GPS relativity error - really?

• I
The fact is that the GPS satellite clocks DO include a frequency adjustment to account for the effects of relativity:
(From https://www.e-education.psu.edu/geog862/node/1714
"Therefore, on balance, the clocks in the GPS satellites in space appear to run faster by about 38 microseconds a day than the clocks in GPS receivers on earth. So, to ensure the clocks in the satellites will actually produce the correct fundamental frequency of 10.23 MHz in space, their frequencies are set to 10.22999999543 MHz before they are launched into space.")

Furthermore, any signal from the earth is subject to unpredictable delays due to atmospheric effects (see https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Atmospheric_effects). That would complicate using a signal from ground to synchronize GPS clocks.

How the time signals from the ground are currently used in the presence of already corrected clocks is not a reliable indicator of how well they would work without the relativity corrections. Anyone who proposes that the relativity corrections are not necessary would have to do a lot of detailed, expert work to back that up. I don't see any convincing evidence of that sort.
So what? Surely there is 38 microseconds time dilation shift per day and it is corrected by frequency modulation. I have written the same too.

FactChecker
Gold Member
The issue is not only the position of the satellites. The errors of the GPS ground locations are a function of how the satellite signals triangulate on the sphere of the Earth. That is a very different problem.

The issue is not only the position of the satellites. The errors of the GPS ground locations are a function of how the satellite signals triangulate on the sphere of the Earth. That is a very different problem.
Yes, this is different but related topic and I have explained and calculated it in post number 25.

FactChecker
Gold Member
Yes, this is different but related topic and I have explained and calculated it in post number 25.
No. Post #25 does not address that issue.

russ_watters
PeroK
Homework Helper
Gold Member
OK here are basics and math:
Time difference between Earth and satellites caused by relativistic time dilation is growing by 38 microseconds per day. When we calculate actual speed of satellite of 4 km/s this gets us 4000 m *0,000038 s = 0,15 m position drift per day. Which makes average position drift of 4,5 m per month for all satellites. This monthly position drift is well within 8 m acceptable position error stated in official GPS guideline and in reality the position of GPS satellites must be corrected at least once per week, mostly once per day, because they are drifting away also from other reasons than due to relativity.

I dont see any realistic way how to get to GPS position error of 12 km per day due to uncorrected relativity effects. If you study about this topic and make the calculations, you should get the same result.
##38 \mu s \times c \approx 12km##

That's the error that the receiver will make if the time is uncorrected.

Nugatory
Mentor
We're two pages in and no closer to a resolution, so we're closing it.

There are a number of good technical papers on the detailed operation of the GPS system; if someone wants to recommend a few we can post links into this thread.

russ_watters, jbriggs444, weirdoguy and 1 other person