The next celebrity in the story of gravity is Sir Isaac Newton. Newton was born on Christmas Day in 1642. He was known as a reclusive, short-tempered man, who did not take criticism very well. Because of his disdain for criticism, his most famous work, "Principia", was only published after strong persuasion by Halley (yes, of Halley's comet), about 20 years after he had developed the ideas presented in the work. In Principia Newton presented his three laws of motion, he invented a new system of mathematics which is called calculus today, and he came up with his Universal Law of Gravitation. Principia was primarily written as an answer to a challenge set forth to physicists by Christopher Wren, who offered a cash prize for the best solution. The challenge was to explain, not just describe, the motions of the planets. Newton was the first person to associate gravity with the orbits of planets. People were familiar with gravity here on Earth, but the idea that this same force could explain the motions of heavenly bodies was new.
Newton used Kepler's Laws in deriving his Universal Law of Gravitation. Deriving Newton's law is fairly simple for the case of a circle, the simplest form of an ellipse.
We tend not to notice gravity so much on the smaller scale; when you are walking past someone in the hall, you probably don't worry about being pulled together by your gravitational attraction to each other. And when we talk about atoms, we generally don't talk about the force of gravity holding them together. That is because there are electromagnetic forces which act over these short distances, and they are much stronger than gravitational forces. On very large scales (like galaxies), these electromagnetic forces tend to cancel each other out over relatively short distances, so they don't really affect the motions of stars and planets. Gravity, on the other hand, is always a positive force; it is additive, and it can never cancel itself out.
There are many interesting similarities between electromagnetic forces and gravitational forces. The laws for electromagnetism were derived much more recently, but just like gravity, the strength of the force is proportional to one over the separation squared. In fact, you will notice that the formulas are very similar, except that it is the charges, not the masses, that cause the electromagnetic forces to exist.