http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

关键是下面这几段话。简单地说，就是广义狭义相对论的影响都必须考虑。在GPS时
钟的这个例子里，广义相对论的影响比狭义相对论大，抵消之后产生的误差仍然大
于可容忍限度:

Because an observer on the ground sees the satellites in motion relative
to them, Special Relativity predicts that we should see their clocks ticking
more slowly (see the Special Relativity lecture). Special Relativity predicts
that the on-board atomic clocks on the satellites should fall behind clocks
on the ground by about 7 microseconds per day because of the slower ticking
rate due to the time dilation effect of their relative motion.

Further, the satellites are in orbits high above the Earth, where the curvature
of spacetime due to the Earth's mass is less than it is at the Earth's surface.
A prediction of General Relativity is that clocks closer to a massive object
will seem to tick more slowly than those located further away (see the Black
Holes lecture). As such, when viewed from the surface of the Earth, the
clocks on the satellites appear to be ticking faster than identical clocks
on the ground. A calculation using General Relativity predicts that the
clocks in each GPS satellite should get ahead of ground-based clocks by
45 microseconds per day.

The combination of these two relativitic effects means that the clocks on-board
each satellite should tick faster than identical clocks on the ground by
about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision
required of the GPS system requires nanosecond accuracy, and 38 microseconds
is 38,000 nanoseconds.