The point of assuming a non-rotating Earth is so that the Earth-surface clock's rest frame is an SR inertial frame, and in the same frame as the Earth-centre clock.Aer said:No, if you chose the center of the Earth as your reference point, the Earth can still be rotating as that would not matter.
If a third clock (Earth-frame-satellite path) is at rest in this frame and is positioned somewhere on the path of the satellite, then these three clocks (the Earth-frame clocks) are all synchronized, right?
And it's easy to see that the satellite clock runs slower than the Earth-frame-satellite-path clock in all frames, right? Including the satellite frame?
Do you agree with this so far? If so, then it's a simple step to move on to a rotating Earth.