Circular orbits represent one possible solution to the equations of motion. For an satellite of mass m, we relate the energy and radius of a circular orbit around a planet of mass M >> m.
Energy conservation: E = U + K.
|and K = ½ mv2|
Applying Newton's Second Law: ΣF = ma → G m M/ r2 = m v2/r.
So the orbital radius and orbital speed are related by:   v2r = G M
Using this result, the kinetic energy is: K = ½mv2 = G m M/ (2 r) = ½ |U|.
Finally, the total energy is:
Negative total energy corresponds to a bound
system. Just like an electron is bound to a proton in a hydrogen atom
with a negative binding energy, a satellite is bound to the Earth, energy
must be added to move the satellite to infinity.