Orbit of the Moon

Newton published his theories of motion and gravity in a book titled Mathematical Principles of Natural Philosophy in 1687, which came to be known as The Principia. Many years later he published a popular version of his ideas, entitled A Treatise of the System of the World (1731). The illustration at left, along with an explanation of orbits was taken from the 1731 volume. It is essentially the same explanation that physics students learn from their textbooks today.

In brief, Newton explains orbital motion by asking his reader to imagine a cannonball fired from the top of a mountain, in a direction that is parallel to the ground. The cannonball follows what at first seems to be a parabolic path, but in reality is an elliptical path.  However, before the object can complete its orbit, it hits the surface of the Earth.  Eventually, with more and more gunpowder, the ellipse is large enough to encircle the Earth and the cannonball goes into orbit. With additional powder the next cannonball goes further, and eventually it goes into orbit. Newton showed that his theory not only explained orbits in a qualitative way, but also predicted the period of the Moon’s orbit—the time needed to circle Earth once—given its distance from Earth, which was known at the time.