State Newton’s law of gravitation in words.
The Earth and the Moon can be treated as isolated in space, with their masses taken to be concentrated at their centres. The Moon moves around the Earth in a circular orbit of radius $3.84 \times 10^{5}\,\text{km}$. The orbital period is $27.3$ days. Show that
the Moon’s angular speed in orbit around the Earth is $2.66 \times 10^{-6}\,\text{rad s}^{-1}$.
the Earth’s mass is $6.0 \times 10^{24}\,\text{kg}$.
the Moon’s mass is $7.4 \times 10^{22}\,\text{kg}$.
From the data in (b), determine the gravitational force between the Earth and the Moon.
Tidal effects on the Earth’s surface make the Moon’s orbital radius increase by $4.0\,\text{cm}$ each year. Use your answer in (i) to determine the change, in one year, in the gravitational potential energy of the Moon. Explain your working.