Comet, Revised

by Carl Sagan

  —JEAN JACQUES D’ORTOUS DE MAIRAN, “ELEGY FOR MR. HALLEY,”

  MEMOIRES DE L’ACADÉMIE ROYALE DES SCIENCES, PARIS, 1742

  Aristotle’s opinion … that comets were nothing else than sublunary vapors or airy meteors … prevailed so far amongst the Greeks, that this sublimest part of astronomy lay altogether neglected; since none could think it worthwhile to observe, and to give an account of the wandering and uncertain paths of vapours floating in the Æther.

  —EDMOND HALLEY, TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON,

  VOLUME 24, PAGE 882, 1706

  When we think of Edmond Halley, if we think of him at all, it tends to be solely in connection with his namesake—humanity’s favorite comet. The comet becomes a kind of mnemonic device, operating at roughly seventy-five-year intervals, that chides us to remember him. To most of us, Halley is like the athlete who makes his way into the record books on the basis of one extraordinary season, or even one memorable play. We consult the records, expecting to find a journeyman who like countless others has contributed a brick or two to the edifice of science. Instead, we find a master builder.

  The date of his birth is uncertain; Halley believed it to be October 29, 1656. He began life in the Borough of Hackney, then a rural community outside London, but since subsumed by the spread of the city. Although we have not a single anecdote, even apocryphal, that indicates the texture of his childhood, we do know that it was then that he first dreamt what he would later become. “From my tenderest years I gave myself over to the consideration of Astronomy,” he recalled while still quite young. “[It gave me] so great pleasure as is impossible to explain to anyone who has not experienced it.” Halley’s sense of science, not as livelihood, but as rapture, was never to leave him. In his boyhood, two comets were seen, one, in 1664, popularly associated with the Great Plague of London, the other, in 1665, connected with the Great Fire. Although no record exists of Halley witnessing these visitors, a young person of his inclination and ability must have been influenced by the comets of 1664 and 1665, so steeped were they in portent, calamity, and disaster.

  His father, also named Edmond, was a businessman, a soap boiler and salter who owned lucrative properties in London. In 1666 the Great Fire devoured his real estate holdings, but his other businesses flourished. The recent horrors of the bubonic plague had instilled in Londoners a regard for personal hygiene. Soap manufacture became a growth industry. Moreover, the expanding British navy had a chronic need for salted meat to sustain its sailors on long voyages. The elder Halley, his businesses flourishing, was happy to use his new wealth to see his son’s evident new promise realized.

  He sent him to St. Paul’s, one of the best schools in England, where Edmond did brilliantly. In 1671, he was elected Captain of the school—a mark of that rarity, an excellent student who is popular with his classmates. We know nothing of Halley’s mother other than that her name was Anne Robinson and that she died on October 24, 1672, nine months before her son’s departure for Queen’s College, Oxford. Additional evidence of his father’s largesse is provided by the quantity and quality of the astronomical instruments that Halley took along to college—among them a twenty-four-foot-long telescope, which he immediately put to good use.

  We know this because on March 10, 1675, the eighteen-year-old Edmond Halley had the audacity to write to John Flamsteed, England’s first Astronomer Royal, informing him that the authoritative published tables on the positions of Jupiter and Saturn were in error. The young man had also found errors in the star positions published by the incomparable Tycho Brahe. The tone of Halley’s letter is not that of the young cowboy come to challenge the legendary gunslinger; but much more the youthful enthusiast, full of admiration for those who have come before him, anxious to join their club—and even more anxious to discover the true nature of the universe. We do not know exactly what Flamsteed’s response was, but it must have been positive, because the next year he helped Halley publish his first scientific report, or “paper.” It appeared in Philosophical Transactions, the journal of the Royal Society of London—then, as now, the leading scientific organization in Britain—and was titled “A Direct and Geometrical Method of finding the Aphelia, Eccentricities, and Proportions of the Primary Planets, without supposing equality in angular motion.”

