Robert McNees on Nostr: Calculating the fractional frequency shift of the satellite clock compared to the ...
Calculating the fractional frequency shift of the satellite clock compared to the ground clock is a homework problem in GR textbooks.
Orbiting at 4.2 Earth radii, SR slows it down by ~ 250 parts in 10¹². The GR effect speeds it up by ~ 697 parts in 10¹².
General relativity produces the larger effect, and the orbiting clocks runs ahead of the earthbound clock by around 446 parts in 10¹². That’s an extra 38,500 nanoseconds per day.
This is a lot for GPS, which requires really precise timing.
Orbiting at 4.2 Earth radii, SR slows it down by ~ 250 parts in 10¹². The GR effect speeds it up by ~ 697 parts in 10¹².
General relativity produces the larger effect, and the orbiting clocks runs ahead of the earthbound clock by around 446 parts in 10¹². That’s an extra 38,500 nanoseconds per day.
This is a lot for GPS, which requires really precise timing.