After his death, the original at Woolsthorpe was still known in the neighborhood as Sir Isaac’s tree. Every effort was made to preserve it as long as possible, until it finally collapsed in a windstorm in 1816. It rerooted itself and can still be seen at Woolsthorpe, while grafts from the tree have been used to propagate clones of Newton’s apples since the 1820s.
But even if Newton watched the apple fall (and thought about gravity as it plummeted) it still took him decades to work out his ultimate theory. He used his newly gained mastery of the mathematics of circular motion to discover why things—including us—don’t simply fly off the surface of the earth, given the Copernican realization that the earth doesn’t sit still at the center of the cosmos but rather travels at an impressive speed, spinning on its axis as it tracks around its central sun. He calculated the strength of the so-called centrifugal force that should be hurling us into space. He put together that number with a rough approximation for the earth’s size—a number refined over the previous two centuries of European exploration by sea. Taken together, that was enough information to estimate the outward acceleration experienced at the surface of a revolving earth—how strongly any of us are being pushed out into space.
Then he performed the other half of the analysis, considering the downward tug at the surface of the earth of what he called gravity in something like the modern sense of the term. Galileo had already observed the acceleration of falling bodies, but Newton trusted no measurement so well as one he made himself, so he reworked that earlier result by studying the motion of a pendulum—an experiment that brought him close to the modern value for the earth’s pull. He knew that his data were still imperfect, but, he wrote, he “found them answer pretty nearly”—by which he meant that he was able to calculate a result that made sense of the evident reality. The gravitational force holding our feet to the ground is (clearly) more than strong enough to do the job—in his calculation, approximately three hundred times stronger than any centrifugal urge to launch us upwards.
That result, at once imprecise and spectacular, would also have placed Newton in the vanguard of European natural philosophy if only anyone had heard about it. He was not yet fixed in his habit of silence, a determination reached a few years later, after a few bruising exchanges with other learned men. But isolated on his farm, he remained focused on the work at hand, applying his almost daily expanding mathematical skill to physical questions. Applying numbers to a concrete question—why stuff sticks to our planet’s surface—transformed the pure mathematical reasoning within his calculus into a literally down-to-earth experience. Newton’s work now became one of the early examples of what we would call a mathematical model, a representation of some aspect of nature abstracted into a form that could be manipulated, extended, and solved. Today we are utterly immersed in the Newtonian worldview, in which these models, systems of equations, are understood to be properties of the universe. During Newton’s miracle year, there was no such recognition, not yet. His next move, though, would push him ever closer to the ultimate triumph, his demonstration that the book of nature is written in the language of mathematics.
The fall of the apple had produced a breakthrough, but not a fully realized theory of gravity itself. In a leap of imagination that is still astounding, Newton realized that whatever pulled that piece of fruit toward the ground must have been the same phenomenon that held the moon in its orbit—tracing a path around the earth as our planet’s inward pull counteracted the moon’s urge to shoot off into space. At some distance from the earth, those two impulses must balance. Sitting there, an object would fall forever, tracing a (nearly) circular path around the center of the earth. Our moon is held to its course by the same phenomenon, the earth’s gravity, that drew Newton’s apple to the ground.
The insight was there, but his first attempt to write down the mathematics of gravity wasn’t quite right; he would arrive at his famous “universal law of gravitation” only in the mid-1680s. But the apple (if Newton’s late-in-life tale is to be believed) did give him the critical piece of the puzzle: laws of nature are universal. Abstracting experience into equations, such laws penetrate beneath all the surface confusion of experience to reveal common patterns and deep truths that govern the cosmos.