Show that the total mechanical energy of a satellite (mass m) orbiting a distance r from the center of the Earth (mass M-e)is:

-(1/2)*(G m M-e)/(r
if U = 0 at r = infinity.
Show that although friction causes the value of E (mechanical energy) to decrease slowly, the kinetic energy must actually increase if the orbit remains a circle.

I was looking at this for hours, can't quite figure out where the (1/2) comes from . . . Give me a push or the answer.
M-e is just the mass of the Earth.

1 answer

Centripetal force is supplied by the gravitational force, so

v^2/r = M G/r^2

Compute the kinetic equation from this equation and add it to the potential energy.