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Solve the following :

Question:

Find the acceleration due to gravity of the moon at a point $1000 \mathrm{~km}$ above the moon's surface. The mass of the moon is $7.4 \times 10^{22} \mathrm{~kg}$ and its radius is $1740 \mathrm{~km}$.

Solution:

The acceleration due to gravity at a point at height ' $h$ ' from the surface of moon of radius $R$ is

$g=\frac{\mathrm{GM}}{(\mathrm{R}+\mathrm{h})^{2}}$

$=\frac{6.67 \times 10^{-11} \times 7.4 \times 10^{22}}{(1740+1000)^{2} \times 10^{6}}$

$=0.65 \mathrm{~m} / \mathrm{s}^{2}$

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