The Hunt for Vulcan

by Thomas Levenson

  He failed. When he attempted to construct a theory of Uranus that could generate by calculation the positions observers had recorded since Herschel’s night of discovery, he couldn’t make the numbers work. Anything he tried that agreed with observations made since 1781 didn’t line up with the rediscovered positions that had been misidentified as stars before that date. Even worse, when he focused only on the more recent, post-Herschel record, it quickly became clear that the planet was again wandering off course—or rather that reality and calculation diverged.

  In the abstract, such uncooperative behavior might point to a very deep problem: if all the gravitational influences on Uranus had been accounted for, the failure to predict its motion would demand a reexamination of the theory behind such analysis. That is: it could threaten the foundations of Newton’s laws themselves. One researcher, the German astronomer Friedrich Wilhelm Bessel, suggested exactly that, wondering if perhaps, just maybe, Newton’s gravitational constant itself might vary with distance.

  Such thoughts were thinkable, but horrifying. There was the worshipful awe the man himself inspired, of course, but more to the point, Newton’s physics worked. The tides obeyed its rules; comets were brought to order under its provisions; cannonballs flew on courses perfectly described and explained by the exquisite logic of the Principia. Better, by far, would be any explanation that captured this seeming anomaly within a Newtonian framework.

  It seems that, privately, Alexis Bouvard was the first to come up with a way to do so. In 1845, his nephew, Eugène Bouvard, reported to the Académie his own, unsuccessful attempt to bring Uranus’s track to mathematical order. Following his uncle, he tried to resolve modern (post-Herschel) observations with older ones. He failed, and admitted as much. But still, he told his learned audience there was a way out, one his uncle had glimpsed two decades earlier. It was not the one Laplace had used to resolve the Jupiter-Saturn mystery. That involved improving the mathematical technique with which he attempted to describe the world out there. Rather, the older Bouvard reasoned, if all the known behaviors of the solar system could not account for the last residue of error—and crucially, if you maintained your faith in Newton—then the only remaining possibility was that something unknown would resolve the matter. Bouvard reminded his readers that if they imagined Uranus had remained undiscovered, then meticulous attention to Saturn would reveal the influence of some more distant unseen celestial body. In exactly the same manner, he wrote, it seemed “entirely plausible [to him] the idea suggested by my uncle that another planet was perturbing Uranus.”

  The Bouvards weren’t the only ones to make that leap. By the early 1830s, several researchers began to think about the possibility of an object yet farther from the sun than Uranus. The older Bouvard had shared his notion with correspondents and visitors, one of whom carried the idea across the channel to England. One obvious difficulty kept this widening circle from doing very much with the idea, though. Uranus was too damn slow. Its eighty-eight-(Earth-)year-long period meant that systematic observations since Herschel had followed roughly half of a single journey around the sun. The Astronomer Royal George Biddell Airy conceded the plausibility of the idea of a trans-Uranian planet but quashed the hopes of one inquirer, writing that the mystery would resist solution “till the nature of the irregularity was well determined from several successive revolutions”—which is to say, only in that long run when all those then concerned would be dead.

  —

  Le Verrier disagreed. Or rather, his sometime-mentor, François Arago, the director of the Paris Observatory, thought that Herschel’s planet had embarrassed astronomers long enough. Late in the summer of 1845, Arago pulled the younger man away from a brief dalliance with comets and, as Le Verrier recalled, told him that the growing errors within the theory of Uranus “imposed a duty on every astronomer to contribute, to the utmost of his powers.” Le Verrier began by identifying several errors in the older Bouvard’s sums. Those mistakes did not eliminate the unexplained wobbles in Uranus’s orbit, so Le Verrier instead recalculated the planet’s tables to define those anomalies as precisely as possible. With the intellectual ground thus cleared, he turned into a detective, seeking the as-yet-unidentified perpetrator that could have led Uranus astray.

  As a good police procedural would have it, he soldiered on, examining—and eliminating—as many suspects as he could. Historian of astronomy Morton Grosser tallied Le Verrier’s potential culprits: perhaps there was something about the space out by Uranus, some resisting stuff (an ether) that affected its motion. Was there a giant moon orbiting Uranus, tugging it off course? Might some stray object, a comet, perhaps, have collided with Uranus, literally knocking it from its appointed round? Le Verrier even paused on the fraught possibility that Newton’s law of gravitation might need modification. Last: was there some as-yet-undiscovered object, another planet, whose gravitational influence could account for the discrepancies between Uranus’s theoretically predicted and the observed track?

  Le Verrier quickly rejected the first three potential candidates. He agreed with virtually every professional astronomer in thinking that modifying or rejecting Newtonian gravitation would be a final, desperate resort. Which meant that after several months of thinking about the problem, he was back to his prime suspect: an as-yet-undiscovered trans-Uranian planet.

  With that, his task was sharply defined: once all the known sources of gravitational influence were accounted for, what were the properties—mass, distance, finer details of its orbit—of the object that could account for the remaining anomalies in the motion of Uranus? In that form, the problem resolved down to a conventional problem in celestial mechanics, establishing and then solving a system of equations that described each of the components of the hypothetical planet’s motion. Even so, given how little could be asserted with any confidence about the still hypothetical planet, then familiar or not, the task was deeply fraught.

