Comet, Revised

by Carl Sagan

  Halley informs Hooke that his preliminary attempts to sketch out a path for the Comet of 1680, based on Cassini’s summary of its apparent movement across the sky, have been unsuccessful; at some future time he hopes to try again. And in the final paragraph, as an aside, Halley lays the groundwork for the science of actuarial statistics. After summarizing the comparative statistics for Paris and London of births, marriages, deaths, and population density—the last facilitated by Halley himself pacing off the dimensions of the city of Paris on foot—he concludes:

  … it will from hence follow, supposing it alwaies the same, that one half of mankinde dies unmarried, and that it is nescessary for each married Couple to have 4 Children one with another to keep mankinde at a stand.

  It was ten years before he would develop this idea further, and even longer before he returned to the subject of comets. Now he was off to Italy for six months. When he returned home to England, he made his first great discovery.

  Her name was Mary Tooke. She was the daughter of the Auditor of the Exchequer. A contemporary memoir describes her as “an agreeable young Gentlewoman; and a Person of real merit.” Another tribute portrays her as “a young lady equally amiable for the grace of her person and the qualities of her mind.” They were married less than three months after his return from the Continent, at St. James, a church notorious or compassionate—depending on your point of view—for choosing elopements as its speciality. There does not seem to have been any opposition to the marriage, nor was Mary pregnant. Perhaps they chose St. James because they did not wish to waste another hour. Their marriage and their love were to last until Mary’s death, nearly fifty-five years later. The few surviving references to them together make clear a deep and enduring happiness. In 1682, toward the end of their first summer together, Edmond, and possibly Mary, witnessed another comet, unimpressive compared to the Great Comet of 1680. He made a few notes to record what he saw. It was his only look at the comet that would one day bear his name.

  Years after the death of Halley’s mother, Edmond Sr. had entered into an unfortunate second marriage. There was talk about his new wife’s extravagances, and her apparent disregard for her husband and stepson. The contrast between the marriages of father and son must have pained them both. On the morning of March 5, 1684, the senior Halley complained that his shoes were too tight, and a nephew offered to cut the linings out of the toes. This seemed to help, and Edmond Sr. told his wife that he was going out; he would return by nightfall. A contemporary broadside recounts what happened next:

  More cometary forms by Hevelius. Note the comets with disrupted tails. The bottom three are called “monstriferous” comets, an echo of the once prevalent cometary mysticism. The sixth and seventh show what are now called “disconnection events.” From the collection of D. K. Yeomans.

  When Night came she accordingly expected him, but not returning she was very much concerned at it, and the next day made all possible Enquiry, but after several days not hearing of him, published his Absence in the News Book. From Wednesday the 5th of March, to the 14th of April, notwithstanding all Endeavours, and the strictest Search that could be made, they received no Account where he was, or where he had been. But on Monday last he was found by a River side at Temple-Farm in Strow’d Parish near Rochester on this manner. A poor Boy walking by the Water-side upon some Occasion spied the body of a Man dead and Stript, with only his Shoes and Stockings on, upon which he presently made a discovery of it to some others, which coming to the knowledge of a Gentleman, who had read the advertisement in the Gazet, he immediately came up to London, and acquainted Mrs Halley with it, withal, telling her, that what he had done, was not for the sake of the Reward, but upon Principles more Honourable and Christian, for as to the money, he desired to make no advantage of it, but that it might be given intirely to the poor Boy; who found him and justly deserved it.

  The same nephew who had adjusted Halley’s shoes was dispatched by Mrs. Halley to identify the body. It must have been a gruesome task; the face had been obliterated. The broadside continues:

  It was concluded by all, that he had not baen in the River ever since he was missing, for if he had, his Body would have been more Corrupted. The Gentleman knew him by his Shooes and Stockings, they being the same Shooes he had cut the Lineing out of, and on one leg he had four Stockings, and on the other three and a Sear-cloath.* The Coroner sat upon him, & the Inquest brought him in Murthere’d.

  The death of Edmond Halley, Sr., remains a mystery. No Sherlock Holmes was at hand to sift through the redundant footwear and deduce Halley’s whereabouts during the five weeks previous. Two and a half centuries after the fact, Eugene Fairfield MacPike, a distinguished Halley scholar, rendered a verdict of suicide, claiming that “the evidence with which we are supplied appears to point to mental aberration.” Perhaps. But the evidence at least as well points to misadventure or murder.

  An additional mystery revolves around the younger Halley’s response to his father’s fate. He is unmentioned in the broadside story, playing no apparent role in the search for his father, the identification of the body, or the coroner’s inquest. His whole life is a case study of a massive, almost compulsive curiosity. And yet we find no record that he made any attempt to resolve the mystery of his father’s death—the man who had so generously encouraged and supported his intellectual development.

  In an unseemly coda to these unhappy events, the “Gentleman” who had brought the second Mrs. Halley news of her husband’s corpse sued for nonpayment of the £100 reward, despite his protestations “that he desired to make no advantage of it.” The case was heard by a Judge Jeffreys, who was infamous for the frequency and variety of the crimes he committed against the defendants who stood before him—harassment and extortion being the mildest among them. In this particular case, Judge Jeffreys seems to have taken the high road, awarding the “Gentleman” only £20, and ordering Mrs. Halley to pay the remaining £80 to the hapless “poor Boy” who had discovered the body. A decade later, Edmond took his spendthrift stepmother to court in what was described as an effort to defend his inheritance.

