Speed/direction of gravity for a moving source

Question

Consider the Earth, and a bowling ball held 186,000 miles (1 light second) above it. When the ball is released, it will start to fall vertically downwards towards the Earth.

Now consider the case if the Earth is moving sideways at 1000 miles/second. The bowling ball is released just as the Earth passes directly underneath.

Does the ball fall

a) vertically again, or

b) does it fall towards where the Earth was 1 second before?

Gravity propagating at the speed of light, would suggest answer b) but as most of the matter in the universe is travelling at very high speed, and planetary orbits are circularish, I think the answer is a)

Answer 1

Well I will risk answer this with the little knowledge I have

Gravity is a curvature in space time while light etc travel in space time. This implies that gravity does not need to be propogated and any object experiencing gravity of one object will feel it instantaneously even and if it changes position so will the curvature and then the new gravity could be felt.

This would then imply that any object would continue to fall towards it in a straight line.

Answer 2

I'll make my comment an answer and expand if needed : Choice b, fall toward where it sees the Earth. How would it know where the Earth is going to be? Note there is a small group of physicists who claim the speed of gravity must be infinite (on philosophical grounds). There is an instrument that could measure the speed of gravity and a very few people work on the problem. –

Answer 3

The gravitational force between two bodies is always along the straight line between the objects. So no matter how speed the heavy object travels, the smaller object ultimately collides with the heavier object along the straight line between the two masses provided there are no other external forces. So the ball ultimately collides the earth. The time depends on the relative velocities of the two masses.

Regarding the infinite velocity of the gravitational field, no matter what are the surrounding conditions, the gravitational force always exists between two masses even at the infinite distance. So the velocity is considered to be infinite. In case of magnetic/electric field, it depends on the permeability of the medium. ....