What would happen to the Earth's orbital motion if the sun were to instantaneously disappear? This is easy to answer if you imagine the fabric of spacetime.
The sun instantaneously disappears, but the fabric of spacetime initially stays the same shape, so the earth keeps traveling the same path for about 8 minutes until the change in the shape of spacetime reaches earth. That gravitational wave, the changing shape of spacetime, travels at the speed of light from the obliterated sun to the earth.
That gravitational wave is an infinitely sharp step function because we posited that the sun disappeared instantaneously. Its first derivative has an infinitely tall spike, so (I think) carries an infinite amount of energy. That gravitational wave, when it reaches earth after the 8 minutes, would destroy the earth, and then the rest of the universe.
Any matter instantaneously disappearing and replaced by nothing (a common fictional trope) would have the same destructive effect. I don't think there's anything that will cause the gravitational wave to get smoothed out as it travels, because infinite energy attenuated is still infinite.
I'm not sure how time (as part of spacetime) will be affected by the gravitational step wave.
Earth never gets a chance to veer off into space tangentially (which is the common answer) after the 8 minute delay.
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