GPS & Relativity: Position Error Lower Than 38000 Feet?

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    Gps Relativity
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Discussion Overview

The discussion revolves around the effects of relativity on GPS positioning, specifically questioning the claim that GPS would generate a positional error of 38,000 feet per day if relativistic effects were not compensated. Participants explore the implications of clock synchronization between GPS satellites and ground receivers, and whether the stated error estimate is valid given the operational mechanics of GPS technology.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants reference a claim by Brian Cox that time runs faster on GPS satellites, leading to a potential positional error of 38,000 feet per day without compensation.
  • Others argue that the GPS system compensates for relativistic effects, suggesting that the actual positional error is much lower.
  • One participant contends that the 38,000 feet per day estimate is incorrect, asserting that the error would not accumulate in that manner over time.
  • Another participant emphasizes that the GPS receiver constantly syncs its clock with satellite clocks, which may mitigate the buildup of positional error even if relativistic effects are not fully accounted for.
  • Some participants discuss the nature of the oscillators used in satellite clocks and how their synchronization with ground clocks is managed, indicating that without compensation, synchronization issues would arise.
  • A later reply suggests that the relativistic effects on satellites would be similar due to their comparable distances from Earth and velocities, implying that this similarity would not lead to significant desynchronization affecting positioning.
  • One participant mentions a paper that discusses relative time shifts but does not provide a definitive conclusion on how GPS position error would behave without clock frequency compensation.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the 38,000 feet per day error estimate and the necessity of relativistic compensation. There is no consensus on whether the error would accumulate significantly or if the GPS system's design effectively mitigates such errors.

Contextual Notes

Some limitations in the discussion include the dependence on specific definitions of synchronization and relativistic effects, as well as unresolved mathematical considerations regarding the impact of clock frequency compensation on GPS accuracy.

  • #61
Even atomic clocks are not perfect. If they were then I think the OP would have been right. For everything to stay synchronized the clocks on each satellite must re-synchronize from time to time with a master clock. The master clock is ground based so if relativistic effects were not compensated for then a satellite that just had its clock synchronized would be out of sync with a satellite that had been synchronized less recently. having satellites out of sync would certainly cause error, though I don't know how much.

http://tycho.usno.navy.mil/gpsinfo.html

Also, the GPS system is designed to provide 4 co-ordinates, not 3. The 4'th being time. If the master clock were space based and time dilation were not accounted for the time co-ordinate would drift. A cheap receiver with a fallible clock would not know how much drift to account for.
 
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