Question

The mass of the earth is 6 × 10^(24) kg and that of the moon is 7.4 xx 10^(22) kg. If the distance between the earth and the moon is 3.84xx10^(5) km, calculate the force exerted by the earth on the moon.​

Answer 1

Given:

$\text { Mass of the Earth } \mathrm{m}_{1}=6 \times 10^{24} \mathrm{~kg}\\\\\text { Mass of the Moon } \mathrm{m}_{2}=7.4 \times 10^{22} \mathrm{~kg}\\\\\text { Distance between the Earth and the Moon } \mathrm{d}=3.84 \times 10^{5} \mathrm{~km}=3.84 \times 10^{8} \mathrm{~m}$

$\text { Gravitational Constant } \mathrm{G}=6.7 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$

$\begin{array}{l}\mathrm{F}=\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2}}{\mathrm{r}^{2}} \\\end{array}$

$\mathrm{~F}=\frac{6.7 \times 10^{-11} \times 6 \times 10^{24} \times 7.4 \times 10^{22}}{\left(3.84 \times 10^{8}\right)^{2}}$

$\begin{array}{l}\mathrm{F}=\frac{297.48 \times 10^{35}}{14.8225 \times 10^{16}} \\\end{array}$

$\mathrm{~F}=20.069 \times 10^{19}$

$\mathrm{~F}=20.1 \times 10^{19} \mathrm{~N}$

Hence the gravitational force of attraction is $20.1 \times 10^{19} \mathrm{~N}$