Error analysis for the Global Positioning System: Difference between revisions

Revision as of 00:41, 24 May 2022

Revision as of 01:03, 24 May 2022

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=== Special and General Relativity ===

[[Special relativityRelativity]] (SR) and [[General Relativity]] (GR) are two separate and distinct theories behindunder the title of the [[theoryTheory of relativityRelativity]]. SR and GR make different (opposite) predictions when it comes to the clocks on-board GPS satellites. Note the opposite signs (plus and minus) due to the different effects.

SR ([[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>{v^{2}}/{2c^{2}}\approx 10 ^{-10}</math>, or result in a delay of about -7.2 μs/day, where the orbital velocity is v = 4&nbsp;km/s, and c = the speed of light. The SR effect is 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]]. 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.

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! Theory !! Value !! Notes

|-

| SR (Special Relativity) || -7.2 μs/day || Clocks slowed in Satellites due to Velocity

|-

| GR (General Relativity) || +45.9 μs/day || Clocks sped up in Satellites due to lower Gravity