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This question already has an answer here:

if all motion is relative to the frame of reference determined by an observer, why would the view that planet earth revolves around the Sun more correct than the view that the Sun revolved around planet Earth and all the other planets revolve around the Sun?

Is there a mathematical proof?

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marked as duplicate by John Rennie, user10851, Brandon Enright, Qmechanic Mar 10 '14 at 17:30

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Neither view is correct. The Earth and the Sun both revolve around the barycenter (center of mass) of the solar system. In fact, some exoplanets have been discovered due to the motion of the star around its system's barycenter.

In special relativity, there is no preferred inertial frame of reference (that is constant velocity frame of reference). But revolving is a non-inertial frame of reference.

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  • $\begingroup$ The last line of your answer isn't really true. Astronauts in the ISS feel no force even though they are revolving round the Earth, and they would not be able to tell from a local experiment that they were revolving round the Earth (though I suppose you could argue this was GR rather than SR). Anyhow, the unique thing about the frame you specify is that it has no fictitious forces, but I wouldn't say other frames are incorrect - they are just mathematically less convenient. $\endgroup$ – John Rennie Mar 10 '14 at 16:32
  • $\begingroup$ couldn't you measure a tidal force, just as water is pulled toward and away from the Earth-Moon barycenter on opposite sides of the Earth? $\endgroup$ – DavePhD Mar 10 '14 at 16:40
  • $\begingroup$ It depends on how you define local. You can always choose a region near you that is small enough to make tidal effects negligable so you would not be able to measure any tidal force. This is the same as saying spacetime always looks locally flat. $\endgroup$ – John Rennie Mar 10 '14 at 16:43

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