How Did Newton Discover Gravity?
The apple story in context, the correspondence with Hooke and Halley, the unification of terrestrial and celestial mechanics, and the law of universal gravitation.
How Did Newton Discover Gravity?
The standard story of how Isaac Newton discovered gravity is a familiar one. A young man, sitting in an orchard in Lincolnshire in the summer of 1666, watches an apple fall from a tree. The young man, struck by the thought that the same force that pulls the apple to the ground might also hold the Moon in its orbit around the Earth, eventually works out the law of universal gravitation. The story is too good to be entirely true, and the historical record suggests that the apple is, at most, a small part of a much longer and more complicated process. The discovery of universal gravitation was, in fact, the work of more than twenty years, and it involved a long correspondence with Robert Hooke, a long detour through the problems of motion under the action of a central force, and a final breakthrough in the 1680s that was, in large part, the work of Edmund Halley. This page looks at the discovery of universal gravitation in its historical context: the first attempts in the plague years, the long silence of the 1670s, the correspondence with Hooke in 1679, the visit of Halley in 1684, and the composition of the Principia in 1685–1687. The full contents of the Principia are surveyed in What Is in Newton’s Principia Mathematica?. The biographical context is on the Newton page. The empirical background is treated in What Are Kepler’s Three Laws of Planetary Motion?.
The Plague Years (1665–1667)
The standard story of the apple is set in the plague years of 1665–1667, when Cambridge was dispersed and Newton returned to the family farm at Woolsthorpe. In a famous passage, written in the 1710s, Newton recalled that “in the same year I began to think of gravity extending to the orb of the Moon… and having thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the Earth, and found them to answer pretty nearly.” The comparison required, in principle, knowing the Earth’s radius, the Moon’s distance, and the Moon’s orbital period. Newton’s first attempt at the comparison did not work out. The Earth’s radius he had was wrong — the value used in the 1660s was about 15 percent off the modern value, in the wrong direction. The comparison would have given a discrepancy of about 15 percent, which was larger than Newton was willing to ignore. He set the problem aside. The first run, in other words, failed. Newton was not, in the plague years, the genius who solved the problem in a flash of insight. He was a young man who ran into a numerical discrepancy and did not know what to do with it. Newton’s later accounts of the plague years were, in any case, partly retrospective. They were written in the 1710s and 1720s, after Newton had become famous and was being asked to explain how he had come to his discoveries. The accounts have the character of polished memoir rather than careful historical record. The actual work of the plague years was, in all probability, a mixture of genuine breakthroughs (the binomial theorem, the beginnings of the calculus) and more fragmentary work that would be developed later.
The Long Silence (1668–1679)
Newton returned to Cambridge in 1667 and was elected Lucasian Professor of Mathematics in 1669. The next decade was, on the surface, unproductive. Newton gave the standard lectures on optics, geometry, and astronomy. He did some experimental work in alchemy. He corresponded with a small circle of natural philosophers, including Robert Hooke, who was the Curator of Experiments at the Royal Society. He did not, however, publish anything of note. The lack of publication was, in part, Newton’s temperament: he was reluctant to publish, and he was afraid of criticism. It was also, in part, a consequence of the state of the sciences: the problems that interested him most were not yet ripe for solution. The decade was, however, not entirely silent. Newton worked on the theory of motion, and he developed a number of important results that he did not publish. He developed his method of fluxions, his version of the calculus. He worked on the theory of light and color, and he built a reflecting telescope. He also continued to think about the gravitational problem, and he made progress on a number of the technical issues, including the theory of motion in non-circular orbits. The most important event of the decade, for the gravitational problem, was the dispute with Hooke over the theory of light and color. In 1672, Newton sent the Royal Society a paper on his prism experiments, arguing that white light is a mixture of the colors of the spectrum. The paper provoked a long dispute with Hooke, who had his own theory of light. The dispute was one of the formative episodes of Newton’s career: it taught him, he said later, “to make no more loos [i.e., casual] attacks upon the publick.” The episode also, perhaps, contributed to Newton’s reluctance to publish his work on the gravitational problem.
The Correspondence with Hooke (1679–1680)
In November 1679, Robert Hooke, in his capacity as Secretary of the Royal Society, wrote to Newton asking his views on a number of topics. The letter included a question about the path of a body under the action of a central force. Hooke suggested that the path might be “an Ellipsis” and that the force might vary inversely with the square of the distance. The letter provoked Newton to return to the gravitational problem, and it led to a long exchange of letters that is the basis for the famous dispute between Newton and Hooke over the priority of the inverse-square law. The exchange is complicated. Hooke, in his letter of November 1679, suggested the inverse-square law and the elliptical orbit. Newton, in his replies, worked out some of the implications, and he showed that the elliptical orbit was consistent with the inverse-square law. Hooke, in a letter of January 1680, claimed that he had also shown that the elliptical orbit followed from the inverse-square law, but he would not say how. The exchange ended inconclusively, with Newton writing, in a letter of December 1679, that “I do not love to be printed on every little occasion much less to be dunned and teazed by foreigners about mathematical things.” The correspondence is important for two reasons. First, it shows that the idea of an inverse-square law of gravitation was in the air in the late 1670s, and that Hooke was one of the people who had it. Second, it shows that the idea by itself was not enough. The elliptical orbit is a consequence of the inverse-square law, but the demonstration of the consequence requires the calculus, or something like it, and Hooke did not have the mathematical tools to work it out. Newton, who did have the tools, was not yet ready to commit to the gravitational theory, in part because the numerical discrepancy that had defeated him in the plague years had not yet been resolved. The discrepancy was eventually resolved by the work of the French astronomer Jean Picard, who in 1669–1670 published a new measurement of the Earth’s radius, based on a careful geodetic survey. The new value was about 15 percent different from the value that Newton had used in the 1660s, and the difference was enough to make the gravitational comparison work out. Newton became aware of Picard’s measurement sometime in the 1680s, perhaps through Edmond Halley, and the gravitational comparison suddenly worked. The story is a parable of the new physics: it depended on accurate empirical measurement, not on philosophical speculation.
