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 is 3.84×10⁵ km, calculate the force exerted by the earth on the moon. (Take G = 6.7 × 10^–11 N m² kg^-2)

The mass of the earth, M = 6 × 10²⁴ kg 

The mass of the moon, m = 7.4 × 10²² kg 

The distance between the earth and the moon, 

d = 3.84 × 10⁵ km 

= 3.84 × 10⁵ × 1000 m 

= 3.84 × 10⁸ m 

G = 6.7 × 10^–11 N m² kg^–2

the force exerted by the earth on the moon is

$F=\mathrm{G}\frac{M\times m}{d^2}$

$$\begin{gathered} \begin{array}{r}=\frac{6.7\times {10}^{-11}{\mathrm{Nm}}^2{\mathrm{kg}}^{-2}\times 6\times {10}^{24}\mathrm{kg}\times 7.4\times {10}^{22}\mathrm{kg}}{{\left(3.84\times {10}^8\mathrm{m}\right)}^2}\\ \end{array} \\ =2.02\times {10}^{20}\mathrm{N} \end{gathered}$$

Thus, the force exerted by the earth on the moon is 2.02 × 10²⁰ N.