Calculating the Return of Halley’s Comet

For centuries comets were believed to be harbingers of doom and destruction: the very fact that they could not be predicted meant that they were interpreted as signs and portents. But in 1705 the astronomer Edmond Halley turned comets into common or garden objects orbiting the sun by claiming to have identified one which reappeared every 75 years or so and announcing that it would return in 1758. The prediction was taken up by Newton in the second edition of his Principia (1713) and Halley later revised it to late 1758 or early 1759. 

We are used to seeing lists of all the occasions on which the comet we now know as ‘Halley’s’ has appeared (at the Battle of Hastings in 1066, for example) and so, at first sight, Halley’s prediction looks pretty straightforward: perhaps he just looked at a list of comets through history and recognised a pattern? Not so: comets which are visible to the naked eye are common; there is one every year or so. The time it takes Halley’s Comet to orbit the sun varies between 74 and 79 years, so there is no simple pattern to its reappearance. Halley’s prediction required two things. First, he needed to be able to accurately identify a particular comet by its unique path through the sky. Because there were only sound measurements of the comet's path from its last three appearances, only these could be used as evidence. Second, his prediction required an explanation as to why the comet’s return seemed so irregular. Halley argued that the comet was slowed down or speeded up depending on how close it passed to Jupiter and the other planets. As a consequence, he recognised that he could only make a very rough estimation of when it would next appear.

In 1758 a team of French astronomers – Alexis Clairaut, Joseph Lalande and Nicole-Reine Lepaute (a woman) – set out to improve on Halley’s prediction by laboriously calculating the relative positions of the sun, the comet and Jupiter, not just when the comet was close to Jupiter but throughout its orbit. (This is a three-body problem – the location of Jupiter has a continuous slight, but not insignificant, effect on both the location of the sun and the comet.) They calculated that the comet would make its nearest approach to the sun in mid-April 1759, give or take a month. They were right, it reached perihelion (the point at which it comes closest to the sun) in mid-March. On January 21st it was observed with the naked eye by the French astronomer Charles Messier, but he kept his discovery secret until April 7th, only announcing it when this sighting was confirmed by another report, dating from as early as Christmas Day 1758, by a German amateur with a telescope. Halley was vindicated.

But it was not just Halley who was vindicated; it was also, more importantly, Newton. His Principia reaches its final climax with the claim that the orbits of comets obey his laws of gravitation. The return of Halley’s Comet was confirmation that Newton’s theory worked and, at the same time, was a refutation of alternative theories. If the comet had simply obeyed Johannes Kepler’s laws of planetary motion, it would have returned at precisely regular intervals. René Descartes had imagined comets bouncing off the whirlpools that surrounded every star, travelling through space from solar system to solar system, never to return or retrace their routes. There were still Cartesians to be found in 1759; had Halley’s Comet returned a few decades earlier we would celebrate it as decisive refutation of the Cartesian theory.

In the heavens

Before 1680 the prevailing assumption was that comets have short lives. According to Aristotle, comets were phenomena in the upper atmosphere of the Earth, along with rainbows, meteors and the Northern Lights. Often credited as the first to mount a systematic attack on this view was the Danish nobleman Tycho Brahe who, after the appearance of the Great Comet in 1577, showed that it was in the heavens and that, as it could move through the heavens, it must have been cutting through the solid spheres which, according to Aristotelian philosophers, carried the planets. Later, Kepler assumed that comets travelled in straight lines. Although he showed that planets move not in circles but ellipses, it never occurred to him that comets, too, might orbit the sun (despite the fact that he invented the very language we use to discuss the subject: the words orbit and perihelion are his coinings). In 1664 Giovanni Domenico Cassini argued that the path of one comet suggested that it was in orbit around the star Sirius and thought this might explain why comets swam into sight and then disappeared, seemingly forever. Johannes Hevelius suggested in 1688 that comets followed a curved path as they neared the sun and claimed that this path was, like the path of a projectile, a parabola; but he did not imagine that comets follow the curve on and on until they orbit the sun.

An extraordinarily bright comet appeared in 1680 and headed straight for the sun and, of course, became invisible as it got close to it. Shortly afterwards another comet appeared heading away from the sun on a roughly parallel course. But were these two comets? John Flamsteed in England and Georg Samuel Doerfel in Germany suggested that the second comet was the same as the first, now returning after circling around the sun. Newton at first rejected this suggestion as paradoxical but, as he developed his theory of gravity, he quickly adopted it and in the first edition of Principia (1687) the parabolic path of the comet of 1680 around the sun (calculated using data purloined from Flamsteed) became the final flourish with which he demonstrated his theory of gravity, although he made no attempt to predict when the comet would return. In the third edition he adopted a mistaken prediction by Halley, that it would return every 575 years; in fact it will not return for another 9,000 years.

Theory before fact?

The return of Halley’s Comet thus illustrates two important principles: the first is that all observations are theory-related. Nobody could see that Halley’s Comet returns every 75 years or so before Newton’s theory of gravity helped them interpret the evidence. As Thomas Kuhn said: ‘The so-called facts prove[d] never to be mere facts, independent of existing belief and theory.’ Second, this does not mean a single fact may not be enough to refute a well-established theory. I stress this because the modern history of science is wedded to what is called the Duhem-Quine thesis, according to which facts can never refute theories. The return of Halley’s Comet was an effective refutation of both Kepler and Descartes. Cartesians had developed elaborate theories which successfully predicted the movement of the planets by claiming they were carried along like driftwood in a whirlpool, but these theories could not explain how the path of a comet could be so different from that of a nearby planet – both should be carried along together. 

Newton was not right (as Einstein would show), but his theory worked well and none of the others did. Thus the return of Halley’s Comet is not only a refutation of Cartesianism, it is also a refutation of the Duhem-Quine thesis. As Karl Popper insisted in The Logic of Scientific Discovery (1934), facts can disprove theories. The Cartesians knew they had lost the argument; unfortunately modern historians of science (who claim that arguments can never be won or lost by appeals to the evidence) are not so perceptive. In the years after 1680 it became apparent to Newton that he could formulate a new science. What we need now is a new history of science; one that acknowledges the significance of the return of Halley’s Comet.

David Wootton is Anniversary Professor of History at the University of York. His latest book is The Invention of Science: A New History of the Scientific Revolution (Allen Lane, 2015).