What is the Speed of Gravity?
<i>The Sun, as it is right now, won't have its gravity affect Earth for another 8+ minutes, and the gravity that the Earth feels right now pulling it towards the Sun is actually pulling it towards where the Sun was 8+ minutes ago! (Weird, isn't it?)</i><p>I'm almost positive this statement is incorrect.<p>Relativistic force laws tend to be forced to contain correction factors that ensure that constant velocity motion is "predicted" and the direction of the force is adjusted accordingly - as long as a body is not accelerating, a purely attractive or repulsive force will be pointing at its current position, <i>not</i> its position 8 mins ago.<p>To see why this must be the case for a repulsive force, at least, imagine two charges riding on frictionless rails that keep them at a constant, finite distance.  Suppose they're both moving with some constant velocity (to start, at least) in the same direction - now the place that the force from the other charge <i>appears</i> to be coming from is behind the charge, so if there was no correction factor, each charge would be getting an extra push forwards.  This would lead to a runaway "bootstrap" acceleration, and the particles would accelerate to the speed of light.  That's a pretty clear violation of the conservation laws, so...<p>With attractive forces like gravity, there's still a conservation problem, since the charges would slow down to zero speed eventually, but it's always more convincing to cite the runaway solution as a violation of conservation laws than the run-down one, because while the energy could possibly leak out of the charges into the fields, there's nowhere to pull infinite energy from, so it's pretty clear there's a problem if we'd need to.<p>And this is somewhat different from the runaway self-action solutions that we grudgingly "accept" in E+M, because those tend to involve some limit to infinitesimal size, whereas this is a completely finite situation that we could theoretically set up in the real world with a couple of charged beads or something like that.