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Mar 24, 2015 at 17:57 comment added Peteris Nope, the orbital movement around the sun is the big point. According to relativity, you may treat any inertial frame as equal to any other and "the center of the universe", however, all inertial frames that intersect with your Time Machine now would very quickly get very far from the surface of the Earth. The closest you can get is a tangent of Earth's orbit, going out in a straight line as if the sun wasn't there and wasn't pulling you towards it.
Mar 23, 2015 at 22:27 comment added k_g Well, the earth's movement around the sun, though it is less non-inertial than its rotation, is still non-inertial and therefore cannot be used as the "center of the universe". The same goes for the sun's movement around the galactic center, and the galactic center's (very slow) "fall" towards Andromeda.
Mar 23, 2015 at 16:05 history answered Dan Smolinske CC BY-SA 3.0