In 1687 Sir Isaac Newton first published his Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) which was a radical treatment of mechanics, establishing the concepts which were to dominate physics for the next two hundred years. Among the book's most important new concepts was Newton's Universal Law of Gravitation. Newton managed to take Kepler's Laws governing the motion of the planets and Galileo's ideas about kinematics and projectile motion and synthesize them into a law which governed both motion on earth and motion in the heavens. This was an achievement of enormous importance for physics; Newton's discoveries meant that the universe was a rational place in which the same principles of nature applied to all objects.
The Universal Law of Gravitation has several important features. First, it is an inverse square law, meaning that the strength of the force between two massive objects decreases in proportion to the square of the distance between them as they move farther apart. Second, the direction in which the force acts is always along the line (or vector) connecting the two gravitating objects. Moreover, because there is no "negative mass," gravity is always an attractive force. It is also noteworthy that gravity is a relatively weak force. Modern physicists consider there to be four fundamental forces in nature (the Strong and Weak Nuclear forces, the Electromagnetic force and gravity), of which gravity is the weakest. This means that gravity is only significant when very large masses are being considered.
In this chapter we will also consider how the gravitational constant) G is determined and how Newton's Theorem can simplify the calculation).