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Is the time dilation suffered by clocks in GPS satellites accurate to what is predicted by special relativity? By "accurate" I mean to ask if the numerical answer given by relativity equations match exactly with the actual time dilation suffered by satellite clocks?

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Yes. Before the satellites were even launched, the frequencies of their radio signals were intentionally detuned by the time-averaged amount predicted by relativity. It's not just a special-relativistic effect. There is also a general-relativistic effect.

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