State Newton’s law of gravitation in words.
Use Newton’s law of gravitation to demonstrate that the gravitational field strength $g$ at a distance $r$ from a point mass $M$ is $g = \frac{GM}{r^2}$.
The Earth has a mass of $5.98 \times 10^{24}\,\text{kg}$ and a radius of $6.37 \times 10^6\,\text{m}$. The Moon has a mass of $7.35 \times 10^{22}\,\text{kg}$ and a radius of $1.74 \times 10^6\,\text{m}$. The Earth and the Moon can both be treated as point masses at their centres. Their centres are separated by $3.84 \times 10^8\,\text{m}$.
Show that the gravitational field strength at the Moon’s surface due to the Moon’s mass is $1.62\,\text{N kg}^{-1}$.
Explain why there is a point $X$ on the line between the centres of the Earth and the Moon where the resultant gravitational field strength due to the Earth and the Moon is zero.
Calculate the distance $x$ of point $X$ from the centre of the Moon.