Comet, Revised

by Carl Sagan

  ON HALLEY’S CONTRIBUTION TO NEWTON’S PRINCIPIA

  And this is how the Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy), the central testament of modern science, the keystone of our present understanding of stars, planets, comets, and much more, came to be. In the first edition of the Principia, as it has come to be known, printed in July of 1687, a poem of worshipful tribute presented to Newton by Halley appeared as preface. Its last lines read,

  Lend your sweet voice to warble Newton’s praise,

  Who searcht out truth thro’ all her mystic maze,

  Newton, by every fav’ring muse inspir’d,

  With all Apollo’s radiations fir’d;

  Newton, that reach’d th’ insuperable line,

  The nice barrier ’twixt human and divine.

  The judgment of posterity is not far from Halley’s. Among the book’s incidental offerings are the invention of the calculus and the theory of interplanetary spaceflight, as well as the central idea behind the inter-continental ballistic missile.

  The year after Halley’s consummate midwifery delivered Newton of the Principia, he and Mary became the parents of two daughters, Katherine and Margaret. At about the same time, Halley became intrigued with Hooke’s suggestion that the Flood, as related in the Bible, could be explained by a change in the Earth’s poles, the Near East slowly sliding under the equatorial bulge of ocean. Halley was familiar with the observations, made over a period of centuries, of minuscule changes in the latitude of the German city of Nuremberg, and reasoned that since even tiny changes in latitude occur with glacial slowness, then the time between the Creation and the Flood must have been far longer than the period allowed in Genesis, in contradiction to a literal interpretation of the Bible. However, in both the Old Testament and the ancient Babylonian accounts of the Flood, events proceeded swiftly, and recovery took less than a year. So Halley tried to imagine how a quick inundation of the ancient Near East could be worked. Were a comet to approach the Earth too closely, he argued, the gravitational tides might sweep the oceans (or just the Persian Gulf) up over a sufficient area of the land to account for the events described in the Bible. Halley also held that comets might from time to time actually impact the Earth, with still more horrible consequences. He seems to have been the first scientist to ask what might happen if a comet were to pass very near the Earth, a question now important to many areas of science—and even to human survival—as we shall see.

  Halley’s interests were now more eclectic than ever. He devised the first weather map, creating a convention to indicate prevailing winds that you can find in televised weather reports today. He attempted to measure the size of the atom. He made valuable observations about magnetism, heat, air, plants, seashells, clocks, caviar, light, Roman history, aerodynamics, the habits of cuttlefish, and a method of keeping flounder alive for midwinter retailing. (These last two efforts were perhaps inspired by all those copies of History of Fish.) By his own testimony, we know that Halley used opium. He gave a discourse on his personal experience of the drug at a meeting of the Royal Society, and hardly seems to have suffered much from the so-called amotivational syndrome sometimes associated with opium and other euphoriants. He also invented, developed, and tested one of the first practical diving bells. “By this means,” he wrote, “I have kept three men 1¾ [hours] under the water in ten fathoms deep without any of the least inconvenience and in as perfect freedom to act as if they had been above.” It worked so well that Halley was able on the side to form a salvage company that prospered, and eventually sold shares to the public.

  That same year Halley published a paper on the means to determine the Earth’s distance from the Sun—by measuring the timing of Venus as, on rare occasions, it transits across the Sun’s disk. Much later, in 1716, he would publish another paper, imploring the astronomical community to organize cooperative international expeditions during the next transits. The first expedition of Captain James Cook in HMS Endeavor was intended specifically as a response to Halley’s plea to measure a transit of Venus from Tahiti on June 3, 1769; for this reason alone (there are others) Halley plays a role in the history of the exploration of the Earth. From observations of the transits of 1761 and 1769, and with Halley’s method of calculation, the astronomical unit was found to be nearly 93 million miles (150 million kilometers), a hair’s breadth from the figure we accept today. Halley gave us the scale of the solar system.

