4.I.3C

Planetary Explorers Ltd. want to put a communications satellite of mass $m$ into geostationary orbit around the spherical planet Zog (i.e. with the satellite always above the same point on the surface of Zog). The mass of Zog is $M$, the length of its day is $T$ and $G$ is the gravitational constant.

Write down the equations of motion for a general orbit of the satellite and determine the radius and speed of the geostationary orbit.

Describe briefly how the orbit is modified if the satellite is released at the correct radius and on the correct trajectory for a geostationary orbit, but with a little too much speed. Comment on how the satellite's speed varies around such an orbit.

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