Question

The mass of the earth is $6\times {10}^{24}kg$ and that of the moon is $7.4\times {10}^{22}kg$. If the distance between the earth and the moon is $3.84\times {10}^{5}km$, calculate the force exerted by the earth on the moon. $G=6.7\times {10}^{-11}N{m}^{2}k{g}^{-2}$

Answer 1

Given that,

Mass of the Earth $m_1=6\times {10}^{24}kg$

Mass of the Moon $m_2=7.4\times {10}^{22}kg$

Distance between the Earth and the Moon $d=3.84\times {10}^{5}km=3.84\times {10}^{8}m$

Gravitational Constant $G=6.7\times {10}^{-11}N{m}^2/k{g}^2$

Now, by using Newton’s law of gravitation

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

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

$F=\frac{297.48\times {10}^{35}}{14.7456\times {10}^{16}}$

$F=20.174\times {10}^{19}$

$F=20.2\times {10}^{19}N$

Hence, the gravitational force of attractionis $20.2\times {10}^{19}N$