How do Gravity and Acceleration affect Clocks?

[cjackson]

I read that stationary clocks on Earth experience time more slowly than clocks on GPS satellites, so the GPS clocks are calibrated to run more slowly to compensate. Since the satellites are in orbit, wouldn't that mean their clocks would be slower since they were moving faster?

 

[PeterDonis]

Since the satellites are in orbit, wouldn't that mean their clocks would be slower since they were moving faster?

They're moving faster, but they're also at a higher altitude, which means they're not as deep in the Earth's gravity well as clocks on the ground are, meaning their gravitational time dilation is smaller. So the two effects, motion and altitude, work in opposite directions; at the altitude of the GPS satellites, the altitude effect wins out, so GPS clocks run faster than ground clocks.

For clocks in low Earth orbit, on the other hand, the motion effect wins out, so such clocks run slower than ground clocks.