Calculate the gravitational force of attraction between two objects separated by a distance of $1.0\mathrm{cm}$ and each having a mass of $100 \mathrm{g}$.

Calculate the gravitational force of attraction between two asteroids separated by a distance of $4.0\times {10}^9\mathrm{m}$ and each having a mass of $5.0\times {10}^{10}\mathrm{kg}$.

Calculate the gravitational force of attraction between a satellite of mass $1.4 \mathrm{x}{10}^4 \mathrm{kg}$ orbiting the Earth at a distance of $6800 \mathrm{km}$ from the Earth's centre. (The mass of the Earth is$6.0\times {10}^{24}\mathrm{kg}$).

Calculate the Earth's gravitational field strength at the position of the Moon. 

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.