Name: Weight of an Object on Moon
Uploaded: 2019-07-19
Duration: 7 min 1 s
Description: In many space videos, astronauts are seen hopping on the surface of the moon due to their reduced weights. Watch the video to learn how to find weight on the...

Question

Compare the gravitational forces exerted by the sun and moon on the earth. Which exerts a greater force and by how many times?

Accepted Answer

Given,

The mass of the sun, $M_{S} = 1 .989 \times 10^{30} kg$ .

The mass of the earth, $M_{E} = 6 \times 10^{24} kg$ .

The mass of the moon, $M_{M} = 7 .4 \times 10^{22} kg$ .

The distance between the sun and the earth, $d_{S E} = 149 \times 10^{9} m$ .

The distance between the moon and the earth, $d_{M E} = 3 .84 \times 10^{8} m$ .

The equation for gravitational force is,

$F = \frac{G m_{1} m_{2}}{d^{2}}$

The gravitational force between the sun and the earth is,

$F_{S E} = \frac{G M_{S} M_{E}}{d_{S E}^{2}} = \frac{6 .67 \times 10^{- 11} \times 1 .989 \times 10^{30} \times 6 \times 10^{24}}{{(149 \times 10^{9})}^{2}} = \frac{79.6 \times 10^{43}}{22201 \times 10^{18}} \approx 3 .6 \times 10^{22} N$ .

The gravitational force between the moon and the earth is,

$F_{M E} = \frac{G M_{M} M_{E}}{d_{M E}^{2}} = \frac{6 .67 \times 10^{- 11} \times 7 .4 \times 10^{22} \times 6 \times 10^{24}}{{(3 .84 \times 10^{8})}^{2}} = \frac{296.15 \times 10^{35}}{14.75 \times 10^{16}} \approx 2 \times 10^{20} N$ .

Thus, the sun exerts a greater force on earth than the moon.

$\frac{F_{S E}}{F_{M E}} = \frac{3 .6 \times 10^{22}}{2 \times 10^{20}} = 1.8 \times 100 = 180$

Thus, the force exerted by the sun on the earth is $180$ times the force exerted by the moon on earth.

Compare the gravitational forces exerted by the sun and moon on the earth. Which exerts a greater force and by how many times?

Important Questions on Gravitation

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