Jupiter's mass is $320$ times that of the Earth and its radius is $11.2$times the Earth's. The Earth's surface gravitational field strength is$9.81 {\mathrm{Nkg}}^{-1}$. Calculate the gravitational field strength close to the surface of Jupiter.

Astrologers believe that the planets exert an  influence on us, particularly at the moment of birth. (They don't necessarily believe that this is an effect of gravity!) Calculate the gravitational force on a $4.0 \mathrm{kg}$ baby caused by Mars when the planet is at its closest to the Earth at a distance of $100 000 000 \mathrm{km}.$ Mars has a mass $6.4\times {10}^{23}\mathrm{kg}.$

Astrologers believe that the planets exert an influence on us, particularly at the moment of birth. (They don't necessarily believe that this is an effect of gravity!). Calculate the gravitational force on the same baby due to its $50 \mathrm{kg}$ mother at a distance of $0.40\mathrm{m}.$

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.