  The cover of Hevelius’ Cometographia, depicting three seventeenth-century savants debating the comparative merits of competing hypotheses on cometary motion, as indicated by the diagrams they display. While the scholars contend, a real comet appears in the sky above—apparently unnoticed by them, but tracked by their assistants on the observatory roof. Courtesy Ruth S. Freitag, Library of Congress.

  In 1691, Halley was being considered for the Savilian Professorship of Astronomy at Oxford. His confirmation required the approval of the Anglican Church, then as now headed by the Sovereign. But Halley was accused of something scandalous: “being guilty of asserting the eternity of the world.” (By these standards, many scientists and all Hindus would be disqualified for the Savilian Professorship today.) His crime had been to consider the cause of the biblical deluge. Halley’s conjectures on religious issues would today be considered irrelevant to his qualifications for teaching astronomy; moreover, the views ascribed to him by the authorities of the Church were a distortion of his true views. He never doubted that the Earth had been formed, or even created, and his efforts assumed the truth of the biblical time scales, or at least of the duration of the Flood.

  Flamsteed—still the Astronomer Royal, or chief astronomical adviser to the Crown—seems to have played a disgraceful part in the affair. So miffed was he that Halley had disagreed with him on ocean tides (and perhaps still smarting about the Hevelius controversy) that overnight he transformed himself from friend to archenemy. In a letter to Newton, Flamsteed insisted that the appointment be stopped, because otherwise the youth of Oxford would be corrupted by Halley’s “lewdness.” Even Newton, who was legendary for his prudishness, could not take this charge seriously. He urged Flamsteed to reconcile his differences with Halley, but the Astronomer Royal was unwilling. Now, the accusations went, Halley was not only lewd, but also a plagiarist, a thief of ideas. Throughout, Halley refused to be provoked. He never uttered an angry word in reply, and when the integrity of his work was attacked, he confined his rejoinders to the scientific merits of the argument.

  The campaign by Flamsteed and the Church was successful, and Halley was denied the Savilian Professorship. During the interrogation on his alleged heretical beliefs, Halley made no attempt to curry favor. His inquisitor, a Chaplain Bentley, must have been outraged: Forty years later, he published a tract entitled The Analyst, or a Discourse Addressed to an Infidel Mathematician, widely understood to be a harangue against Halley.

  However Bentley may have scolded the applicant, it is clear that Halley emerged from the experience in good spirits, and with his scientific convictions intact. He continued his investigations into the age of the Earth, this time using the salinity of seawater as a kind of clock that had begun ticking at the time the oceans were formed. He thought that regular measurement of ocean water would reveal increasing salinity as time went on. Rivers carry salt into the oceans at a rate that Halley crudely calculated. Extrapolating back to a time when seawater was fresh, Halley found that the world is much older than the Bible implies—not six thousand years, but at least a hundred million years old. Halley’s method cannot be used to determine the exact age of the Earth, because seawater has long been saturated with salt. But it is a perfectly suitable way of arriving at a lower limit for that age. Moreover, it is a brilliant anticipation of a range of modern techniques for dating rocks (see Chapter 16), and gave heart to geologists and biologists of the next century, when they came upon evidence that the Earth and life are ancient beyond all human imagining. The age of the Ea
rth—and the rest of the solar system—is now known, from a range of independent lines of evidence, to be a little over 4.5 billion years.

  When he was thirty-nine, Halley began the work for which he is chiefly remembered. Newton had demonstrated that the comets, like the planets, moved in orbits that were conic sections (see the diagram on this page), but which conic section was a matter of dispute. Newton himself was of the opinion that comets moved along open parabolic orbits—or at least he used the parabola as an approximation to the ellipse in the calculations; Cassini preferred circles; and the same Bishop of Salisbury whom Halley tried not to offend in his first published paper was leaning toward the ellipse. In addition, there were champions of the hyperbola. It was difficult to know who was right, because Earthbound observers with feeble telescopes could see comets only when they came close to the Sun. The little arc that their paths described during this briefest and swiftest part of their journey could be accounted for by almost any of the conic sections, although circles were more difficult to justify.

