Relativity in the Global Positioning System
Neil Ashby
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The satellite navigation system in every phone is also the largest continuously running test of general relativity ever built, and this review is the standard account of how the relativity is actually done. Neil Ashby, who worked on the problem for the system's operators, walks through every effect that has to be handled: the constancy of the speed of light, which is what lets four timing signals be solved for one position and one time; the equivalence principle; time dilation from satellite motion; the gravitational frequency shift, which runs the opposite way; the Sagnac effect from the earth turning underneath the signals; and the relativity of simultaneity. The headline is that these are not small corrections bolted on afterwards. The satellite clocks are deliberately built to run at the wrong rate before launch so that they keep the right one in orbit, and the review tracks a real episode in which one term of that offset was computed wrongly and took eight years to correct. It also reports the on-orbit measurement that checked the prediction to about one per cent.
Dlaczego ma tu znaczenieChapter 4 asks the reader to take the metric tensor seriously as an engineering quantity rather than a piece of notation. This is the document that shows an operational system doing exactly that: coordinate time, proper time and the earth's gravitational potential appear in the specification of a navigation satellite, and a clock is manufactured to a frequency derived from the metric. It is the strongest available answer to the question of whether spacetime geometry is something engineers already work with.
Co twierdzi
01Clocks at rest on the rotating geoid run slow, compared with clocks at rest at infinity, by about seven parts in ten to the tenth; the International Astronomical Union's Terrestrial Time scale adopts the value 6.969290134 times ten to the minus ten for this effective potential divided by the speed of light squared. That is about ten thousand times larger than the fractional frequency stability of a high-performance caesium clock.Section on the earth's geoid, following equation 18
Settled physics02A caesium clock left alone for a day should be correct to within about five parts in ten to the fourteenth, roughly four nanoseconds; relativistic effects are huge compared with this, which is why the article says that without carefully accounting for them the system would not work.Introduction, discussion of the Allan deviation plot
Settled physics03The Sagnac effect is large enough to be an operational quantity rather than a curiosity: carrying clocks once eastward around the equator and synchronising as you go, the last clock in the chain lags the first by 207.4 nanoseconds, and carrying them westward it leads by the same amount.Section on the Sagnac effect and synchronisation in the rotating frame
Settled physics04Satellite clocks carry a factory frequency offset, applied before launch, so that they beat at the rate of reference clocks on the earth's surface once in orbit; a second, time-varying correction for orbit eccentricity, the e sine E term, has to be applied by the receiver rather than the satellite.Sections on the factory frequency offset and the eccentricity correction, equations 38, 39 and 54
Settled physics05The offset was checked on orbit. After the caesium clock in the NTS-2 satellite was turned on it was run for about twenty days before the synthesiser was engaged, and its rate was measured at 442.5 parts in ten to the twelfth faster than clocks on the ground against a general-relativistic prediction of 446.5 parts in ten to the twelfth, giving about a one per cent verification of the combined second-order Doppler and gravitational frequency shift for a clock at 4.2 earth radii.Section on the NTS-2 satellite clock experiment
Settled physics06What to watch, and what the article records as a caution for anyone building such a system: when the satellites were first deployed the specified factory frequency offset was slightly wrong because the contribution from the earth's centripetal potential had been inadvertently omitted at one stage of the evaluation, and although the system's managers were made aware of the error in the early 1980s, eight years passed before the specifications were changed. Smaller terms are still being pushed down, with the effect of the earth's quadrupole potential on satellite clock frequency at about one part in ten to the fourteenth.Section on the factory frequency offset; section on the earth's quadrupole potential
What to watch
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https://doi.org/10.12942/lrr-2003-1SOURCE READ IN FULL, TEXT NOT REPRODUCED. The full text was read on 2026-09-11 from the PubMed Central deposit of the article, PMC5253894, obtained through the public NCBI E-utilities interface. The copyright line carried in that deposit is the whole of the rights statement the article gives: copyright The Author(s) 2003. No open licence is declared anywhere on the record, and a freely readable article is not a licensed one, so no sentence of Ashby's text is carried here. The summary and the claims below are written in this site's own words from the article read in full, and each locator names the section the number comes from. Numbers are quoted as figures because figures are facts, not expression.
Jak cytować
Neil Ashby (2003) Relativity in the Global Positioning System. doi:10.12942/lrr-2003-1
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