Question

Find the gravitational force exerted by earth on moon if distance between them is $3.84\times {10}^{5}Km$.

Mass of earth is $6\times {10}^{24}Kg$

Mass of moon is $7.35\times {10}^{22}Kg$

Answer 1

Step 1:Given data

Mass of earth=$m_e=6\times {10}^{24}Kg$

Mass of moon=$m_n=7.35\times {10}^{22}Kg$

Distance between earth and moon is

$$\begin{gathered} r=3.84\times {10}^5\times {10}^3 \\ =3.84\times {10}^8\mathrm{m} \end{gathered}$$

Step 2 : Finding force

Value of gravitational constant is specified and is given as

$G=6.7\times {10}^{-11}N{m}^{2}K{g}^2$

According to universal law of gravitation “Each body attracts every other body through a force of attraction which is directly proportional to masses of bodies and inversely proportional to square of distance between them”.

Mathematically it is given as

$F=\frac{G{m}_1{m}_2}{r^2}N$

Substituting the values into the formula

$$\begin{gathered} F=\left(\frac{6.7\times {10}^{-11}\times 6\times {10}^{24}\times 7.35\times {10}^{22}}{{\left(3.84\times {10}^8\right)}^2}\right)N \\ =2\times {10}^{20}N \end{gathered}$$

Thus $2\times {10}^{20}N$ is the gravitational force on the body.

Hence, the calculated value of force of gravitation exerted by earth on moon is given as $2\times {10}^{20}N$.