If the Sun disappeared out of nowhere, would the Earth leave its orbit sooner, later or at the same time that the Sun would disappear from the sky and darkness would come?
The special theory of relativity shows that it is not possible for any information to spread faster than the speed of light. Thus, the Earth would “learn” of the disappearance of the Sun at the same time that the light from the Sun would stop to fall on it. The speed of gravity spread is the same as the speed of light. The improved theory of relativity (general theory of relativity) deals with the principle of gravity, which describes gravity as a deformation of space-time. When we place a body in the middle of a trampoline, the rubber in the trampoline will deform under its influence. But it does not happen immediately, only in (a very short) time. The deformation spreads much slower in the trampoline material (at the speed of sound), so we are able to notice it even with a high-speed camera. And when we remove the body from the trampoline, the trampoline returns to its original state — also with a certain delay. The larger the trampoline, the more time will pass between removing the body and leveling it. This way we can at least imagine what would happen if the Sun disappeared.
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