Earth rotates about its axis once every T seconds. A satellite is to be placed in a circular orbit such that it remains fixed relative to the same point on Earth.
(i) Show that the required orbital radius r is given by r3=4π2GMT2, where M is Earth’s mass.
(ii) Using this result, calculate the altitude above the surface of Mars required for a Martian geostationary satellite, given MMars=6.42×1023kg, RMars=3.39×106m, and Mars’s rotation period 24.6h. Express your answer in kilometres.
(iii) Comment briefly on one practical advantage and one limitation of deploying such a satellite around Mars.