Problem 9-76 Geosynchronous orbit - A

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?

No. The satellite has weight $mg'$ at all times where $g'$ is the acceleration due to gravity (or gravitational potential) at its height.

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