Newton’s Law of Universal Gravitation
Putting together all the pieces of the puzzle, Newton was finally able to describe a universal law of gravitation that applied both to falling objects on Earth and to the moon and planets orbiting in the solar system. Remember from Newton's laws of motion that a force is equal to a mass multiplied by an acceleration: F=ma. Newton knew from this equation that it was not only the distance between two objects that determined the force with which they attracted each other. Since force is proportional to mass, from this he surmised that the gravitational force was also dependent on the masses of the two objects.
Newton's law of universal gravitation can be summarized as follows:
Here, F is the gravitational force, G is a constant of proportionality, m1 and m2 are the two masses that are attracting each other, and r is the distance between them.
The reason that Newton's discovery is called “universal” is that it applies to all objects. Everything with mass attracts everything else with mass, with a force that is proportional to the masses of the two objects and the distance between them. This theory applies to all matter in the universe, from the smallest atom to the largest galaxy.
If all matter attracts all other matter, why don't we feel a gravitational attraction from a person standing next to us?
There is in fact a gravitational force, but it is very small. Gravity is a relatively weak force, and it can be felt only when objects become very large and massive. For this reason, the gravitational force of the Earth pulls you down much more strongly than the gravitational force of a person pulls you toward her.