  Le Verrier first set up his calculation with thirteen unknowns—too many for someone with even his gifts to solve in any timely manner. So he simplified his assumptions. He argued that there had to be a sweet spot for at least some of the orbital parameters of the missing planet. As he would later write, it couldn’t be too close to Uranus, for then its effects would have been too obvious. It couldn’t be terribly far away, as that would imply a large enough mass to affect Saturn as well, and no such influence had been detected. He simply guessed that its orbit wouldn’t be too sharply angled to the plane of the rest of the planets. He constructed a few more such arguments to fill in some of the gaps in the observational data from Uranus, which left him with a system of equations with just nine unknowns—which is to say, merely a hugely difficult operation, instead of an impossible one.

  Calculating a unique solution within that model—one that would give him a prediction of the mass and position for the planet—proved almost ludicrously laborious. Being clever helped, as when he came up with a way to transform some of the essentially intractable nonlinear equations in the model into a larger set of linear expressions.*1 That made the calculation easier—possible, really—but at the cost of a horrific amount of grunt work to crank through the much greater number of steps the new approach required.

  Even so, by the end of May 1846, Le Verrier had advanced to the point where he could report to the Académie that Uranus’s orbit could be exactly described assuming “the action of a new planet”—and that it would be possible to show that “the problem is susceptible to only one solution…there are not two regions in the sky in which one can choose to place the planet in a given epoch”—which was his rather grandiose way of saying he was nearing his answer. Near, but not yet all the way there: in this communiqué, he could do no better than suggest that the hypothesized trans-Uranian planet should lie in a region measuring about ten degrees across the sky.

  Even that rather loose guidance was subject to a fair amount of uncertainty, too much to help anyone interested take a look. So Le Verrier returned to the ma
thematical grind, reworked his calculation, and on August 31, 1846, delivered an update: if anyone happened to have time to spare on a good telescope, they should find a planet beyond the orbit of Uranus at a distance of about 36 astronomical units,*2 visible about five degrees east of ∂ Capricorn—a fairly bright star within the Capricorn constellation. Its mass, Le Verrier declared, would be about thirty-six times that of Earth, and to the telescope-aided eye, it would reveal itself not as a point (like a star), but as a clearly discernible disk, 3.3 arcseconds in diameter.

  And then, given that the cream of French astronomy had been told there was a new planet waiting to be discovered, what happened next?

  Nothing.

  The pursuit of Uranus’s invisible companion is littered with in-hindsight incomprehensibly missed opportunities, but this one seems particularly hard to explain. Le Verrier had attacked Uranus at the direct request (almost an order) of the director of the Paris Observatory, at a time of nationalist competition on just about every axis imaginable, from the pursuit of empire to the pursuit of knowledge. He was acknowledged by his peers as the best analyst of celestial mechanics in France, offering up what would be (on the precedent of Herschel’s fame after his accidental find) the discovery of a lifetime. And yet, none of his French colleagues could be bothered to point a telescope at the patch of night where, he had just told them, a career-making triumph could be theirs. It’s true that the main telescope at the Paris Observatory was a mediocre instrument, and, as important, the astronomers there lacked the latest sky charts needed to check if anything that appeared in an eyepiece was already a known and distant star. Still, it remains odd that none of the astronomers who had first crack at Le Verrier’s conclusions thought to try. All they risked was a night or two under the observatory dome, against a potential gain of a whole new world. But none did.

  Finally, on September 18, Le Verrier lost patience with his compatriots. He wrote to a young German astronomer named Johann Gottfried Galle. Galle had tried and failed to catch the more senior man’s attention the year before, but now Le Verrier needed him. Some belated praise for Galle’s research sweetened his plea: “Right now I would like to find a persistent observer who would be willing to devote some time to an examination of a part of the sky in which there may be a planet to discover.” Galle received the letter five days later. Swallowing any lingering resentment for earlier neglect, he set to work that evening.

  —

  September 23, 1846, Berlin.

  The night is quiet, very dark. Gaslights had come to Prussia’s capital back in 1825, but there still weren’t that many of them, and most were doused by midnight. After that Berlin belonged to those who cherished the night sky—among them, the watchers at the Royal Observatory, near the Halle Gate.

  Credit 3.1

  The “new” Royal Observatory in Berlin, depicted sometime after 1835.

  This Saturday, Galle and a volunteer assistant, Heinrich Ludwig d’Arrest, command the main telescope. Galle stands at the eyepiece and guides the instrument, pointing toward Capricorn. As each star comes into view, he calls out its brightness and position. D’Arrest pores over a sky map, ticking off each candidate as it reveals itself as a familiar object. So it goes until, sometime between midnight and 1 A.M., Galle reels out the numbers for one more mote of light invisible to the naked eye: right ascension 21 h, 53 min, 25.84 seconds.

  D’Arrest glances down at the chart, then yelps: “that star is not on the map!”

