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=== Special and general relativity ===
According to the [[theory of relativity]], due to their constant movement and height relative to the Earth-centered, non-rotating approximately inertial [[special relativity#Reference frames, coordinates and the Lorentz transformation|reference frame]], the clocks on the satellites are affected by their speed. [[Special relativity]] predicts that the frequency of the atomic clocks moving at GPS orbital speeds will tick more slowly than stationary ground clocks by a factor of <math>\frac{v^{2}}{2c^{2}}\approx 10 ^{-10}</math>, or result in a delay of about 7 μs/day, where the orbital velocity is v = 4 km/s, and c = the speed of light. This [[time dilation]] effect has been measured and verified using the GPS.
The effect of gravitational frequency shift on the GPS due to [[general relativity]] is that a clock closer to a massive object will be slower than a clock farther away. Applied to the GPS, the receivers are much closer to Earth than the satellites, causing the GPS clocks to be faster by a factor of 5×10<sup>−10</sup>, or about 45.9 μs/day. This gravitational frequency shift is noticeable.
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