Transmit / receive frequency differences from ground to satellites due to relativity Clocks on GPS satellites run faster than on the surface due to relativity and must be periodically corrected to compensate (i.e. we definitely observe the difference on the ground).
So, if I were transmitting a radio signal to a communications satellite, doesn't that mean that either:


*

*More clock ticks pass per cycle at the satellite than on the ground, so if I transmit a radio signal to a satellite on a given frequency, the satellite receiver sees a slightly lower frequency, or

*The frequency increases at the satellite where time moves more quickly, and so the satellite sees more cycles per ground second, and so it sees the future.


I don't really understand relativity, and 2 seems impossible. Is it 1? It seems like it would be; because I guess from the satellite's POV time on the Earth is moving more slowly (that's why they can't beam back images of the future, I think)... except this would mean the frequency relative to the ground is unaffected by relativity? Or ... how does this work?
 A: You definitely see quite a large Doppler shift when you transmit a signal to a satellite (that is, the frequency observed at the satellite will be different when it's moving away from the source compared to when it's moving towards the source), and that is a much bigger effect than the relativistic clock shift (but it cancels over a complete revolution). But that is not the point of your question.
As pointed out in the link in your question, the difference in clock speed at the satellite is actually a combination of two effects: the gravitational effect (less gravity = faster clock, by about 45 µs per day) and the velocity (faster motion = slower clock, by about 8 µs per day), with the net effect being that the clock is slightly fast. If we simplified the situation to a satellite on a very tall tower, with an earth that was not rotating, we would still have the problem that the clock at the top of the tower is ticking faster - with 45 µs / day being approximately 1 part in 2 billion.
In fact, from the perspective of the observer on earth, if they transmitted a 2 GHz signal it would arrive at the satellite with a frequency of 2 billion waves per second; but the observer in the satellite, who sees the clock on earth run more slowly (because our time appears to run slowly on their clock), believes we only sent 1,999,999,999 waves in one of their seconds - and that is the number of waves they receive per second. 
So the problem is just that because we have a different definition of a second, our transmitter and receiver have to be tuned to a different frequency; but after that, no waves get "gained" or "lost".
