CAIE A-Level Physics 13.3.2 Point-Mass Field Calculations

Practise calculating and rearranging g = GM/r² for field strength, mass or radius, comparing gravitational fields at different distances and masses.

Exam points

calculate gravitational field strength using g = GM/r²
rearrange g = GM/r² to determine mass, radius or field strength and convert units consistently
compare field strength at different distances or around different masses

[Maximum number: 1]

The Earth has a mass of $5.98 \times 10^{24} \mathrm{~kg}$ and a radius of $6.37 \times 10^{6} \mathrm{~m}$ .

The Moon has a mass of $7.35 \times 10^{22} \mathrm{~kg}$ and a radius of $1.74 \times 10^{6} \mathrm{~m}$ .
The Earth and the Moon can both be considered as point masses at their centres. Their centres are a distance of $3.84 \times 10^{8} \mathrm{~m}$ apart.

Show that the gravitational field strength at the surface of the Moon due to the mass of the Moon is $1.62 \mathrm{~N} \mathrm{~kg}^{-1}$ .

$g=\left(6.67 \times 10^{-11} \times 7.35 \times 10^{22}\right) /\left(1.74 \times 10^{6}\right)^{2}=1.62 \mathrm{~N} \mathrm{~kg}^{-1}$

A1

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13.3.2—G = GM / r 2 question 1