  Halley approached this challenge—reconstructing a comet’s whereabouts during the time it is invisible—with the discipline of a great detective. He steeped himself in every piece of recorded testimony on the subject, every surviving declaration made by a string of witnesses that stretched back to Pliny and Seneca. Through calculus and gravitational theory, Newton had provided the detection technology, which Halley mastered. And there was also an element of luck; it was Halley’s good fortune to live in a century graced with an abundance of comets, and therefore a mass of recent, relatively accurate evidence on their behavior.

  Where the Comet of 1682 was concerned, Halley regarded Flamsteed as the most reliable observer, and wrote to Newton, asking him to obtain the observations from Flamsteed, because “he will not deny it you, though I know he will me.” Newton did as he was asked. Halley then compared the orbital characteristics, or elements, of the comets of 1531, 1607, and 1682, and found many striking similarities (see the box on this page): in the tilt, or inclination of the cometary orbit to the zodiacal or ecliptic plane (Chapter 2); in the distance of the comet from the Sun at perihelion; in the region of the sky in which perihelion occurs; and in the place where the comet’s orbit crosses the zodiacal plane (called the node). These similarities were already enough to suggest that the same comet was being seen in three different apparitions. When Halley compared the dates of the apparitions, he found something like a periodic return—just as Newtonian theory had promised if the comets were on elliptical orbits.* The case was almost broken.

  But Halley worried that the differences in orbital elements from one apparition to another, while small, were much larger than what could be ascribed to errors of observation. The longitude of perihelion, for example, varied by more than a degree in the sky, yet the measurements were accurate to a few minutes of arc. Furthermore, the interval between the 1531 and the 1607 apparitions was more than a year longer than the interval between the 1607 and the 1682 apparitions. Thus, in addition to the metronomic regularity of an isolated comet in elliptical orbit around the Sun, there must, Halley believed, be some other influence or force that perturbed the comet one way in one apparition and another way in the next.

  Newton had proposed that the variations in the periods of the comets were produced by the gravitational attraction of undiscovered comets. But Halley knew that Jupiter and Saturn were perturbed by one another, and thought it likely that a comet, of much lower mass than either of these giant planets, would be more perturbed by even moderately distant approaches to either planet than by close approaches to a comet. He made a crude estimate of the effects on the comet’s motion of the gravity of Jupiter and Saturn, and found they fit well with the measured discrepancies. Halley concluded that the slight differences in the orbital elements of the comets of 1531, 1607, and 1682 had a ready explanation. These were visitations of the same comet, vulnerable, as all travelers are, to detours, delays, and road conditions.

  Halley’s investigation of comets constituted an enormous undertaking, requiring the painstaking calculation of the orbits of twenty-four comets that had achieved perihelion passage between 1337 and 1698. He was struck, as were Aristotle and Seneca, by the random character of their inclinations:

  Their orbits are disposed in no certain order.… They are not confined like the planets to the Zodiac, but … move indifferently, every way both retrograde and direct.*

  In their distance from the Sun at perihelion passage, the comets Halley studied ranged from about 1 A.U. to less than 0.01 A.U.—this was the Great Comet of 1680, that nearly grazed the Sun. And at aphelion, he found, the comets—including the Comet of 1682—ranged well beyond the orbit of Saturn, then the most distant planet known.†

  In 1705 Halley published the results of his “immense labor” in a paper entitled A Synopsis of the Astronomy of Comets. It was the first application of the laws of the universe, as revealed by Newton, by a scientist other than Newton to solve an astronomical mystery. This in itself was enough to guarantee Halley a place in the history of science. But he went much further, making a courageous leap that earns him a place in the larger history of civilization. For millennia, comets had been—at least in the public perception—the almost exclusive property of the mystics, people who considered comets as portents, symbols, wraiths—but not things. Halley shattered the monopoly by beating them at their own game, a game that (with the single exception of eclipses) no scientist had ever before played: prophecy. He predicted that the comet seen in 1531, 1607, and 1682 would return more than fifty years in the future. And he did not hedge his bet. It would return, he stated flatly, at the end of 1758—from a particular part of the sky, with specific orbital elements. There is hardly a prophecy of the mystics that even strives for comparable precision. He was, for his time, remarkably free of nationalism, but this once, he indulged himself in a bit of chauvinism: “Wherefore, if according to what we have already said it should return again about the year 1758, candid posterity will not refuse to acknowledge that this was first discovered by an Englishman.”

