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The force that the earth exerts on the moon is identical to the force that the moon exerts on the earth. It can be calculated using the simple formula of Newtonian gravitation:

F = G M1M2/R2

F = the force between the two objects

M1 and M2 are the masses of the two objects

R = the distance between the centers of the two objects

G = the constant used to derive a numerical value from the proportionalities

Mass of the earth = 5.97 x 1024 kg

Mass of the moon = 7.3 x 1022 kg

Distance between earth and moon = 3.844 x 108 m

G = 6.27 x 10-11

Now we have all the numbers we need to calculate the force:

F = (6.27 x 10-11) (5.97 x 1024) (7.3 x 1022) / (3.844 x 108)2

= (6.27 x 5.97 x 7.3) (10-11+24+22) / (14.776 x 1016)

= (273.253 x 1035) / (14.776 x 1016)

= 1.84925 x 1020 Newtons = 4.1686 x 1019 pounds = 20,843,000,000,000,000 tons.

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14y ago
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11y ago

Newton's third law states that when a body exerts a force on another body then the second body also exerts an equally large force on the first, but in the opposite direction.

In the case of the Earth and the Moon, the Earth exerts a gravitational force on the Moon of magnitude F=GMm/r2, where M is the mass of the Earth, m is the mass of the Moon, r is the distance from the Moon to the Earth and G is a constant. This force acts from the Moon towards the Earth. Likewise the Moon exerts a gravitational force on the Earth of magnitude F=GMm/r2, which is exactly the same, but this one acts from the Earth towards the Moon.

So here we have two forces of equal magnitude, similar nature (both of gravitational origin) and opposite direction. Hence the reaction force of the Moon on the Earth is the force of the Earth on the Moon.

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Q: How do you calculate the force the earth exert on the moon?
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