  The younger man runs to fetch the observatory’s director, who earlier that day had only reluctantly given his permission to attempt what he seems to have thought a fool’s errand. Together, the trio continue to watch the new object until it sets at around 2:30 in the morning. True stars remain mere points in even the most powerful telescopes. This does not, showing instead an unmistakable disk, a full 3.2 arcseconds across—just as Le Verrier had told them to expect. That visible circle can mean just one thing: Galle has just become the first man to see what he knows to be a previously undiscovered planet, one that would come to be called Neptune, just about exactly where Urbain-Jean-Joseph Le Verrier told him to look.

  —

  Galle’s sighting was the climax of what was almost immediately understood to be the popular triumph of Newtonian science. It’s unsurprising, given the stakes, that the discovery of Neptune produced its share of controversy. The English astronomer John Couch Adams had followed the same reasoning as Le Verrier, performed commensurate feats of calculation, and had come to a very similar prediction at almost the same moment. However, he failed to persuade any of the astronomers at either Cambridge or the Royal Observatory at Greenwich to pursue a rigorous search. Still, a nationalistic priority battle followed, with British scientists pressing the case for Adams to receive co-discoverer credit with Le Verrier. That view held sway for more than a century, at least in the English-speaking world, though current historical analysis reserves pride of place for the Frenchman. A claim of discovery requires both the prediction and the actual measurement made on the basis of that prediction—and by that yardstick Le Verrier got there first.

  Still, the fact that the priority battle was so important to the British astronomical establishment tells its own tale. The discovery of Neptune—driven by the mathematical interpretation of fundamental laws, so exactly as to reveal itself within hours of the start of the search—was recognized at once as both a stunning display of individual genius and a triumph for a whole way of knowing the world. In point of fact, Le Verrier (and Adams) had made several arbitrary choices to simplify parts of the problem, most notably guessing how far away the perturbing planet had to be. Those estimates were off by a lot, which would seem to undercut any claim of prescience for their theoretical calculations. And yet even such a miscue actually conveys something of the power of Le Verrier’s reasoning, as he also figured out a way to frame the question to reduce the importance of distance for determining Neptune’s position.*3 It wasn’t luck (or not much) that delivered the new planet; it was the skill with which a very gifted Newtonian scientist had set up a calculation to tolerate a fair amount of wrongness in his assumptions. And in any event, for both the public and the world of professional astronomers, such slips simply disappeared in the glow of the bright, beautiful truth that Le Verrier had said go and look—there!—and you will see…and someone searched…and everyone saw.

  That sequence transformed the discovery of Neptune from being merely spectacular (like Herschel’s stumbling upon Uranus) into something more, a celebration of science as a whole. Le Verrier had confronted an uncomfortable fact, and then subjected it to theory, the theory, Newton’s system of the world, to risk a prediction that then proved true. If ever there was a demonstration of how science is supposed to advance, here it was.

  For Le Verrier himself Neptune was the golden ticket, his ride to the top of his corner of the world. Almost instantaneously it made him the most famous physical scientist in the world, and it pushed him up Paris’s professional ladder at truly impressive speed. The romance of his victory, though, offered something more: validation for his faith, the belief that he (and humanity) could by pure force of intellect impose order on the natural world.

  * * *

  *1 A linear equation is one in which change in one variable produces a directly proportionate change in the result—producing a straight line when its results are graphed. In a nonlinear expression, a graph of the output produces a curve; systems of nonlinear equations are more difficult to solve than linear ones—often enormously so.

  *2 The astronomical unit is roughly (and historically) the mean distance between the earth and the sun. (In modern astronomical units of measure, it is strictly defined as 149,597,870,700 meters, or about 93 million miles.)

  *3 Le Verrier was able to take advantage of the fact that Uranus’s track suggested that it and its unseen companion were in reasonably close conjunction in 1846, which meant a mistake in his estimate distance would affect the apparent position of Neptune much
less than if the two planets were more widely separated.

  Interlude

  “SO VERY OCCULT”

  With Neptune in hand, one matter was settled. No working astronomer, no physicist, had any residual doubt about gravity. As Newton had described it, so it was: a universal force, at play throughout the cosmos, depending only on the masses contained within a system and on the inverse of the square of the distance between any two objects (in the simplest case). A century and a half of applying that law to ever more complicated arrangements had encountered no exceptions. Quite the reverse: with Neptune came the prospect of yet more to be discovered, as observers and the theoreticians honed their instruments and ideas.

  Credit col1.1

  This nineteenth-century map of the solar system emphasizes the rigor with which Newton and his heirs ordered the cosmos.

  Such unbroken success vindicated Newton on another matter as well. He never publicly said he knew what gravity was. He refused to propose any specific notion to explain why one hunk of matter pulls on another. Such an account was, to him, unnecessary. He said so in one of his most famous one-liners, added in response to critics to the third edition of Principia: “I do not feign hypotheses”—or, in full, “I have not as yet been able to deduce from phenomena the reason for these properties of gravity and I do not feign hypotheses.”