The Law of Gravitation is an inverse-square law. Look at the formula F_g = -G m₁m₂ d² , F is on one side, and d is on the other side squared and on the bottom of the fraction. It means that as the distance between two object increases, the force of gravity between them decreases by the SQUARE of the distance. Also, if the distance decreases, the force of gravity will increase by the SQUARE of the distance between them. If I double my distance, I have ¼ the force of gravitation, and if I triple it, I have 1/9 the force. If I cut my distance in half, I have 4 times the force of gravitation, and if I cut it to 1/3, I have 9 times the force.

Inverse-square Square Problem

Two masses exert 100 N of gravitational force on one another. What would happen to the strength of the force they exert on one another if I change the separation distance between them?

Separation	Force	Hint	Solution
d (original separation)	100 N
3d	?	Interactive popup. Assistance may be required. Hint 32→ 1 9 the force	Interactive popup. Assistance may be required. Solution 11.1 N
½ d	?	Interactive popup. Assistance may be required. Hint 1 2 2 = 1 4 → 4 x the force	Interactive popup. Assistance may be required. Solution 400 N
5 d	?	Interactive popup. Assistance may be required. Hint 52 = 25 → 1 25 the force	Interactive popup. Assistance may be required. Solution 4 N