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And isn't the solar system moving at like 500000 miles an hour around the milkyway too?
Teleportation and timetravel both have this issue where you have to take a fuckload of moving parts we don't even completely understand yet, into account.
Time travel would have to imply teleportation as well. If teleportation is actually instant or ftl, it would also be at least some level of time travel as you would be able to move outside your causal envelope.
Why would you teleport relative to the sun or the center of the milky way? Wouldn't it be easier to teleport relative to the nearest surface?
The universe doesn't care what you think is easier.
It moves, you moving from one point in the universe to another needs to take into account where all the moving parts are going.
Only instant teleportation, where nothing has had time to move, would work. But that would be akin to traveling back in time.
The Universe doesn't give a damn about the Sun or the Milky Way, either, idiot. There is no defined central point for all coordinates. Everything is relative to something else or might as well be staying perfectly still for all intents and purposes.