30 POINTS PLEASE ANSWER A satellite of mass, m, orbits a planet of mass, M, and radius, R, with a period of rotation, T.

a. Derive an expression for the altitude of the satellite above the planet's surface.

b. If the mass of the planet doubles, by what factor does the orbital frequency change if the satellite's altitude remain's unchanged?

c. If the original known values remain unchanged, describe the motion of the satellite in terms of velocity, speed, acceleration, and displacement over one full orbit.

d. If the original known values remain unchanged, describe what happens to the satellite's orbit if it fires its engines and moves at a greater speed.