Chapter 8, Problem 53P

(II) (a) Show that the total mechanical energy of a satellite (mass m) orbiting at a distance r from the center of the Earth (mass M_E) is

$E=-\frac{1}{2}\frac{Gm{M}_E}{r}$,

if U = 0 at r = ∞. (b) Show that although friction causes the value of E to decrease slowly, kinetic energy must actually increase if the orbit remains a circle.