Two identical uniform spheres each of radius R are placed in contact. The gravitational force between them is F. They are then separated until the force between them is one ninth of the magnitude. What is the distance between the surfaces of the spheres?

With electostatics, it is important to remember that inthe equation giving the force between two point charges, the force is inversely proportional to the square of the distance of the charges. 

It is important to note that with spheres, we will effectively treat them with point charge and hence the distances we will take for our equation is from the centre. 

When placed next to each other, the distance between the centres is 2R. Hence if the force decreases by a factor of 9, the distance between the spheres must increase by a factor of 3 (root 9 is 3). Hence the new distance between the spheres is 6R.

However, the question asks for the distance between the surfaces. Hence 2R must be subtracted from our answer, leaving us with the correct answer, 4R.