Error analysis for the Global Positioning System: Difference between revisions

Revision as of 13:06, 27 August 2024

Revision as of 14:58, 28 January 2025

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=== [[Special relativity]] ===

Special relativity predicts that as the velocity of an object increases (in a given frame), its time slows down (as measured in that frame). For instance, the frequency of the atomic clocks moving at GPS orbital speeds will tick more slowly than stationary clocks by a factor of <math>{v^{2}}/{2c^{2}}\approx 10 ^{-10}</math> where the orbital velocity is ''v'' = 4&nbsp;km/s and ''c'' =is the [[speed of light]], approximately <math>300 \times 10^6</math>m/s. The result is an error of about -7.2 μs/day in the satellite. The special relativistic effect is due to the constant movement of GPS clocks relative to the Earth-centered, non-rotating approximately inertial [[special relativity#Reference frames, coordinates and the Lorentz transformation|reference frame]]. In short, the clocks on the satellites are slowed down by the velocity of the satellite. This [[time dilation]] effect has been measured and verified using the GPS.

=== [[General relativity]] ===