Problem 9-76 Geosynchronous orbit - Part 4 - B

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?

Accumulated Solution

Diagram of earth and satellite.

\(F = GmM/r^2\)

Correct.

But this force supplies the centripetal force for the uniform circular motion. The expression for that is:

(A)   \(F = mv^2/r\)

(B)   \(F = mv^2r\)

(C)   \(F = mv/r\)