Question

Find the gravitational force between earth and moon given that mass of earth = $6\times {10}^{24}\mathrm{kg}$, mass of moon = $7.2\times {10}^{22}\mathrm{kg}$ and the center to center distance of earth and moon = $3.84\times {10}^8\mathrm{m}$.

Answer 1

Step 1: Given data:

Mass of earth, ${\mathrm{m}}_{\mathrm{e}}$ = $6\times {10}^{24}\mathrm{kg}$

Mass of moon, ${\mathrm{m}}_{\mathrm{m}}$ = $7.2\times {10}^{22}\mathrm{kg}$

Center to center distance of earth and moon, $\mathrm{r}=3.84\times {10}^8\mathrm{m}$

Step 2: Finding gravitational force between earth and moon:

Force of gravitation between earth and moon is calculated by using the formula of Newton's law of gravitation-

$\mathrm{F}=\mathrm{G}\frac{{\mathrm{m}}_{\mathrm{e}}{\mathrm{m}}_{\mathrm{m}}}{{\mathrm{r}}^2}\left(1\right)$

where $G$ is universal gravitational constant which is equal to $6.67\times {10}^{-11}\mathrm{N}{\mathrm{m}}^2{\mathrm{kg}}^{-2}$

Putting the values in the equation (1), Calculating the value of force-

$\mathrm{F}=6.67\times {10}^{-11}\frac{(6\times {10}^{24})(7.2\times {10}^{22})}{{(3.84\times {10}^8)}^2}$

$$\begin{gathered} \mathrm{F}=\frac{6.67\times 6\times 7.2}{3.84\times 3.84}\times {10}^{19} \\ =\frac{288.14}{14.75}\times {10}^{19} \\ =19.53\times {10}^{19} \\ =1.95\times {10}^{20}\approx 2\times {10}^{20}\mathrm{N} \end{gathered}$$

Hence, the gravitational force between earth and moon is $2\times {10}^{20}\mathrm{N}$.