The fact is that I have never tried to produce an equation for GPS clocks because I have no information about them. I am sure that you would like nothing better than to goad me into making some kind of erroneous statement about this incongruous project of faction that scientists have put together in order to justify more public revenues going to them.
I'll tell you what. Give me the same amount of time and money that they spent, and we will call it reasonable that I should tell you everything there is to know about these GPS clocks. Otherwise, they do not seem very interesting to me.
Here is one interesting thing you might consider about these satellites and their orbits. If the time in a GPS satellite is different than on a clock on earth, what is the distance of the satellite's orbit?
From earth we can calculate the orbit by Newton's equation for centripetal force.
F = ma = m*4(pi^2)R/T^2
As you can see, the orbit will have a specific radius which relates to time.
Since the time of an orbit is different when measured from the satellite, what happens to the distance of an orbit?
Is the radius different?
What happens in the above equation to compensate for the difference in time?
A change in mass does not really change the result of the equation because the principle of equivalence says that no matter what the mass of the satellite, the radius of orbit and velocity of the satellite will be the same.
Einstein says that the value of pi changes. I believe this about as much as I believe that there is a distance contraction.
Robert B. Winn