The famous story goes that Sir Isaac Newton’s ideas about gravity were catalyzed by an apple falling from a tree in his mother’s garden. He observed its descent in some versions of the tale; in others he was struck on the head. In either case, the falling apple purportedly made a deep impression on him. But what, one might ask, does an apple have to do with the orbits of planets as governed by gravity?
This is how Newton described it in his book, Philosophiae Naturalis Principia Mathematica . He asked, why doesn’t the moon fall like an apple? To get a handle on this question, he modified it somewhat. Suppose there is a tall mountain on the North Pole, and we fire a cannonball from the top of the mountain as in Fig. 56 . It will fall down to the ground, of course. But suppose you fire the cannonball with more force. Then it will still fall to the ground, though landing much farther away in this instance. And if you fire it really hard, it will move a distance comparable to the size of the Earth, perhaps falling on the equator. If you fire it even harder, it falls even farther, perhaps landing on the South Pole. Suppose you now give it an even stronger kick. Then the cannonball will miss hitting the Earth completely and come all the way back around. 1
