A satellite of mass m moves in an elliptical orbit of semimajor axis a about a planet of mass M. At some point in its orbit the satellite is at distance r from the planet’s center and has speed v. No external torques act on the system.
(a) Starting from appropriate expressions for the system’s total mechanical energy and its angular momentum, derive a relationship among v, r, a, and GM.
(b) Show that your result can be rearranged into the form v2=GM(r2−a1).
(c) Discuss the physical significance of the two terms inside the parentheses in the expression derived in part (b).