  What was this paper about? Since the work of Tycho’s student, Johannes Kepler, it had been known that each planet moves along a path called an ellipse, a kind of stretched-out circle. The eccentricity is a measure of how stretched out the ellipse is; an ellipse with zero eccentricity is a circle, and an ellipse with an eccentricity of 1 or greater is not even a closed curve, but rather a parabola or hyperbola (see this page). The eccentricity of the Earth’s orbit is 0.017—to the naked eye, indistinguishable from a circle. Mercury’s orbital eccentricity, by contrast, is 0.21—perceptibly elongated. Many years later, it would be one of Halley’s triumphs to determine that comets move in elliptical orbits, one of the keys to their origin.

  In a roughly circular orbit such as the Earth’s, we are always pretty much at the same distance from the Sun. But in a highly elliptical orbit, the distance to the Sun varies depending on where the moving object is in its orbit. The nearest point to the Sun, when the planet or comet is moving fastest, is called the perihelion (plural, perihelia). As the object sweeps around the Sun, it is said to be making perihelion passage. The phrase has a nice ring to it, as if it were something experienced on steamships of the old P&O line. The far point in the orbit is called aphelion. The more elliptical the orbit is, the bigger the difference between aphelion and perihelion. It is perfectly possible for a comet to have its perihelion near the Earth, and its aphelion far beyond the most distant known planet. But this was before Halley began studying the comets. In his first paper, Halley proposed a new and more accurate method of calculating the orbits of the planets.

  The paper had to be rewritten many times, in part due to Halley’s inexperience, but also because the Bishop of Salisbury had published a contrary view, and so, Halley was told, might construe the paper as a personal insult. Halley had no intention to offend, and made the suggested changes happily. This was not the last time that Halley’s pursuit of science would offend ecclesiastical sensitivities.

  The same year that Halley’s paper on orbits brought him to the attention of the world astronomical community, he chose to leave Oxford without taking his degree, and to travel to the distant island of St. Helena, west of Africa, to make the first map of the southern skies. The constellations you can see from high northern latitudes are almost completely different, of course, from those you see from close to the South Pole. At the equator you see all of the northern and all of the southern constellations. St. Helena was then the southernmost outpost of the British Empire and a good vantage point from which to observe not only the southern skies, but also some of the charted stars of the Northern Hemisphere—important because, if Halley’s proposed map of the southern stars were to be useful to European astronomers, it would have to share some points of reference with star positions that had been previously determined. Besides its latitude, St. Helena had something else to recommend it; by all accounts, the weather was invariably clear, a matter of critical concern for astronomical observations.

  Halley’s new friends at the Royal Society wrote a letter to the government in support of the proposed expedition, which soon found favor with King Charles II. But the king was only the titular monarch of far-off St. Helena; in reality, the little island was a fiefdom of the powerful East India Company. Charles was, however, not without influence, and after he wrote to the company’s directors, they volunteered to provide passage for Halley and a scientific companion. Halley’s father, “willing to gratify [Edmond’s] Curiosity,” provided him with a huge allowance that more than covered the cost of the best observing equipment then available and such other expenses as he might incur.

  The conic sections. When a cone is sliced or sectioned at various angles, several different sh
apes or curves are produced which collectively are called conic sections. If the four pieces shown here were put together, the cone would be reassembled. The top of the cone is called the apex, and the flat bottom on which it stands is called the base. If you make a cut parallel to the base, you produce a circle. If you cut at an angle, you produce a stretched-out circle, a little like an oval, called an ellipse. If you slice perpendicular to the base, the surface you expose is a hyperbola; unlike the circle and the ellipse, the hyperbola does not curve back upon itself. There is one other curve, not shown here, which lies at the transition between an ellipse and a hyperbola; it is called a parabola. These pretty conic sections were first described by Apollonius of Perga in the second half of the third century B.C. It is astonishing that planets and comets know to move about the Sun precisely along such paths; and that the trajectory of a rock thrown up into the air follows a parabola. So does a ballistic missile. Newton showed that the inverse square law of gravitation forces bodies to move through space along conic sections. Such connections between seemingly abstract mathematics and the way the world actually works characterize the major discoveries that have molded modern science. Diagram by Jon Lomberg and Jason LeBel/BPS.