  At about the time that his father vanished, Halley had been trying to develop a deeper understanding of planetary motion. Kepler had pointed out that there is a precise proportionality between the period it takes for a planet to go once around the Sun (its year) and the distance of the planet from the Sun (this page). The year on Mercury, close to the Sun, is only 88 Earth days; the year on Saturn, far from the Sun, is almost 30 Earth years. The period of a planet in the outer solar system is longer than an Earth year not only because it has a bigger orbit to traverse, but also because it is moving more slowly. Why? Halley and several others had a notion that the planets move as they do because of a balance of two forces—one directed outward from the Sun, and provided by a planet’s own velocity, and the other directed inward, but provided by a previously undiscovered gravitational force from the Sun. It was clear that the force had to decline with distance, so that far-off planets could move slowly and still balance the force of gravity. But how fast must the gravitational force diminish as you move away from the Sun, in order to account for the observed planetary motion? By intuition—or false analogy with the propagation of light, or more likely from Kepler’s Third Law—Halley and his colleagues suggested that gravity was an inverse square law. Move the planet twice as far from the Sun, and the force diminishes to a quarter its original strength; three times farther away and the force decreases to one-ninth; and so on. The law of gravity, whatever it might happen to be, dominated the heavens. This problem is central to our understanding of nature. But the much more difficult problem they were all stuck on was not why planets in circular orbits are propelled by an inverse square gravitational force, but why planets in elliptical orbits are.

  The time it takes for a planet or comet to complete a single orbit of the Sun increases the farther from the Sun it lies—according to a particular law of nature described by the diagonal straight line. The orbit
al period is given in Earth years and the distance from the Sun is given in Astronomical Units. Note that each vertical line denotes a distance from the Sun ten times that of the previous line. At lower left, we see that a body 1 A.U. from the Sun takes one year to go around the Sun, the case for the Earth. At a distance of 100 A.U. from the Sun a comet would take a thousand years per orbit, and in the outer parts of the Oort Cloud of comets (Chapter 11), indicated by the dots, a comet may take millions of years to go once around the Sun. This relationship, which was central to the work of Newton and Halley, was discovered by Johannes Kepler and is called Kepler’s Third Law. Diagram by Jon Lomberg/BPS.

  Halley, Hooke, and Christopher Wren—an astronomer turned architect who rebuilt London after the Great Fire—considered the challenge of proving the proposed inverse square law in a coffee house after a meeting of the Royal Society in January 1684. Hooke boasted that he had already done so, but declined to produce the proof. Wren must have had his doubts, because he offered a reward of any book that did not cost more than forty shillings to anyone who could provide a proof before two months had passed. Hooke maintained that he had found the solution, but was delaying showing it to others so all could appreciate the difficulty and significance of his work. Wren was in no danger from this quarter of losing his forty shillings.

  Months passed and the challenge remained unanswered, so Halley made up his mind to pay a visit to Trinity College, Cambridge, where there lived a man who might be equal to the task. This scholar had been judged a prodigy, primarily on the basis of his remarkable work on the nature of light and color. But that had been many years before, and he had squandered his genius during most of the interim in the pursuit of alchemical recipes and in strident attacks on the character of Athanasius, a theologian of the early Christian Church who did much to establish the orthodox doctrine of the Trinity. He believed Athanasius guilty of deliberate falsification and historical fraud. Unable to maintain normal relationships with anyone, especially women, this scholar was given to fits of paranoia and depression. Moreover, he was afflicted with an apparent inability to complete anything. Still, he was known to be a brilliant mathematician, and Cambridge was not so far from Halley’s home in London. So on an August morning in 1684 he set out to visit Isaac Newton.

  Halley’s encounter with Newton (1642–1727) was a watershed for Halley, for Newton, for science, and, in ways so numerous as to be incalculable, for the fate of the world. The mathematician Abraham De Moivre took down Newton’s version, related many years later, of this momentous encounter:

  The Dr [Halley] asked him what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it. Sr [Newton] replied immediately that it would be an Ellipsis, the Doctor struck with joy & amazement asked him how he knew it, why saith he I have calculated it, whereupon Dr Halley asked him for his calculation without any further delay, Sr Isaac looked among his papers but could not find it, but he promised to renew it, & then send it to him.…

  This promise might well have had a familiar and therefore hollow ring. But where Hooke prevaricated, Newton delivered. In November a copy of Newton’s De motu corporum in gyrum (“On the Motion of Bodies in Orbit”—scholarly works were still being written in Latin) was hand-carried to Halley. Only nine pages long, it contained the proof that the inverse square law implied all three of Kepler’s Laws, as well as the seeds of a broad new science of dynamics. Halley instantly recognized what Newton had accomplished. Rushing back to Cambridge, he extracted from Newton a promise to expand his ideas into a book, and to do it quickly.

