Question

Compare the Gravitional Forces exerted by the Sun and the moon on the Earth. Which exerts a greater force by how many times?

Answer 1

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First write the values :-

Mass of the Earth M = 6 × ${10}^{24}$Kg

Mass of the Sun Ms = 2 × ${10}^{30}$Kg

Mass of the Moon M' = 7.3 ${10}^{22}$Kg

Distance from Sun R~ = 1.5 × ${10}^{11}$ m

Distance from Moon R' = 3.84 × ${10}^{8}$m



Gravitional force exerted by Sun on the Earth :


Fs = G$\frac{MsM} {{Rs}^{2}}$



Gravitional force exerted by Sun on the Earth :


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


$\frac{Fs}{F'}$ = G$\frac{MsM} {{Rs}^{2}}$ × $\frac{{R'}^{2}} {GM'M}$



=》$\frac{Ms} {M'}\times{ (\frac{Rs}{R'} }^{2})$



=》 $\frac{2\times{10}^{30}} {7.3\times{10}^{22}}\times (\frac{3.84\times{10}^{8}}{1.5\times{10}^{11}})$



=》 179.55 $\boxed{Ans}$




Thus, the Sun exerts force, about 180 times force exerted by the moon on the earth.




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Hope this helps . . . . . . .☺☺