Consider Earth moving around the Sun. Is the force of gravity exerted by Earth onto the Sun directed towards the point where Earth is "right now", or towards the point where Earth was 8 minutes ago (to account for the speed of light)? If it's the former, how does the Sun "know" the current orbital position of Earth? Wouldn't this information have to travel at the speed of light first?
If it's the latter, it would force a significant slowdown of Earth's orbital motion, because the force of gravity would no longer be directed perpendicular to Earth's motion, but would lag behind. Obviously, this isn't happening.
So it appears that the force of gravity is indeed directed towards the current orbital position of Earth, without accounting for the delay caused by the speed of light. How is this possible? Isn't this a violation of the principle that no information can travel above the speed of light?
Answer
Cuckoo asked: So it appears that the force of gravity is indeed directed towards the current orbital position of Earth, without accounting for the delay caused by the speed of light. How is this possible?
If the motion is straight or circular the aberration cancels out, see Steve Carlip: Aberration and the Speed of Gravity:
Steven Carlip wrote: The observed absence of gravitational aberration requires that "Newtonian'' gravity propagates at a speed ς>2×10¹⁰c. By evaluating the gravitational effect of an accelerating mass, I show that aberration in general relativity is almost exactly canceled by velocity-dependent interactions, permitting ς=c. This cancellation is dictated by conservation laws and the quadrupole nature of gravitational radiation.
or to quote the Wikipedia article on the subject:
Wikipedia wrote: Two gravitoelectrically interacting particle ensembles, e.g., two planets or stars moving at constant velocity with respect to each other, each feel a force toward the instantaneous position of the other body without a speed-of-light delay because Lorentz invariance demands that what a moving body in a static field sees and what a moving body that emits that field sees be symmetrical. In other words, since the gravitoelectric field is, by definition, static and continuous, it does not propagate.
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