Consider a planet of mass M and radius R. Assume only the gravitational interaction between the planet and a small mass m.
a. (i) Derive an expression for the speed that the mass m must have in order to remain in a stable circular orbit of radius r (r>R) around the planet.
b. (ii) Derive an expression for the minimum launch speed required for the mass m to escape completely from the planet when it starts from a distance r from the planet’s centre.
c. (iii) Hence, show that the escape speed obtained in part (ii) is 2 times the orbital speed obtained in part (i).