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I've heard that flying an atomic clock by a jet plane around the world can test the time dilation effect of special relativity. I've also heard that the clocks in GPS satellites would tick faster than clocks on the earth because of weightlessness (general relativity). I have not learned how to do calculations in general relativity. So can someone please do a calculation here to show clearly how the two effects (special vs general relativity) compete as a moving clock orbits the earth at orbit radius $r$ and speed $v$, given the speed of light $c$, gravitational constant $G$, and earth's mass $M$? An exact solution would be best. Thanks!

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