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Originally posted by Ambitwistor
If you fall freely in a straight line in space radially down towards a planet, you're also travelling along a straight line in spacetime. But if you accelerate off in a straight line in space in another direction (which is impossible if you fall freely, in an elliptical orbit or whatnot), you're travelling along a curved path in spacetime.
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But if you free fall in orbit around a planet, then you travel a curved path through space, but a straight path through space-time, correct?