What happens to the gravitational force between two masses when the distance between the masses is doubled?

It decreases by a factor of 4

Explanation:

The gravitational force between two masses is given by

where

G is the gravitational constant

m1, m2 are the two masses

r is the separation between the two masses

In this problem, the distance between the masses is doubled, so

r' = 2r

Substituting into the equation, we see that the new force is

So, the force decreases by a factor of 4.