How many times will the gravitation force decrease if the distance between two object is doubled?

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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Hello!

The gravity force (its direction and magnitude) is described by Newton's law of universal gravitation. Let two bodies which may be considered as point masses (i.e. their dimensions are much smaller than the distance between them) have the masses `m_1` and `m_2` and the distance between them `d.`

Then Newton's law states that the force acting on each body from the side of another body has a magnitude of

`F=G*(m_1m_2)/(d^2).`

`G` is the absolute constant called gravitational constant.

 

What if the distance `d` is doubled? The new distance become `2d` and the new force become

`F'=G*(m_1m_2)/((2d)^2)=G*(m_1m_2)/(4d^2)=(1/4)F.`

 

So the answer: the gravity force will decrease four times.

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