  Although the effects of solar (and lunar) gravitational potentials on the
frequencies of orbiting Global Positioning System (GPS) clocks are actually no
more than a few parts in 10^(15), a na\"ive calculation appears to show that
such effects are much larger, and depend on whether the orbiting clock is
between the earth and the sun, or on the side of the earth opposite to the sun.
Consequently questions about whether such effects have been properly accounted
for in the GPS continue to arise. This issue has been discussed in a misleading
way in terms of cancellations arising from a second-order Doppler shift in the
literature for almost 50 years. The purpose of this article is to provide a
correct argument, based on fundamental relativity principles, so that one may
understand in a simple way why the effects of external solar system bodies on
orbiting or earth-bound clocks in the GPS are so small. The relativity of
simultaneity plays a crucial role in these arguments.
