Regarding to the speed of information.

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If the sun were to suddenly vanish, Earth would continue on its circular path for approximately 8 minutes and 20 seconds before moving tangentially due to the lack of gravitational pull. This phenomenon illustrates the finite speed of information transfer, as gravitational effects propagate at the speed of light. The discussion highlights the implications of this scenario on concepts like faster-than-light (FTL) communication, which could violate causality. The conversation emphasizes the importance of understanding the relationship between gravity, motion, and the speed of information. Ultimately, the laws of physics dictate that changes in gravitational forces are not instantaneous.
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If the sun suddenly vanished, hypothetically ceased to exist. Would the Earth still continue on its circular path for 8 min 20 sec? and then leave its orbit tangentially?
 
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Basically - yes.
Otherwise moving a massive object about could be used for FTL communication, violating causality.

(There's a lot of other stuff, but I know what you are asking.)
 
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