Halley’s Visit (1684)
The decisive event was the visit of Edmund Halley to Cambridge in August 1684. Halley, Christopher Wren, and Hooke had been discussing the planetary orbits. The question was: what curve would a planet trace if it were attracted to the Sun by a force varying inversely with the square of the distance? Hooke claimed to have solved the problem, but he would not say how. Wren offered a book or other prize for a demonstration. Halley, in some frustration, went to Cambridge to ask Newton. Newton told Halley that the curve was an ellipse. Halley, in astonishment, asked how he knew. Newton replied that he had computed it. Halley asked to see the computation. Newton, rummaging through his papers, could not find the relevant ones, and he wrote to Halley promising to redo the calculation and send it on. The result was a short treatise, De Motu Corporum in Gyrum (“On the Motion of Bodies in Orbits”), which Halley received in November 1684. The treatise contained, in embryonic form, much of the argument of the Principia. It set out the laws of motion, the theory of central forces, and the demonstration that an inverse-square law implies an elliptical orbit. Halley was impressed, and he urged Newton to develop the argument into a full book. Newton, who had been working on a variety of other projects, agreed. The result was the Principia, published in 1687.
The Composition of the Principia (1685–1687)
Newton worked on the Principia for about two and a half years, from the spring of 1685 to the spring of 1687. The first book was drafted in 1685, the second in 1686, and the third in 1687. The composition was interrupted by the political events of the Exclusion Crisis, by the death of Newton’s mother in 1685, and by a serious illness in 1685. The Principia is, in its final form, a much larger and more ambitious work than the De Motu that Halley had asked for. The book sets out the laws of motion, the theory of central forces, the motion of bodies in resisting and non-resisting media, the lunar theory, the theory of tides, the figure of the Earth, the orbits of comets, and the demonstration that the inverse-square law implies Kepler’s three laws. The full contents are surveyed in What Is in Newton’s Principia Mathematica?. The book was published at Halley’s expense, and Halley also served as editor and proofreader. The Royal Society, which had originally agreed to publish the book, found that it had used its publication budget to underwrite Willughby’s History of Fishes, and Halley had to find the money elsewhere. The publication was a financial sacrifice for Halley, and it is one of the more striking examples of the patronage system of early modern science.
The Unification of Terrestrial and Celestial Mechanics
The deepest significance of the discovery of universal gravitation was not the law itself. It was the unification of celestial and terrestrial mechanics that the law made possible. Before Newton, the heavens and the Earth were, two different realms. The heavens were perfect, unchanging, eternal, and moved in circles. The Earth was imperfect, changeable, and subject to decay. The two realms obeyed different laws. The Aristotelian tradition had codified this distinction, and it had been the framework of European natural philosophy for two thousand years. The discovery of universal gravitation showed that the distinction was not necessary. The force that held the Moon in its orbit around the Earth was the same force that made a stone fall to the ground. The force that held the planets in their orbits around the Sun was the same force that drove the tides. The same mathematical laws — the three laws of motion and the law of universal gravitation — applied to the heavens and to the Earth. The unification of the two realms was the central project of the Scientific Revolution, and it was the central achievement of the Principia. The unification had been prepared, by the work of Copernicus, Kepler, and Galileo. Copernicus had shown that the Earth was a planet, like the others, and that the heliocentric system was the natural way to describe the solar system. Kepler had shown that the planetary orbits were ellipses, and that the periods and sizes of the orbits were related by a single mathematical law. Galileo had shown that the heavens were not perfect, and that the physics of motion on the Earth could be described mathematically. Newton completed the project by showing that the same laws applied to both realms. The full the unification is the central narrative of the Newton page and of the Laws of Motion and Gravity section. The empirical content of the gravitational law is treated in the Newton’s Three Laws of Motion and Gravity section. The way Newton derived Kepler’s three laws from the inverse-square law is described in What Are Kepler’s Three Laws of Planetary Motion?.
The Long-term Impact
The discovery of universal gravitation was, one of the most consequential events in this history. The law of universal gravitation became, for two hundred years, the central law of theoretical physics. The unification of celestial and terrestrial mechanics was the foundation of the modern scientific worldview. The mathematical methods that Newton developed — the calculus, in particular — became the language of physics. The story of how Newton arrived at the law, and how he worked out its consequences, is the central story of the Scientific Revolution, and it is the central story of modern science.