Question

Sorry for the layman question, but it's not my field.

Suppose this thought experiment is performed. Light takes 8 minutes to go from the surface of the Sun to Earth. Imagine the Sun is suddenly removed. Clearly, for the remaining 8 minutes, we won't see any difference.

However, I am wondering about the gravitational effect of the Sun. If the propagation of the gravitational force travels with the speed of light, for 8 minutes the Earth will continue to follow an orbit around nothing. If however, gravity is due to a distortion of spacetime, this distortion will cease to exist as soon as the mass is removed, thus the Earth will leave through the orbit tangent.

What is the state of the art of research for this thought experiment? I am pretty sure this is knowledge that can be inferred from observation.

Answer 1

Gravitational influences do propagate at the speed of light, not instantaneously.

The question of what would happen if the Sun instantly disappeared is actually a funny one in general relativity. The equations of general relativity imply as a mathematical consequence that energy must be locally conserved. Therefore, there is no valid solution to the equations that describes the Sun suddenly disappearing (since that scenario violates local energy conservation).

(A similar statement holds in electromagnetism, by the way: charge conservation is a logical consequence of Maxwell's equations, so if someone asks you what the electric field does when a charge suddenly disappears, there is no correct answer.)

But you can sensibly ask what would happen if the Sun suddenly changed its mass distribution -- if it exploded, say, sending its mass in different directions at high speeds. The answer is that the Earth's orbit wouldn't change for 8 minutes.