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All hypothetical time machines must also be space machines, i.e. they must take into account the movement of the planets, the galaxy, the universe to avoid materializing their passengers in the middle of space or the centre of the sun. My question is what frame of reference would they use?

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This is exactly what always bothers me in time travel movies.

You never hear about the poor time traveler who got the calculation slightly wrong and ended up deep in space or inside of a mountain.

Only when you find their fossils.

You can use a time machine as a very good space drive.

"All" you do is jump back / forwards in time repeatedly so that gravity pulls you in the direction you want to go. (In actuality: good luck plotting a flight path)

Want to get to 20% of the speed of light? Sit in freefall near Jupiter for 5 weeks (assuming 20m/s/s acceleration), jumping forward / backward in time as appropriate to stay in roughly the same spot relative to Jupiter.

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