  The Global Positioning System (GPS) provides an excellent educational example
as to how the theory of general relativity is put into practice and becomes
part of our everyday life. This paper gives a short and instructive derivation
of an important formula used in the GPS, and is aimed at graduate students and
general physicists.
  The theoretical background of the GPS (see \cite{ashby}) uses the
Schwarzschild spacetime to deduce the {\it approximate} formula, $ds/dt\approx
1+V-\frac{|\vv|^2}{2}$, for the relation between the proper time rate $s$ of a
satellite clock and the coordinate time rate $t$. Here $V$ is the gravitational
potential at the position of the satellite and $\vv$ is its velocity (with
light-speed being normalized as $c=1$). In this note we give a different
derivation of this formula, {\it without using approximations}, to arrive at
$ds/dt=\sqrt{1+2V-|\vv|^2 -\frac{2V}{1+2V}(\n\cdot\vv)^2}$, where $\n$ is the
normal vector pointing outward from the center of Earth to the satellite. In
particular, if the satellite moves along a circular orbit then the formula
simplifies to $ds/dt=\sqrt{1+2V-|\vv|^2}$.
  We emphasize that this derivation is useful mainly for educational purposes,
as the approximation above is already satisfactory in practice.
