Error analysis for the Global Positioning System: Difference between revisions

Revision as of 19:36, 12 January 2024

Revision as of 21:37, 12 January 2024

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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 Earth than the satellites, causing the clocks at the altitude of the satellite to be faster by a factor of 5×10⁻¹⁰, or about +45.8 μs/day. This gravitational frequency shift is measurable. During early development some{{who|date=januariJanuary 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 ===