A spaceship of mass m has its engines switched off and is moving in a circular orbit at
height R above the surface of a planet of mass M and radius R.
a) Derive an expression for total mechanical energy E of the orbiting spaceship, in terms of G, m,
M and R.
b) Derive an expression for the minimum speed V the spaceship would need to escape from this
orbit into deep space, in terms of system parameters. (The engines can’t fire for the whole trip;
they can only give the spaceship one boost so it obtains this velocity. Ignore all other celestial
objects.)