  In November 1676, Halley set sail on the Unity, beginning a journey that would take three months and cover nearly ten thousand kilometers of ocean. His destination was an island so remote that 130 years later, the British would deem it the only prison secure enough to contain the captive Emperor Napoleon. For almost two centuries European mariners had been sailing the southern seas, mapping every coastline they could lay their eyes on, and not one of them had accurately mapped the very different constellations above them. Halley’s self-imposed assignment was to bring back half the sky. He had just turned twenty-one.

  Travelers’ tales to the contrary, the weather on St. Helena was rotten. Halley would wait for weeks for an hour’s window on the stars. English weather was better than this. At least in England, in inclement weather, there were other things to do. Halley had exiled himself to little more than a rock in the middle of a vast ocean. And he had more than clouds and boredom to worry about; the governor of St. Helena was a certified madman who quickly grew to hate Edmond Halley. Eventually the governor’s behavior became so bizarre that he was recalled and dismissed, but not before Halley himself was ready to return. Despite the difficulties, his trying year on St. Helena was well-spent. He came home with the first map of the southern skies and much more. He had discovered stars and nebulae that European astronomers had not known. In St. Helena he had observed a transit of the planet Mercury across the face of the Sun, later significant in the determination of the Sun’s distance from the Earth. He confirmed that there was no Pole Star in the southern skies, and that accurate time-keeping on St. Helena with a pendulum clock calibrated in England was impossible unless you shortened the pendulum. (Although Halley didn’t know it at the time, this is because the spin of the Earth creates a small centrifugal force that slightly counteracts gravity at the equator, but weakens with increasing latitude.)

  His catalogue of the southern skies was presented to the Royal Society by Robert Hooke, a neurotic polymath who was the first person to see Jupiter’s Great Red Spot through the telescope, and the first person to see a living cell through the microscope. (He also was the first to use the word “cell” in its biological context.) Hooke made lasting contributions to physics, astronomy, biology, and engineering. The Fellows of the Royal Society were quick to appreciate Halley’s achievement, but as far as Oxford was concerned, Halley was just another dropout. They would not let him return to take his degree because he had departed for St. Helena before fulfilling his residency requirements—so serious a breach of regulations that nothing short of a royal decree could put the matter right. He appealed once more to Charles II, and once more Charles signed a letter on his behalf, this time requesting that he be granted the degree of Master of Arts “without any condition of performing any previous or subsequent conditions of the same.” The Vice-Chancellor of Oxford complied. At about the same time he was granted his degree, Halley was elected a Fellow of the Royal Society, a considerable distinction for so young a man.

  Halley soon turned his attention to an intensifying controversy involving Hooke, Flamsteed, and Johannes Hevelius of the free city of Danzig, the preeminent observational astronomer of the time. Hooke and Flamsteed swore by the recently invented telescopic sight, which, when mounted on a measuring instrument, improved the precision with which the relative position of the stars could be determined. But the older Hevelius rejected the new technology and persisted in using an open sight, without optics, a mechanism as simple as the sight on a rifle. Appalled, Hooke and Flamsteed conducted an increasingly shrill campaign against Hevelius, asserting to everyone who would listen that Hevelius’ observations were untrustworthy. It was an unlikely topic for a vitriolic controversy. Hevelius, quite reasonably, began to feel beleaguered. He too was a Fellow of the Royal Society, but he lived in Danzig, far from the pubs and parlors in which Hooke and Flamsteed were pursuing their curious assault. He appealed to the Fellows, writing that every scientist should be permitted to serve astronomy as he believed best; that the results should be tested and judged solely on their merits; that it was unseemly for scientists to disparage the work of a colleague in the absence of supporting evidence. He had been observing with an open sight for more than thirty years, and if it had been good enough for Tycho Brahe it was good enough for him. The Royal Society responded officially by affirming its confidence in Hevelius and challenging Hooke and Flamsteed to document their case, or desist. They would do neither. The parties had reached an impasse.

