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By relativity theory, would it be correct to say that a planets surface accelerates toward us when we jump and then fall toward it? Or both (a planet and a person) do?.

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Inertial frames of reference are defined differently in relativity than in newtonian mechanics. A free-falling frame is considered to be inertial. So while you sit in your chair reading this, the chair is accelerating upward, and so are you. If you fall off your chair, you stop accelerating.

No, it is not correct to say that both you and the floor accelerate as you're falling. Only the floor accelerates. An accelerometer attached to your body reads zero while you're falling.

You don't want to talk about the whole planet, because g has different directions and magnitudes in different places. General relativity does not have global frames of reference, only local ones.

Nihar Karve says in a comment:

Does this answer your question? Why doesn't the Earth accelerate towards us?

This question is about relativity. The one you linked to isn't.

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  • $\begingroup$ You're right, I've removed the original comment and added a new one to reflect that it is a related question in the Newtonian framework $\endgroup$ Dec 12, 2020 at 17:37

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