Speed/direction of gravity for a moving source [duplicate]

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)

marked as duplicate by John Rennie, DavePhD, Jim, Kyle Kanos, Brandon EnrightMay 14 '14 at 15:24

• b. 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. – C. Towne Springer May 14 '14 at 13:17
• See the question I've linked. The bowling ball will start to accelerate to where the Earth was 1 second ago. – John Rennie May 14 '14 at 13:51
• If the Bowling ball accelerates to where the Earth was, then would this determine a way to work out Earth's speed through the universe? My understanding was that if the earth and bowling ball were travelling through space a long distance from anything else, it would be impossible to work out its speed. – Graham May 14 '14 at 15:04
• @user46513 you may be able to determine Earth's speed relative to the bowling ball. But unless you know a priori that the bowling ball is motionless in the universe, you cannot tell its "absolute" speed (as if such a thing exists) – Jim May 14 '14 at 15:17
• – Kyle Oman May 14 '14 at 16:48

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.

• Changes in the mass distribution need to be communicated to the spacetime curvature. This happens via gravitational radiation which indeed does propogate at the speed of light, much in the same way that changes in a charge distribution are communicated to far away points in the electric field via EM radiation that only travels at the speed of light. – Jerry Schirmer May 14 '14 at 15:39

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. –

• What philosophical grounds? If you can transmit a gravitational signal at superluminal speeds, you can break causality. There are strong philosophical grounds to believe that the answer HAS to be b). – Jerry Schirmer May 14 '14 at 15:40
• I agree. That doesn't stop them. There is a guy at Caltech (or a school near) who argues for infinite at every opportunity. Not gravitational waves, but the effect of the shape of space-time on masses. Do a search on "is the speed of gravity infinite?" and you will get some interesting results. I conceived an instrument to make the measurement in 1971/72 but there was no interest at the time. I expected to find it the same as c and so did (almost) everyone else. – C. Towne Springer May 14 '14 at 17:35

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. ....