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.
Solution
The acceleration due to gravity at a point at height h from the surface of the moon is given by \[g = \frac{GM}{r^2}\] ,
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.
\[\therefore g = \frac{GM}{\left( R + h \right)^2}\]
\[ \Rightarrow g = \frac{6 . 67 \times {10}^{- 11} \times 7 . 4 \times {10}^{22}}{\left( 1740 + 1000 \right)^2 \times {10}^6}\]
\[ \Rightarrow g = \frac{6 . 67 \times 7 . 4 \times {10}^{11}}{\left( 1740 + {1000}^2\times {10}^6 \right)}\]
\[ \Rightarrow g = \frac{6 . 67 \times 7 . 4 \times {10}^{11}}{2740 \times 2740 \times {10}^6}\]
\[ \Rightarrow g = 0 . 65 m/ s^2\]
