The image above shows earth at an altitude of 20200 + 9.08 km. The red line I drew is a straight line of 696 km, 3-D straight line — perhaps non-Euclidean, near the CERN – Gran Sasso Baseline, parallel to the latter, which is not straight and about 733 km long.
— Isn’t that a reason to worry?
This altitude is where the GPS satellites are “falling towards earth”.
Why should different baseline ends not introduce any error, to synchronization?
Also if we imagine 13.7 km/s at this altitude, the satellite is almost not moving. It takes 2 minutes for a deviation of 1 degree angle on earth surface — or anywhere, which is “49000 time of flights” of a neutrino bunch from CERN to Gran-Sasso.
That is, 3.54375 E-7 rad / time-of-flight.
The earth spin is 3.000823 E-2 rad / time-of-flight — earth spin being 7.292 E-5 / s.
I have shown that static earth effect is less than 1 pico-sec — special-relativistic-effect is small and negative, compared to general-relativistic-effect.
Spinning earth effect being 1% order of static earth, and earth spinning speed being E-5 orders higher, than satellite angular speed, again the “1% general relativistic effect of 1 pico-sec” will preside over the special relativistic effect, of the satellite.
So, the non-inertial effect of earth, will be ~1% of static earth, which is 1 picosecond. In other words, the total relativistic effect, of the GPS satellite, considering even earth-spin will be, within, about, 1-pico-sec.
We need not worry about this.