Question

Compare the gravitational forces exerted by the Sun and the Moon on the Earth. Which one exerts a greater force on the Earth? (Given: mass of the Sun, $M_s=4\times {10}^{31}$ kg; the mass of Moon, $M_m=6.3\times {10}^{22}$ kg; distance between Sun and Earth, $r=1.3\times {10}^{12}$ m and the distance between Moon and Earth,$r=4.5\times {10}^8$ m)

• A. Moon exerts a greater force and it is about 76 times the force due to the Sun
• B. Sun exerts a greater force and it is about 25 times the force due to the Moon
• C. Sun exerts a greater force and it is about 76 times the force due to the Moon
• D. Both exerts equal force on the Earth

Answer 1

The correct option is C

Sun exerts a greater force and it is about 76 times the force due to the Moon

If mass of sun is $M_s$ and mass of earth is $M_e$ and distance between the sun and the earth is $r_{se}$, then force exerted by the sun on earth is

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

Similarly, if mass of moon is $M_m$, mass of earth is $M_e$, the distance between moon and earth is $r_{me}$, then force exerted by moon on the earth is

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

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

$\frac{F_s}{F_m}$ = $\frac{G{M}_s{M}_e}{{\left(r_{se}\right)}^2}$ x $\frac{{\left(r_{me}\right)}^2}{G{M}_m{M}_e}$ = $\frac{M_s}{M_m}$ x $\frac{{\left(r_{me}\right)}^2}{{\left(r_{se}\right)}^2}$

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

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