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# Gravitational Force between the earth and the moon?

What is the approximate magnitude of the gravitational force of attraction between Earth and the Moon??

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F = G mM / r^2, where

F = gravitational force between the earth and the moon,

G = Universal gravitational constant = 6.67 x 10^(-11) Nm^2/(kg)^2,

m = mass of the moon = 7.36 × 10^(22) kg

M = mass of the earth = 5.9742 × 10^(24) and

r = distance between the earth and the moon = 384,402 km

F

= 6.67 x 10^(-11) * (7.36 × 10^(22) * 5.9742 × 10^(24) / (384,402 )^2

= 1.985 x 10^(26) N

• Anonymous
Lv 4
4 years agoReport

Sam, 384 000 km already accounts for the radius of either body. But indeed it should be multiplied by 10^-3 in advance of squaring since the SI unit (which G relies on) of s (r) is m not km. All other units are fine though

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• 1/6 is 16%, not 60%... The moon and the earth would give equal and opposite gravitational forces at 84% the way to the moon, directly in line between them. So the net force would be 'zero' even though you're still feeling force from both.

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• You can easily determine this using Newton's law of gravitation:

F = G*M(moon)*M(earth)/distance^2

where G is the gravitational constant, 6.67x10^-11 m^3/kg/s^2, the mass of the earth is 6x10^24 kg, the mass of the moon is 7.3x10^22 kg, and the distance between them is about 3.84x10^8 m.

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RE:

Gravitational Force between the earth and the moon?

What is the approximate magnitude of the gravitational force of attraction between Earth and the Moon??

Source(s): gravitational force earth moon: https://biturl.im/bLrXo
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• For the best answers, search on this site https://shorturl.im/axAPd

There is never a zero point, only an equal point. The moons gravity is one 6th that of earth, so the equal point is 60% of the distance from the earth, but only when directly in line between the two!! Think of it like waves in the sea, there is never a point where there is no water, no matter which direction the waves come from!!!

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• The Earth's gravitational force on the moon is 3600 times weaker than it is at the surface of the Earth. Gravitational force decreases inversely by the square of the distance. The moon is 240.000 miles from the Earth, the radius of the Earth is 4.000 miles. Divide 4.000 into 240.000, you get 60. the square of 60 is 3600.

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• Anonymous
7 years ago

Madhukar's answer is close, and his methodology is sound, but his answer has a problem with units. The Gravitaional constant he used calls for the distance between the two bodies to be in units of meters, but he has used the distance in kilometers.

If you first convert the distance between the earth and moon form kilometers to meters, then recrunch the numbers the correct answer is:

F = 1.985 x 10^(20) Newtons

The unit error in the distance measurement leads to an error of 10^6 (a factor of one million!)

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