CONTINUOUSWAVE

The orbit of a typical GPS satellite has an altitude above the Earth of about 12,550-miles. The average radius of the Earth is about 3,959-miles. This means the radius of the GPS satellite orbit is then 12,550 plus 3959 or about 16,509-miles. The orbit is nominally a circular orbit, so we can compute the circumference of a circle with radius 16209-miles as 2πr, or 103,729-miles.

The orbital period of a GPS satellite is nominally 11-hours and 58-minutes or 11.967-hours We can roughly approximate the speed by using

Speed = Distance/Time
Speed = 103729-miles/11.967-hours
Speed = 8,668-MPH

In terms of feet-per-second, the satellite is moving at a rate of 12,713-feet-per-second.

Amazing that, together with a couple of other satellites, [the global positioning system] can tell us that we are walking 2.4-MPH when [the satellites] travels that fast per second.

What I find neat is with all those abouts, approximates and nominals is that the 2.4 mph is not only accurate, but can postion you to within a few feet.