Quick & Short Question on General Relativity

[stevmg]

A satellite orbiting the globe at some 300 miles at 18000 mph. Does the clock on the GPS tick slower or faster than the same clock on Earth?
1) the clock is distant to Earth and is under less gravitational pull, resulting in time slowing down less than the Earth clock, therefore ticks faster - General Relativity
2) the speed of the satellite clock dilates time and therefore the satellite clock ticks slower than the Earth clock - Simple Relativity

What is the net effect?

 

[PeterDonis]

It depends on the altitude of the satellite. At an altitude of 300 miles, relative to a clock on the Earth's surface, the slowing of the satellite's clock due to its velocity outweighs the speeding up due to being at a higher altitude, so the satellite's clock ticks slower than a clock on Earth.

At the altitude of the actual GPS satellites, however, which is about 12,600 miles, the speeding up due to higher altitude outweighs the slowing due the velocity; so the "natural" tick rate of clocks aboard the GPS satellites is faster than that of clocks on Earth. The GPS satellite clocks have an extra correction applied to compensate for this, so the clock signals they send out are synchronized with clocks on Earth.

 

[stevmg]

Also noted to PeterDonis reply, at higher altitude, the linear velocity necessary to maintain orbit is less than when closer to Earth which gives additional evidence in support of his reply.