The total energy of a circularly orbiting satellite is

Step-by-step solution

The gravitational potential energy of a satellite in circular orbit at radius r about a central mass M is U = - GMm r . For stable circular motion, the gravitational force provides the centripetal acceleration such that GMm r^2 = mv^2 r , yielding kinetic energy K = 1 2 mv^2 = GMm 2r . The total mechanical energy is E = K + U = GMm 2r - GMm r = - GMm 2r . Observing that E = -K , or equivalently E = 1 2 U , the total energy is half the potential energy. Thus, the total energy of a circularly orbiting satellite is ha