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'm almost positive this statement is incorrect.
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, not its position 8 mins ago.
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 appears 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...
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.
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.