# What is the gravitational potential energy stored in the gravitational field between the earth and the moon?

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### 1 Answer

When two objects with mass m1 and m2 are at a distance r from each other, the force of attraction between the two is given by `F = (G*m1*m2)/r^2` , where G is a constant equal to 6.67384*10^-11 m^3*kg^-1*s^-2. Work has to be done to move the two objects away from each other. This work is the gravitational potential energy between the two objects and is equal to `PE = (G*m1*m2)/r` .

To determine the gravitational potential energy between the Earth and the Moon, treat the two as point objects with mass Me and Mm. The mass of the Earth is 5.972*10^24 kg and the mass of the Moon is 7.347*10^22 kg.

The distance between the two is 384400 km

The gravitational potential energy between the two is `(6.67384*10^-11*5.972*10^24*7.347*10^22)/384400000` = 7.6176*10^28 J

The gravitational potential energy between the Earth and the Moon is approximately 7.6176*10^28 J