Re: Challenge for Paul; Probe that with Mercury ds^2>0 and the solution is spacelike

Paul B. Andersen <relativity@paulba.no> wrote:

Den 13.02.2025 18:26, skrev rhertz:

Can you derive, for GPS satellites, the alleged shift in frequency:
 
?f/f ≈ GM/c?  [1/r_E ? 1/(r_E + h)]? GM/[2 c? (r_E + h)]

 
https://paulba.no/pdf/Clock_rate.pdf

If you ever are in the mood, you could add a section
on non-circular GPS orbits.
(they all are a little, no point in wasting precious fuel in keeping
orbits exactly circular)

When the orbit is elliptical the clock correction varies over the orbit.
Only the average is corrected for in the constant clock offset.
Relativistic corrections for this have to be applied in the receivers.
(based on the almanac date that the sat also transmits in the full
message)

And yes, it does matter if you want the best possible accuracy.
It will for example decrease the CEP of GPS-guided munitions
from perhaps 10m to a few meter.
This may make the difference between a shell landing in a trench
rather than next to it.

Russian soldiers must hate relativity,

Jan