With what force does the earth atract the moon ?

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william1941's profile pic

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

TO solve the force of attraction between the Earth and the Moon we use Newton's Law of Gravitation.

The gravitational force between two objects of mass m1 and m2 placed a distance d apart is m1*m2*G*r^2, where G is the universal gravitational constant.

So now the mass of the moon is 7.35E+22 Kg. Mass of the Earth is 5.98E+24 Kg. The Gravitational constant is 6.67E-11 nt-m2/Kg2.

The distance between the Earth and the Moon is 3.85E+08 m

Therefore the gravitational force of attraction between the Earth and the Moon is:

6.67* 10^-11 nt-m^2/Kg^2 * 7.35*10^22 kg* 5.98*10^24 kg *(3.85E+08) ^2 m^2

= 1.98* 10^20 N

So the force of attraction between the Earth and the Moon is 1.98* 10^20 N.

Top Answer

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll write the Universal Law of Gravitation:

Fg = G*Mm*Me/r^2 (1)

Mm and Me are the masses of the moon and the Earth.

r^2 is the orbital radius that express the distance between the moon and the Earth.

G = 6.67*10^-6 dyne cm^2/g^2

Mm = 7.35*10^25 g

Me = 5.96*10^27 g

r = 3.84*10^10 cm

We'll substitute the values in the expression  (1):

Fg = (6.67*10^-6)*(7.35*10^25)(5.96*10^27)/(3.84*10^10)^2

Fg = 2*10^25 dynes

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