The Moon is Falling!

I want to do justice to two great figures. The first is Sir Isaac Newton and the second is the Moon. We all know a version of the story between these two, but their relationship is so often degraded by the unwarranted elevation of another character: the apple.

Somehow the story usually seems to come out like this: Mr. Newton was sitting under an apple tree looking at the Moon. He was wondering why it stayed up in the sky. Suddenly, an apple fell from the tree and hit Newton on the head! “Eureka!” he thought, “I’ve discovered gravity! That makes the moon stay up!”

It’s an interesting story, I suppose, but for some reason we like to focus on the visceral image of the apple striking a noggin and sparking an idea when in reality all it does is obscure the depth of the question Newton was considering and dull the exciting implications of his answer.

So what was Newton thinking about? Quite a lot, actually. By 1619 Johannes Kepler had published his “three laws.” Heliocentricity was in. Kepler’s detailed observations of the objects in our solar system had allowed him to deduce three remarkably general statements about their behavior. He knew that the planets traced out ellipses as they orbited the sun. He knew that if you draw a line from the sun to a planet and look at its position at regular time intervals you find that it sweeps out shapes of equal areas. That means that for some reason the speed at which a planet moves is related to its distance from the sun. The closer the planet gets the faster it moves. When it moves further away it slows down. Finally, Kepler even found a precise mathematical relationship between the total time of each planet’s orbit and its average distance from the sun.

These findings were massively impressive. To add perspective, consider that the telescope was first patented in 1608; Kepler published his first two laws in 1609. Despite this success, however, Kepler’s “laws” were not really laws but observations. There was no explanation for why they were true. Newton was surely searching for something better.

Newton’s mind was probably also on what would become his namesake Three Laws (it seems having Three Laws was fashionable in the 17^th century!) In his earlier publications we see these principles as “hypotheses” in various forms, but when he solidified them in his Principia Mathematica they fundamentally altered the way the world thought about physics. And yet they are remarkably simple: The first is that objects move in straight lines without stopping unless something acts on them to stop them turn them or make them speed up. The second is a more mathematical formulation of the first, and introduces “forces” as the mediators of change. The third is that forces go both ways. If I push on a wall, the wall pushes back on me equally and in the opposite direction. When the apple fell these laws were not officially published or finalized, but were surely looming large in Newton’s thoughts.

What about the moon, then? Well, the moon was doing what it had always done, but it seemed close to revealing why. Newton had been struggling with this problem for some time. The moon moved, that was obvious. But it didn’t move in a straight line. In fact, it was known that the moon also moved in an ellipse. To Newton that meant that there had to be a force on it. But what kind of force? What kind of force is strong enough to move an object as massive as the moon in so regular a shape?

Now this is where the apple comes in. No, it didn’t hit Newton on the head. In his own telling, he saw it fall as he was looking out over his garden one evening. There was nothing remarkable about that. Children know that apples fall. The idea of a downward force of gravity was nothing new. The new question that occurred to Newton was why the apple always falls straight down. There are many kinds of forces that move objects in all sorts of different directions, but falling things always move straight down. Given that the earth is round, the only way that can happen is if there is a force that doesn’t pull downwards, but inwards! And what if that same inwards-pulling force acted on the moon and made it move? What if the moon is falling!

Newton made use of his mathematical skills and showed that an inwards force can indeed make an object like the moon orbit about a center point. Imagine trying to jump down from a height onto a small target. It’s very easy to miss! Now imagine that you are so far away from the earth that it looks like a small target. If you’re far enough away and moving fast enough you can even miss the earth (no matter how coordinated you are). But as you pass the earth, Newton imagined, there will still be an inward force on you. You’ll be falling again, but from a different direction! The moon does the same thing. It’s not being driven around the earth like a car on a track, but is simply falling continuously!

The mathematics Newton used even allowed him to characterize this new gravitational model. To make a moon or a planet move in an ellipse a force between it and its center has to weaken the object moves away from the center, and it must weaken in a precise way. Newton deduced exactly how it had to vary and showed that his model could predict Kepler’s laws! Suddenly Kepler’s observations had a reason behind them.

Newton’s development of his theory of gravity is one of the greatest steps forward in the history of physics. Newton’s work was fundamental in creating the magnificently useful relationship between mathematics and physics that we have today. He was able to take physical data (Kepler’s observations) and deduce a complex physical law expressed mathematically. That process basically defines physics today, and Newton was one of the first to do it. And he was remarkably successful; his theory of universal gravitation was considered accurate for nearly three hundred years until Einstein developed the theory of general relativity.

I hope that I’ve conveyed the impressiveness of what Newton was able to do. This was no feat of an ordinary man that happened to be under the right apple tree at the right time. Of course we’ll probably keep telling ourselves the simpler story because we enjoy the image of Newton’s noggin getting bonked, but we would do well to remember the amazing things that went on inside that noggin as well.