GPS timing (from Time and relativity (split from The Nature of Time))

[swansont]

16 hours ago, Markus Hanke said:

If so, then yes, you’d get a gravitational and a kinematic component to the total time dilation - though the kinematic contribution will be very small. This is in no way different from the GPS receiver in your car - the software installed on it will correct for both the gravitational as well as kinematic time dilation between yourself and the satellite. If it didn’t, your position would be off by a whopping 10km per day!

I’ve seen this claim before, but it’s actually erroneous. It’s true that if the GPS clocks were not adjusted they would accumulate a time difference of ~38 microseconds a day as compared to ground clocks (and ct would be around 10 km), but this would not show up as a positioning error in GPS, since the GPS clocks nominally run at the same rate, and the trilateration uses timing differences between signals from the GPS clocks. These clocks would random walk away from each other, and accumulate differences from orbital variations, if not synched up. But this would be on the scale of nanoseconds, not microseconds, per day.

One of the reasons the clocks are adjusted is so that you can do clock corrections from the ground station, which uses time from the USNO master clock. If you didn’t do that, you would be forced to have clocks synchronize within the constellation (whose clocks are less stable than the master clock) which would be less efficient and less precise, so you’d potentially end up with a larger positioning error. But measured in meters, not kilometers

[studiot]

35 minutes ago, swansont said:

I’ve seen this claim before, but it’s actually erroneous. It’s true that if the GPS clocks were not adjusted they would accumulate a time difference of ~38 microseconds a day as compared to ground clocks (and ct would be around 10 km), but this would not show up as a positioning error in GPS, since the GPS clocks nominally run at the same rate, and the trilateration uses timing differences between signals from the GPS clocks. These clocks would random walk away from each other, and accumulate differences from orbital variations, if not synched up. But this would be on the scale of nanoseconds, not microseconds, per day.

One of the reasons the clocks are adjusted is so that you can do clock corrections from the ground station, which uses time from the USNO master clock. If you didn’t do that, you would be forced to have clocks synchronize within the constellation (whose clocks are less stable than the master clock) which would be less efficient and less precise, so you’d potentially end up with a larger positioning error. But measured in meters, not kilometers

Very interesting to get the up to date facts. +1

I haven't done any of this stuff since the late 1970s/early 1980s

My textbook then was Laurila.

[Markus Hanke]

7 hours ago, swansont said:

I’ve seen this claim before, but it’s actually erroneous. It’s true that if the GPS clocks were not adjusted they would accumulate a time difference of ~38 microseconds a day as compared to ground clocks (and ct would be around 10 km), but this would not show up as a positioning error in GPS, since the GPS clocks nominally run at the same rate, and the trilateration uses timing differences between signals from the GPS clocks. These clocks would random walk away from each other, and accumulate differences from orbital variations, if not synched up. But this would be on the scale of nanoseconds, not microseconds, per day.

One of the reasons the clocks are adjusted is so that you can do clock corrections from the ground station, which uses time from the USNO master clock. If you didn’t do that, you would be forced to have clocks synchronize within the constellation (whose clocks are less stable than the master clock) which would be less efficient and less precise, so you’d potentially end up with a larger positioning error. But measured in meters, not kilometers

Ok, that’s fair enough! I freely admit that I’m more versed in the physics of time dilation than I am in the engineering details of the GPS system. The salient point here is though that if you didn’t account for gravitational and kinematic time dilation at all, the system couldn’t work in the way it does now, or at least it would be a lot less accurate.

[StringJunky]

13 hours ago, swansont said:

I’ve seen this claim before, but it’s actually erroneous. It’s true that if the GPS clocks were not adjusted they would accumulate a time difference of ~38 microseconds a day as compared to ground clocks (and ct would be around 10 km), but this would not show up as a positioning error in GPS, since the GPS clocks nominally run at the same rate, and the trilateration uses timing differences between signals from the GPS clocks. These clocks would random walk away from each other, and accumulate differences from orbital variations, if not synched up. But this would be on the scale of nanoseconds, not microseconds, per day.

One of the reasons the clocks are adjusted is so that you can do clock corrections from the ground station, which uses time from the USNO master clock. If you didn’t do that, you would be forced to have clocks synchronize within the constellation (whose clocks are less stable than the master clock) which would be less efficient and less precise, so you’d potentially end up with a larger positioning error. But measured in meters, not kilometers

All in all, GR is pretty intrinsically accurate then. 

Edited January 13, 2023 by StringJunky