A satellite of mass m moves in a stable circular orbit of radius r around a planet of mass M.
(i) Derive an expression for the orbital speed v of the satellite in terms of G,M and r.
(ii) Using the result of part (i) together with the expression for gravitational potential energy, obtain the kinetic energy, the potential energy and hence the total mechanical energy of the satellite in the orbit.
(iii) Show that the total mechanical energy is negative and equals −2rGMm. Comment briefly on the physical meaning of this negative value.