  With his tact, integrity, and genius for observation (and his father’s money), there could be no one better suited than Halley to make the journey to test Hevelius’ method. Halley sent Hevelius a copy of his southern star catalogue with a request for an invitation to visit. Hevelius agreed, and Halley arrived in Danzig in May of 1679. For ten nights they observed together. Halley was soon convinced that Hevelius, with the obsolete open sight, consistently achieved better results than Flamsteed and Hooke with state-of-the-art equipment. He immediately wrote to Flamsteed, describing his painstaking, systematic efforts to find flaws in Hevelius’ observations: “Verily I have seen the same distance repeated several times without any fallacy,” he informed his mentor, who was doubtless anxious to learn otherwise, “… so that I dare no more doubt his [Hevelius’] Veracitye.”

  Johannes Hevelius of Danzig was also an observer of comets. Here from his Cometographia (1668) are a variety of cometary forms seen between 1577 and 1652. Compare with the Chinese cometary atlas, this page.

  Despite Halley’s testimonial, Flamsteed and Hooke lacked the capacity to apologize, or even to relent. The “open sight” controversy did not die until Hevelius himself died, eight years later. Halley’s conduct had been a model of fairness and candor, risking the displeasure of powerful friends in the interest of truth.

  In 1680, as a great comet appeared in European skies, science was certainly not widely accepted as the favored approach to an understanding of nature. Gibbon mentions, as a perfect example of a world view in transition, an astronomer who “was forced to allow that the tail, though not the head [of the Comet of 1680] was a sign of the wrath of God.” Even Gottfried Kirch, the German astronomer who discovered the Great Comet of that year, was convinced of the supernatural nature of comets:

  I have read through many books on comets, heathen and Christian, religious and secular, Lutheran and Catholic, and they all declare comets to be signs of God’s wrath.… There are some that oppose the belief but they are not very important.

  Comet Arend-Roland (1957 III), famous for its sunward spike. Compare with Hevelius’ depiction of the Comet of 1590 (second comet from top on facing page). Photographed through the University of Michigan telescope by F. D. Miller, April 24, 1957. Courtesy National Aeronautics and Space Administration.

  Halley also saw the Great
Comet of 1680, but his response was different from Kirch’s. On board a ferry in the English Channel, somewhere between Dover and Calais, Halley glanced up as the clouds broke and saw something splendid. As soon as he reached France, he hurried to the Paris Observatory to confer with its director.

  Jean-Dominique Cassini, discoverer of the major gap in Saturn’s rings, as well as four of the planet’s moons, received the young author of A Catalogue of the Southern Stars with lavish hospitality. Cassini entertained Halley, introduced him to friends and colleagues, gave him unrestricted use of the observatory’s equipment and library, and, most significantly, presented Halley with an idea. In a remarkable letter to Hooke dated May 1681 Halley wrote:

  Monsieur Cassini did me the favour to give me his booke of ye Comett Just as I was goeing out of towne; he, besides the Observations thereof, wch. he made till the 18 of March new stile, has given a theory of its Motion wch. is, that this Comet was the same with that that appeared to Tycho Anno 1577, that it performes its revolution in a great Circle including the earth.

  Halley recounts the details of three cometary apparitions, adding:

  … this is the sume of his Hypothesis and he says it will answer exactly enough to the Motions of the two Comets as likewise to that of Aprill 1665; I know you will with difficulty Embrace this Notion of his, but at the same tyme tis very remarkable that 3 Cometts should soe exactly trace the same path in the Heavens and with the same degree of velocity.

  No one had yet determined the orbit of a comet, but Cassini had noticed that three comets had come from the same part of the sky with similar speeds, and made the daring proposal—unprecedented in the scientific literature,* and explicit only in the folk tradition of the Bantu-Kavirondo people of Africa—that the same comet was returning to Earth in widely separated times.