Question

Find the acceleration due to gravity of the moon at a point 1000 km above the moon's surface. The mass of the moon is 7.4 × 10²² kg and its radius is 1740 km.

Answer 1

The acceleration due to gravity at a point at height h from the surface of the moon is given by
$g=\frac{\mathrm{G}M}{r^2}$,
where M is the mass of the moon; r is the distance of point from the centre of the moon and G is universal gravitational constant.

$$\begin{gathered} \therefore g=\frac{GM}{{\left(R\mathit{+}h\right)}^2} \\ \Rightarrow g=\frac{6.67\times {10}^{-11}\times 7.4\times {10}^{22}}{{\left(1740+1000\right)}^2\times {10}^6} \\ \Rightarrow g=\frac{6.67\times 7.4\times {10}^{11}}{\left(1740+{1000}^2\times {10}^6\right)} \\ \Rightarrow g=\frac{6.67\times 7.4\times {10}^{11}}{2740\times 2740\times {10}^6} \\ \Rightarrow g=0.65\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$