He compared this to the distance between the Moon and center of the Earth to the distance between the Apple on the Earth's surface and the Earth's center.

The moon is 60 times farther away than the apple and feels 1/3600 time the centriptal acceleration. (Remember, it is gravity that supplies the centripetal acceleration.) Newton discovered that

Where the acceleration is the centriptal acceleration supplied by gravity and the distance is the distance between the two bodies' centers. The symbol "~" means proportional. It is not an equation yet.

This is a special type of equation called an inverse square law. If you look at the formula you can see what this label makes sense.

In 1689 Netwon publishes Philosophiae Naturalis Principia Mathematic. In the third part of this book, Newton shows that he has figured out how the acceleration due to gravity and the distance are related. This must tie into the force of attraction because F=ma. Through a little more work he gets.

Where m₁ and m₂ are the two masses experiencing the force of attraction. This is still not an equation and will not become an eqaution for another 100 years. While this is a great achievement it is not why Newton is so reverred. It is because this law extends beyond the Earth to the universe. It shows that the laws that work on Earth also work beyond the Earth. This is why is if called "Newton's Law of Universal gravity."

But Newton's Law is not complete until in 1798 Henry Cavindish, (109 year later,) made the law a mathematical formula by finding exactly how the two side of Newton's law of universal gravity relate to each other. Details about Caviendish's experiment can be found here, http://en.wikipedia.org/wiki/Cavendish_experiment. He calculates the universal gravitational constant, "G."

The proportianality can become the equation we use today,

Gravity is the weakest force in the univeverse, however it's influence is literally infinite. The Sun's gravitational pull extends beyond our solar system, beyond our galaxy. It extends an infinite distance.

Science is knowledge based on a body of facts. As ability ot measure and calculate improves our model changes. Click here for the advanced readings about gravitational theories.