David Sang and Graham Jones Solutions for Chapter: Gravitational Fields, Exercise 5: Question

During the manned Moon landings in the $1960\mathrm{s}$, the command module orbited the Moon in an elliptic orbit with a maximum height of $310 \mathrm{km}$ above the surface of the Moon, whilst the lunar module descended and landed on the Moon's surface. Explain why the potential energy of the command module varied during its orbit. 

During the manned Moon landings in the $1960\mathrm{s}$, the command module orbited the Moon in an elliptic orbit with a maximum height of $310 \mathrm{km}$ above the surface of the Moon, whilst the lunar module descended and landed on the Moon's surface. Calculate the maximum gravitational potential difference between the lunar surface and the position of the command module.