shifted. That would make the universe a much more interesting, and chaotic, place.
The very equations used to compute gravitational effects include a kludge factor to estimate the current position of the attractor from its apparent position. Because the math only works if you assume that gravity is instantaneous.