A satellite of mass is revolving in a circular orbit of radius around a planet of mass .
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A satellite of mass m is revolving in a circular orbit of radius r around a planet of mass M.
(i) Show that the kinetic energy of the satellite in this orbit is half the magnitude of its gravitational potential energy.
(ii) Hence derive an expression for the total mechanical energy of the satellite in terms of G, M, m, and r.
(iii) Using your result from (ii), calculate the minimum additional energy per unit mass that must be supplied to the satellite so that it just escapes from the planet’s gravitational influence starting from this orbit.