A satellite is geostationary when it hangs over one fixed point of the ground. Its orbit must be circular, equatorial, and of period one sidereal day, ( ): the time the Earth takes to turn once relative to the stars. (The day is relative to the Sun, toward which the Earth also advances a degree a day.)
Examples
Example 27.10 (The geostationary altitude)
Kepler’s third law, read backward, dictates the radius: — an altitude , traveled at . Every relay that “hangs still” sits on this one circle over the equator — there is no other.
Example 27.11 (The navigation constellation)
Satellite-navigation systems fly some thirty satellites at (altitude ), where Proposition 27.3 gives : half a sidereal day, so each satellite retraces its ground track daily. Your receiver compares the arrival times of their clock signals against orbits known to meters.