Question

Compare the gravitational forces exerted by the sun and the moon on earth. Which exerts a greater force on earth ?
(Given : mass of sun, Ms = $4\ast {10}^{31}$ kg; mass of moon, Mm = $6.3\ast {10}^{22}$ kg; distance between sun and earth, R_se=$1.3\ast {10}^{12}$ m and the distance between moon and earth, R_me= $4.5\ast {10}^8$m)

Answer 1

. If mass of sun is Ms and mass of earth is Me and distance between the sun and earth is rse, then force exerted by the sun on earth is

$F_s=\frac{G{M}_s{M}_e}{r_{se}^2}$ -(1)

Similarly, if mass of moon is Mm, mass of earth is Me, the distance between moon and earth is rme, then force exerted by moon on the earth is

$F_m=\frac{G{M}_m{M}_e}{r_{me}^2}$...(2)

Dividing equation (1) by equation (2), we get

$\frac{F_s}{F_m}=\frac{G{M}_s{M}_e}{r_{se}^2}\ast \frac{r_{me}^2}{G{M}_m{M}_e}$ = $\frac{M_s}{M_m}\ast \frac{{r_{me}}^2}{{r_{se}}^2}$

= $\frac{4\ast {10}^{31}}{6.3\ast {10}^{22}}$ x $(\frac{4.5\ast {10}^8}{1.3\ast {10}^{12}}{)}^2$ = 76.07

The force exerted by the sun on earth is about 76 times the force exerted by the moon on earth.