Question

The mass of the earth is 6 × 10²⁴ kg and that of the moon is 7.4 ×10²² kg. If the distance between the earth and the moon be 3.84 × 10⁵ km, calculate the force exerted by the earth on the moon. (G = 6.7 × 10⁻¹¹ Nm² kg⁻²​)

Answer 1

The gravitational force between two bodies of masses m₁ and m₂ separated by the distance r is given by, $F=\mathrm{G}\frac{m_1{m}_2}{r^2}$

Mass of the earth = 6 × 10²⁴ kg
Mass of the moon = 7.4 ×10²² kg
Distance between the earth and the moon = 3.84 × 10⁵ km
G = 6.7 × 10⁻¹¹ Nm² kg⁻²

Hence, the gravitational force between the earth and the moon,

$$\begin{gathered} F=6.67\times {10}^{-11}{\mathrm{Nm}}^2{\mathrm{kg}}^{-2}\times \frac{6\times {10}^{24}\mathrm{kg}\times 7.4\times {10}^{22}\mathrm{kg}}{(3.84\times {10}^8\mathrm{m}{)}^2} \\ \Rightarrow F\mathit{=}2.08\times {10}^{20}\mathrm{N} \end{gathered}$$