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=== [[General relativity]] ===
Special relativity allows the comparison of clocks only in a flat [[spacetime]], which neglects gravitational effects on the passage of time. According to general relativity, the presence of gravitating bodies (like Earth) curves spacetime, which makes comparing clocks not as straightforward as in special relativity. However, one can often account for most of the discrepancy by the introduction of [[gravitational time dilation]], the slowing down of time near gravitating bodies. In case of the GPS, the receivers are closer to the center of Earth than the satellites, causing the clocks at the altitude of the satellite to be faster by a factor of 5×10<sup>−10</sup>, or about +45.8 μs/day. This gravitational frequency shift is measurable. During early development some{{who|date=January 2024}} believed that GPS would not be affected by general relativistic effects, but the [[Hafele–Keating experiment]] showed that it would be.
=== Combined kinetic and gravitational time dilations ===
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: <math> 5.307\times 10^{-10}\times 60\times 60\times 24\times 10^9\approx 45850 \text{ ns} </math>
That is, the satellites' clocks gain 45850 nanoseconds a day due to gravitational time dilation.
==== Combined time dilation effects ====
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: (1 – {{val|4.472|e=-10}}) × 10.23 = 10.22999999543
That is, we need to slow the clocks down from 10.23 MHz to 10.22999999543 MHz in order to negate both time dilation effects.
=== Sagnac distortion ===
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