In 1705 Edmond Halley published a thin book of comet orbits and put a bet in it. The comets recorded in 1531, 1607 and 1682 had, he argued, nearly identical paths, and the intervals between them were suspiciously close to seventy six years. They were not three comets. They were one comet, on an enormous ellipse, coming back.
If he was right it would return around 1758. He also knew he would not be there to see it. He was forty nine when he wrote it and he asked, in print, that posterity remember an Englishman had called it.
He died in 1742. What happened next is the part that usually gets left out, and it is the more interesting half of the story, because the prediction as Halley left it was not good enough to be tested.
Why Halley’s Own Number Was Not Enough
The intervals were not equal. From 1531 to 1607 was about 76 years and 2 months. From 1607 to 1682 was about 75 years and 11 months. The difference is not a rounding error, and Halley knew exactly what caused it: the comet passes near Jupiter and Saturn, and they pull on it.
In Newton’s Principia the law of gravitation is universal, which means Jupiter attracts the comet for the same reason the Sun does, only more weakly. That is the strength of the theory and also its practical nightmare. Two bodies orbiting each other have a clean solution. Add a third and the problem has no general solution in closed form at all, a fact that was not proved until the nineteenth century but was obvious in practice long before.
So a real prediction meant tracking, step by step, how much Jupiter and Saturn had shifted the comet during the previous orbit, and then summing all those shifts into a date. There was no method for doing that quickly. There was only arithmetic, an enormous quantity of it, performed by hand.
If nobody did the arithmetic, the return of the comet would prove nothing. A comet arriving in 1757 or 1759 or 1760, with no calculated date to compare it against, is just a comet.
Six Months at the Table
Alexis Clairaut had the mathematical method. He had worked on the perturbations of the Moon and he knew how to set up the approximations. What he did not have was time: the comet was already overdue by the crude estimate, and a prediction published after the fact is worthless.
He recruited two collaborators. Joseph Jérôme Lalande was a young astronomer at the Paris Observatory. Nicole Reine Lepaute was a skilled calculator married to the royal clockmaker, and she had already worked with Lalande on the timing of oscillations in clocks, which is to say she was fast and she was accurate.
They began in June 1757 and worked through to November 1758. Lalande’s own account is the best description of what this kind of science physically involved:
“During six months we calculated from morning to night, sometimes even at meals, and the assistance of Mme Lepaute was such that without her we should never have dared to undertake this enormous labour, in which it was necessary to calculate the distance of each of the two planets Jupiter and Saturn from the comet, separately for each successive degree, for 150 years.”
He also notes that the effort made him seriously ill, and that his health never entirely recovered.
The division of work was the same one that every large calculation has used since. Clairaut set the theory and the equations, and the other two ground through the numerical evaluation, degree by degree, orbit by orbit, checking each other. The word for what Lalande and Lepaute were doing was “computer”, and it stayed the job title for a human being for another two hundred years, through the Nautical Almanac offices and the women who computed the Apollo trajectories at NASA.
The Announcement and the Margin
On 14 November 1758 Clairaut presented the result to the Académie des Sciences. Jupiter and Saturn between them had delayed the comet by about 618 days. Perihelion, the moment of closest approach to the Sun, should fall around the middle of April 1759.
He was careful to state a margin, and the care is what makes it a scientific prediction rather than a prophecy. He allowed roughly a month of uncertainty, and he said openly why: small quantities had been neglected in the approximations, the masses of Jupiter and Saturn were not precisely known, and there might be bodies out there acting on the comet that nobody had catalogued.
On Christmas night 1758 the comet was spotted by Johann Georg Palitzsch, a farmer near Dresden with a good telescope and the habit of using it. Charles Messier, who had been sweeping the sky for it deliberately for months from Paris, found it independently on 21 January 1759.
Perihelion came on 13 March 1759. Clairaut was about a month early, inside the margin he had published.
What That Month of Error Actually Proved
A miss of thirty days on a prediction made seventeen months in advance, for an object that had been out of sight for seventy five years, travelling on an orbit reaching far beyond Saturn, is the moment gravitation stopped being an English theory and became a fact about the solar system.
Before 1759 the Principia explained things that had already been observed. Kepler’s laws, the tides, the shape of the Earth, the orbit of the Moon. All of that is retrodiction, and a sufficiently flexible theory can usually be made to fit what is already known.
After 1759 it had named a date for an event that had not happened yet, and the sky had complied. Cometary appearances had been read as omens within living memory. Now one arrived on a schedule computed in a Paris apartment by three people with pens.
The same method, refined, later did something even more striking. In 1846 the residual wobble in Uranus’s orbit was used to calculate the position of a planet nobody had ever seen, and Neptune was found within a degree of where the arithmetic said to look. That is the direct descendant of Clairaut’s six months.
The Name That Was Removed
When Clairaut published his full account of the comet theory in 1760, Nicole Reine Lepaute’s name was not in it.
Lalande was furious and said so repeatedly in print for the rest of his life, crediting her contribution in his own books and in the Connaissance des Temps, of which he later took charge. In his telling the omission was not a scientific judgement but a personal one, arising from pressure inside Clairaut’s own circle.
Lepaute kept working regardless. She computed the tables for the annular solar eclipse of 1 April 1764 and produced a map of its progress across Europe at fifteen minute intervals, the kind of public prediction that Halley himself had pioneered in 1715. She contributed to the Connaissance des Temps for years and calculated the transits of Venus.
There is a crater on the Moon named Lepaute, on the edge of the Mare Humorum. It is a small one.
Reading the Book the Prediction Came Out Of
What Clairaut, Lalande and Lepaute were doing was applying, arithmetically, the propositions of the third book of the Principia. Newton had written the comet theory himself, in Book III, and had fitted the orbit of the comet of 1680 from observations, including data supplied by Flamsteed at Greenwich.
Our edition of the Principia reproduces that third book in full, including the cometary propositions that almost nobody reads and that turned out to be the part of the work with the most dramatic test attached to it. It is worth seeing how little Newton claimed and how much followed from it.
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