State Newton’s law of gravitation in words.
Use Newton’s law of gravitation to demonstrate that the gravitational field strength $g$ at distance $r$ from a point mass $M$ is $g = \frac{GM}{r^2}$.
The Earth’s mass is $5.98 \times 10^{24}\,\text{kg}$ and its radius is $6.37 \times 10^6\,\text{m}$. The Moon’s mass is $7.35 \times 10^{22}\,\text{kg}$ and its radius is $1.74 \times 10^6\,\text{m}$. Both the Earth and the Moon may be treated as point masses at their centres, and the separation between their centres is $3.84 \times 10^8\,\text{m}$. 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 a point $X$ exists on the line between the centres of the Earth and the Moon at which the resultant gravitational field strength from the Earth and the Moon is zero.
The Earth’s mass is $5.98 \times 10^{24}\,\text{kg}$ and its radius is $6.37 \times 10^6\,\text{m}$. The Moon’s mass is $7.35 \times 10^{22}\,\text{kg}$ and its radius is $1.74 \times 10^6\,\text{m}$. The Earth and the Moon may both be treated as point masses at their centres, and their centres are separated by $3.84 \times 10^8\,\text{m}$.
Calculate the distance $x$ from the Moon’s centre to point $X$.