So Newton deduced that when an apple accelerates towards the Earth (drop bean bag) it does so because the earth is pulling on it. Moreover, with an amazing example of intuition and logic, he figured out that it was the same external influence (the Earth's gravitational field) that caused the apple to fall, and kept the moon in orbit around the Earth.

As this diagram indicates, without the Earth's influence the moon would go in a straight line and escape from orbit: the difference between what the moon wants to do, and what the gravitational pull of the Earth forces it to do is an acceleration towards the center of the Earth that is identical to the acceleration of the apple. This was truly a remarkable feat of synthesis, and the beautiful structure created by Newton (Newtonian mechanics) stood unscathed for three hundred years. In the following lectures we will see in some detail how this remarkable synthesis works and, in the true spirit of the scientific method, we will also see where it begins to fail.