I heard that if the sun were to vanish it would take the same amount of time (about 8 minuets) for the light vanish on earth as well as the earth to spin out of the sun's gravity. Why exactly is gravity close to or is the same speed as the speed of light? Are the two connected somehow? I'm trying to learn more about physics.
Energy conservation, once properly expressed (not naively) is a theorem of general relativity. The mass of the sun cannot just vanish. It has to be moved to somewhere else, and it cannot be moved faster than light. But it is true that whatever the way this mass is moved, the changes to the gravitational field precisely go at the speed of light.
I remember being shown a thesis that claimed the speed of Gravity was practically 'instant'. They claimed to have calculated it based on gravitational forces from the sun using it's actual and apparent position.
This argument is flawed, based on the same mistake as a mistake between phase velocity and group velocity for waves.
Indeed the gravitational "force" of the sun, points to where the sun would simultaneously be (with only a very little difference related to the emission of gravitational waves), but this should not be confused with the speed of changes in the gravitational field if the sun suddendly behaved differently.
when you have a black hole it is strong enough to even overcome the speed of light
With black holes, gravity does not overcome the speed of light.
The gravitational field of a black hole does not come from inside the black hole. It is there outside the black hole because it was already there outside the black hole in the first place, and there is no reason for it to change.
