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Considering that all frames are equivalent, isn't it up to the observer to say "The earth turns around the sun" or "The sun turns around the earth"? Isn't this more or less like arguing about which meridian should be considered the null-meridian, or whether time should be counted according to years before/after Jesus Christ or the conquest of Mecca?

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marked as duplicate by Dilaton, Emilio Pisanty, Qmechanic Aug 12 '13 at 23:07

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All frames are not equivalent. All inertial frames of reference are equivalent.

Having said that, you don't really need to appeal to relativity to sort this one out. If you have two bodies revolving around each other due to gravity, usually one would say that both bodies are revolving around a common centre of mass. But in the case of the Earth-Sun system the Sun is so much more massive than the Earth, that the centre of mass of the combined system is inside the sun (you can verify this yourself using Newtonian gravity).

This means that effectively the Earth is revolving around the sun, and you can't really look at it any other way. But the centre of mass of the system is slightly off centre, and this causes the Sun to wobble just a tiny bit around it's axis.

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    $\begingroup$ But a reference frame attached to the center of the earth is free-falling, and therefore an inertial frame, isn't it? $\endgroup$ – yippy_yay Aug 12 '13 at 21:24
  • $\begingroup$ @SebastianHenckel: In GR, an inertial frame has to be both free-falling and non-rotating. $\endgroup$ – Ben Crowell Aug 12 '13 at 21:46
  • $\begingroup$ @Ben Crowell What about a reference frame centered at the center of the earth with one axis always pointing to the north star? That is free falling and non-rotating. $\endgroup$ – yippy_yay Aug 12 '13 at 21:57
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    $\begingroup$ @SebastianHenckel: Right, and the earth rotates as seen in that frame. Note that in GR, we don't have global frames, and we don't have a notion that inertial observers' relative displacements change linearly with time. For example, if I drop a rock in LA and someone else drops a rock in Mumbai, the rocks are both inertial, but their relative displacements don't change linearly with time. Likewise for earth and sun. $\endgroup$ – Ben Crowell Aug 12 '13 at 22:14

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