Asatellite is in a circular orbit around mars, which has a mass m = 6.40 × 1023 kg and radius r = 3.40 ×106 m.

a) derive an expression for the orbital speed assuming that the orbital radius is r.

b) derive an expression for the orbital period assuming that the orbital radius is r.

c) the orbital period of the satellite can be synchronized with mars’ rotation, whose period is 24.6 hours. determine the required orbital radius for this to occur.

d) determine the escape speed from the surface of mars.