Suppose a satellite in geosynchronous orbit has just passed above the International Space Station with respect to the Earth, and its orbit is coplanar with the International Space Station.
a) Find the velocity of the satellite relative to that of the International Space Station half an hour after the pass over.
b) If the satellite the moves to an elliptical orbit from its geosynchronous orbit, using a Hohman transfer maneuver, such that the major axis of the new elliptical orbit is four times the diameter of its old geosynchronous orbit, calculate the minimum speed of the satellite in its new orbit.
c) If the satellite eventually moves to a circular orbit from its current elliptical Hohman transfer orbit by use of an apogee burn, come up with an expression the amount of time (t) it would need to burn its engines as a function of the mass of the satellite (m) and the force of the engine burn (F). Assume for the short duration of the burn that the force from the engines is constant.
d) Give the Power (P) as a function of the force (F) that the engines need to generate part (c).