Two identical satellites A and B revolve in separate circular orbits of radii r and 2r respectively around the same planet of mass M. Neglect the mass of each satellite compared with M.
a. (i) Determine the ratio of the orbital speeds vA:vB.
b. (ii) Find the ratio of their kinetic energies KA:KB.
c. (iii) Find the ratio of their total mechanical energies EA:EB.
d. (iv) State whether the magnitude of the potential energy of satellite A is greater than, equal to, or less than that of satellite B, giving a brief reason for your answer.