  In the spring of 1696, Newton was appointed Warden of the Royal Mint. It required him to live in the Tower of London. His task was to prevent clipping or shaving of the coinage of the realm. Months later, Newton appointed Halley—who had just begun his study of comets—deputy comptroller of the mint at Chester. Under the Master and the Warden in the Tower were masters, wardens, comptrollers and the like in provincial facilities of the mint. Halley spent two miserable years at Chester supervising the mechanized production of milled coins out of the old handmade ones. When he and his local warden discovered two clerks skimming precious metals for their own gain, they spoke out—unaware that their own superior, the Master of the Mint at Chester, was getting a cut from the clerks. An acrimonious feud followed, and there were threats of a duel; but the mints were closed in 1698, and Halley was liberated to return to London.

  He arrived just in time for a more agreeable assignment. The twenty-six-year-old Czar of Russia, who would later be known as Peter the Great, had come to England to learn how to Westernize his nation. He was ensconced at a grand country home near the Deptford shipyards, where he performed manual labor as part of an effort to gain firsthand experience of the British genius for shipbuilding. (One’s powers of imagination protest when asked to contemplate some modern equivalent—an American president laboring in the spacecraft assembly facility in Tyuratam, say, or the Russian president installed for months in a hard-hat job at Cape Canaveral.) Peter had hoped to spend time with Newton, but Newton sent Halley in his stead. By all accounts, the English astronomer and the Russian Czar became fast friends, sharing passions for knowledge and brandy. For the duration of Peter’s stay in England, Halley remained his chief science adviser and drinking partner. One disputed, though contemporary, account depicts Halley raucously pushing the Czar of all the Russias through the streets of Deptford in a wheelbarrow in the dead of night. It was said that the two of them were inebriated, and
that the escapade caused grave damage to the topiary hedges.

  That same year Mary Halley gave birth to a son named Edmond, and her husband began yet another career, described in a contemporary account replete with italics:

  In 1698 the King [William III] who had been inform’d of Mr. Halley’s ingenious Theory of the Magnetic Needle, was desireous the variation shou’d, for the Benefit of Navigation, be carefully observed, in diverse parts of the Atlantic Ocean; for which purpose His Majesty, the 19th Aug. 1698, appointed Mr. Halley Commander of His Ship the Paramoor* Pink, with orders to seek by observation the discovery of the Rule of the variation of the Compass, and at the same time to call at his Majestys Settlements in America, making some observations there, in order to the better laying down the Longitudes and Latitudes of those places, and to attempt a discovery of what Lands lay to the South of the Western Ocean.

  Seventy years before Cook set sail (in pursuit of a Halleyan objective), Halley was commanding the first marine scientific expedition to be commissioned by a British monarch. The Paramour sailed to Spain, the Canary Islands, Africa, Brazil, and the West Indies, before an incipient mutiny on the part of Halley’s second-in-command necessitated an unscheduled return to England. In the course of the court-martial that ensued, it was revealed that the disgruntled lieutenant was a closet magnetic theorist, whose own writings on the subject had earlier been found wanting by the Royal Society. He nursed his indignation, and when the landlubber Halley was commissioned his captain, he became unhinged. Halley assumed the role of navigator and took great pride in the fact that he was able to bring his ship home without loss of life.

  Halley commanded two additional voyages on the Paramour—one, amidst many perils, up the coast of South America to Trinidad, bound for Cape Cod. They found the seas off Nantucket too high, and were forced to sail on to Newfoundland. There the Paramour took friendly fire from an English fishing fleet that mistook her for a pirate ship. Again the captain safely returned his ship to England, but this time was denied the satisfaction of seeing every member of his crew at the homecoming. The cabin boy had been swept overboard and lost during a wild storm off the Canary Islands. For the rest of Halley’s life, he was unable to speak of the boy’s death without tears.