Problem 9-76 Geosynchronous orbit

Most telecommunications satellites are in geosynchronous orbits above the earth, that is, they have periods of \(24 \;h.\) As a result, since the earth turns on its axis once in \(24\; h\) and each satellite goes around the earth once in \(24\; h,\) any individual satellite stays positioned above a particular point on the earth. (a) How far above the earth's surface must a geosynchronous satellite be? The earth's mass and average radius are \(5.98 \times 10^{24}\; kg\) and \(6368 \;km.\) (b) What is the satellite's speed?

The satellite remains in orbit because:

(A)   It is in a weightless environment.

(B)   There is a centripetal force provided by gravity.

(C)   There is a forward force from the launch propelling it around in the orbit.