Find the ratio of the gravitational force between two planets if the masses of both planets are quadrupled but the distance between them stays the same.

The ratio of the new force over the original force is 16

Explanation:

Recall the formula for the gravitational force between two masses M1 and M2 separated a distance D:

So now, if the masses M1 and M2 are quadrupled and the distance stays the same, the new force becomes:

which is 16 times the original force.

So the ratio of the new force over the original force is 16

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