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Same spot relative to what? What object do time machines use as a reference for their coordinates? It would make sense to be Earth, so it would be in the same spot all the time.
Weeeeell, not exactly.
It is true that things are all relative to each other. But think about it this was, if you fly out in a Starship in one direction for a light year, then turn around exactly 180 degrees and fly back, you wouldn't arrive back at earth, right? Mainly because things are accelerating due to gravity. And acceleration breaks symmetry.
It would of course depend on how time travel works, but since time and space are linked, it wouldn't be unreasonable to assume that you follow the same trajectory in space as you move through time. But that would be a straight line in the space+time dimensions still. Think of the paths in Minkowski diagrams.
Obviously I would. The trip would take two years.
Earth is a good one if you're only interested in time traveling on your home planet that happens to be Earth. But for a more universal perspective, I suppose the CMBR is the least arbitrary frame among all arbitrary frames