A mission planner wishes to place a satellite in a circular orbit around the Moon such that the satellite completes exactly one revolution in 7200s (2.0 h). The Moon’s mass is 7.35×1022kg and its radius is 1.74×106m. Take G=6.67×10−11N m2kg−2.
(i) Show that combining the given orbital period with the condition for a stable circular orbit leads to a cubic equation in the orbital radius r measured from the Moon’s centre.
(ii) Solve the equation to find the required orbital radius and hence determine the altitude of the satellite above the lunar surface (answer to the nearest kilometre).
(iii) Calculate the total mechanical energy per unit mass of the satellite in this orbit.