  Isaac Newton, the greatest British scientist, commemorated on the one-pound note.

  Halley’s first visit to Newton had awakened the latter from a kind of mystic trance. Now Newton was wide awake to the point of sleeplessness, obsessed with this new challenge, unable to eat or to think of anything else. For the next year and a half he would live as a recluse, in monomaniacal pursuit of gravity and planetary motion.

  Meanwhile, Halley was back in London, busily trying to get himself demoted. The Royal Society had operated since its inception in the early 1660s as a kind of club for gentlemen with scientific inclinations. But by 1685 the scientific revolution had assumed such dimensions that the voluntary services of its fellows were inadequate to the task at hand. What was needed was a paid full-time secretary, someone who would deal with the growing correspondence, arrange the details of the meetings, and edit the Philosophical Transactions. Halley correctly understood that this position would afford him an ideal exposure to everything that was happening in science. He was elected to the job on the second ballot, early in 1686. But his salary from the Royal Society meant that he would have to relinquish his fellowship, sit at the lower end of the table, and be denied the high honor of wearing a wig.

  Cheerfully Halley turned his voracious curiosity to the feast at hand, a banquet of geology, geography, biology, medicine, botany, meteorology, mathematics, and of course astronomy. He played a significant role in transforming the Royal Society from a club to the world’s central clearinghouse for scientific ideas, and at the same time managed to publish many original papers of his own.

  As Newton neared the completion of his masterwork, Halley approached the Royal Society with the proposition that they publish it. Since everyone agreed that the book would be important, the society would under normal circumstances have been only too happy to pay for its publication. However, it had unwisely exhausted all its publication funds on another book. This was the long-awaited History of Fish, which unaccountably had failed to find its anticipated audience. So Halley decided that he would pay for the publication of Newton’s work out of his own pocket. Oh yes, on the matter of his salary … This, too, would be a problem for the Society. Would Halley mind terribly taking the wages that had cost him his wig in remaindered copies of the History of Fish? Halley cheerfully accepted and lugged home seventy-five. By this time he was no longer wealthy, in part because of his stepmother’s incursions into his father’s estate, but he chose not to make an issue of it.

  The level of expectation surrounding Newton’s forthcoming work was more than Robert Hooke could bear. He resurrected the old pretense that the inverse square law belonged to him. He would be satisfied with nothing less than an acknowledgment of his priority in the preface of Newton’s book. Halley, who had already taken on the responsibilities of agent, editor, publisher, and proofreader for the book, now assumed another role: psychotherapist to the author. Fearing that Newton would hear of Hooke’s charges from a less thoughtful source, Halley wrote him a letter. It begins with expressions of admiration and gratitude, but you can sense Halley’s anxiety as he finally gets to the point:

  There is one thing more that I ought to inform you of, viz, that Mr Hook has some pretensions uipon the invention of ye rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center. He sais you had the notion from him.…

  Newton’s initial reaction was restrained, but the more he thought of it, the more enraged he became. He would withdraw the third volume of the work rather than become enmired in odious controversy with Hooke. But Book III was critical. Richard S. Westfall, in his brilliant biography of Newton, writes of Book III,

  In a word, it proposed a new ideal of a quantitative science, based on the principle of [gravitational] attraction, which would account not only for the gross phenomena of nature, but also for the minor deviations of the gross phenomena from their ideal patterns. Against the background of inherited natural philosophy, this was a conception no less revolutionary than the idea of universal gravitation itself.*

  Book III also contained Newton’s monumental work on comets. He had painstakingly collected observations of the Comet of 1680, acquired from a wide range of locales, including London, Avignon, Rome, Boston, the island of Jamaica, Padua, Nuremberg, and the banks of the Patuxent River in Maryland. (Even then, worldwi
de cooperation was essential to understand the comets.) He showed that together they defined a highly eccentric orbit, almost a parabola (see figure on this page). Newton noted from examination of the history of comets that they are seen much more often in the part of the sky near the Sun than opposite the Sun, and understood this to be evidence that comets generally—not just the Comet of 1680—are in orbit about the Sun, and brighten when they are nearest to it. Tycho had shown that the comets move among the planets; now Newton, with Halley’s prodding, had demonstrated that they have the same kinds of orbits (conic sections, this page) as the planets.

  “The comets shine by the Sun’s light, which they reflect,” Newton wrote. “Their tails … must be due either to the Sun’s light reflected by a smoke arising from them, and dispersing itself through [space], or to the light of their own heads.… The bodies of comets must be hid under their atmospheres.”

  To Halley, it was unthinkable that these vital contributions might be lost to the world, a casualty of Newton’s snit over Hooke’s vanity and posturing. He reassured Newton that no one took Hooke’s claims seriously and told the story of Wren’s wager, back in 1684. He insisted that without Book III, the work would appeal only to mathematicians. He argued that Hooke’s demands had been exaggerated by others. He cajoled, he flattered. Finally Newton relented and allowed the publication of the entire work.

  But for him, in all human probability, the work would not have been thought of, nor when thought of written, nor when written printed.

  —AUGUSTUS DE MORGAN (1806–1871)