As Sylvia but not Maciej know:
GR predicts that a clock in GPS orbit will run fast by
a factor 4.4546E-10 as observed from the ground.
https://paulba.no/paper/Ashby.pdf
quote (page 16-17):
"
At the time of launch of the NTS-2 satellite (23 June 1977),
which contained the first Cesium atomic clock to be placed
in orbit, it was recognized that orbiting clocks would
require a relativistic correction, but there was uncertainty
as to its magnitude as well as its sign. Indeed, there were
some who doubted that relativistic effects were truths that
would need to be incorporated! A frequency synthesizer
was built into the satellite clock system so that after
launch, if in fact the rate of the clock in its final orbit
was that predicted by general relativity, then the synthesizer
could be turned on, bringing the clock to the coordinate rate
necessary for operation. After the Cesium clock was turned on
in NTS-2, it was operated for about 20 days to measure its
clock rate before turning on the synthesizer.
The frequency measured during that interval was +442.5 parts
in 10^12 compared to clocks on the ground, while general
relativity predicted +446.5 parts in 10^12. The difference
was well within the accuracy capabilities of the orbiting clock.
This then gave about a 1% verification of the combined
second-order Doppler and gravitational frequency shift effects
for a clock at 4.2 earth radii.
"
The original report of the measurements mentioned in the quote above:
https://paulba.no/paper/Initial_results_of_GPS_satellite_1977.pdf
So direct measurements right from the real world indicate
dt'/dt = 4.4647E-10 as predicted by GR.
And 38 years of operation of the GPS has confirmed
GR's prediction to much better than 1% precision.
As a consequence of this all GPS SV clocks are adjusted to run
slow by the factor 4.4647E-10 as specified in this document:
http://www.gps.gov/technical/icwg/IS-GPS-200H.pdf
quote from Chapter 3.3.1.1 Frequency Plan (page 13):
"
The carrier frequencies for the L1 and L2 signals shall be
coherently derived from a common frequency source within the SV.
The nominal frequency of this source -- as it appears to
an observer on the ground -- is 10.23 MHz.
The SV carrier frequency and clock rates -- as they would
appear to an observer located in the SV -- are offset to
compensate for relativistic effects. The clock rates are
offset by \Delta f/f = - 4.4647E-10, equivalent to a change
in the P-code chipping rate of 10.23 MHz offset by
a \Delta f = - 4.5674E-3 Hz.
This is equal to 10.2299999954326 MHz.
"
>> Game over.
Indeed. The game was over 38 years ago.
--
Paul
https://paulba.no/