Newton realized that the force of gravity on an object depends not only on distance but also on the object's mass. In fact, it is directly proportional to its mass. According to Newton's third law, when the earth exerts its gravitational force on an object, such as the moon, that object exerts an equal and opposite force on the earth. Because of this symmetry, Newton reasoned, the magnitude of the force of gravity must be proportional to both the masses. Thus: F is proportional to (Me*Mo)/(r^2) where Me is the mass of the earth, Mo the mass of the other object, and r the distance from the earth's center to the center of the object.

Newton went a step further in his analysis of gravity. In his examination of the orbits of the planets, he concluded that the force required to hold the different planets in their orbits around the sun also must diminish as the inverse square of their distance from the sun. This led him to believe that it is also the gravitational force that acts between the sun and each of the planets to keep them in their orbits. And if gravity acts between these objects, why not between all objects? Thus he proposed the famous law of universal gravitation, stated above.

The magnitude of the gravitational force can be written as

where m1 and m2 are the masses of the two particles, r is the distance between them, and G is a universal constantwhich must be measured experimentally and has the same numerical value for all objects. Since we do not notice any gravitational attraction between ordinary objects (such as a person and a ball), G must be very small. In 1798 (over 100 years after Newton published his Law), Henry Cavendish confirmed The Law of Universal Gravitation and determined G as well. The accepted value for G today is: