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Nice question!

Let's take those one step at a time:

-- Start with a gravitational force of ' F ' between two masses.

-- Double the mass of one object. The product of the masses doubles.

The force changes from ' F ' to ' 2F '.

-- Double the mass of the other object. The product of the masses doubles again.

The force changes from ' 2F ' to ' 4F '.

-- Double the distance between the centers of the objects.

The force is multiplied by 1/22 = 1/4 .

The force changes from ' 4F ' to ' F '.

The force ends up the same as it was before things began to change.

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How does the gravitational force between two objects change if the distance between the objects is doubled?

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How does the gravitational force between two objects change if the mass of both objects is doubled?

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