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 distance between the earth and the moon be $3.84\times {10}^5$ 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

According to the universal law of gravitation,

$F=\frac{G{M}_e{M}_m}{R^2}$

Where $M_e$ = Mass of the earth

$M_m$ = Mass of the moon

$R$ = Distance between the earth and the moon

$G$ = Universal gravitational constant
$\Rightarrow F=\frac{6.7\times {10}^{-11}\times 6\times {10}^{24}\times 7.4\times {10}^{22}}{(3.84\times {10}^8{)}^2}$
$=\frac{297.48\times {10}^{-11+24+22}}{(3.84{)}^2\times {10}^{16}}$
$=20.17\times {10}^{19}$
$=2.017\times {10}^{20}N$