Question

Compare the gravitational forces exerted by the Sun and the moon on the Earth. (Given: mass of the Sun, $M_s=4\times {10}^{31}$ kg, mass of moon, $M_m=6.3\times {10}^{22}$ kg, distance between the Sun and the Earth, $r=1.3\times {10}^{12}$ m and the distance between moon and the 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 moon
• C. Sun exerts a greater force and it is about 76 times the force due to the moon
• D. Both exert 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 the Sun is $M_s$ and mass of the 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 the Earth is $M_e$, the distance between the moon and the 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:
$\frac{F_s}{F_m}$ = $\frac{G{M}_s{M}_e}{{\left(r_{se}\right)}^2}$ $\times$ $\frac{{\left(r_{me}\right)}^2}{G{M}_m{M}_e}$ = $\frac{M_s}{M_m}$ $\times$ $\frac{{\left(r_{me}\right)}^2}{{\left(r_{se}\right)}^2}$ = $\frac{4\times {10}^{31}}{6.3\times {10}^{22}}$ $\times$ ${\left(\frac{4.5\times {10}^8}{1.3\times {10}^{12}}\right)}^2$ = 76.07
$\therefore$The force exerted by the Sun on the Earth is about 76 times the force exerted by the moon on the Earth.