At the same time, there’s a common trick nature plays on its would-be investigators: resemblance, the human urge to map the unknown onto the already known, can be a snare. Just because something looks like something else doesn’t mean that the backstory for both must be the same. Rocks scattered across the sky may appear to be a rubble field left behind by an explosion…but unless you stop to think how else you might get there, you rely on assumptions not in evidence. Olbers couldn’t escape his sense of the familiar. Le Verrier would.
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Le Verrier’s first brush with the asteroids had come a decade earlier, when he determined that Jupiter and Olbers’s own Pallas had orbital periods locked in an 18/7 ratio—a gravitational resonance analogous to the one Laplace had earlier found linking Jupiter and Saturn. Now, returning to the minor planets, he rejected Olbers’s hypothesis. There was no need, he argued, to invoke a catastrophe. Instead, taking the formation of the asteroids as merely another example of the process that gave birth to the rest of the planets, he made two predictions: first, even though the catalogue of “petites planètes” listed just twenty-six asteroids with known orbits, his view coincided with Olbers: there should be a “prodigious number” more, begging to be discovered as soon as observers got their hands on better instruments. As those new bodies swam into view, he reasoned, it would become possible to determine their true distribution across the night sky. In doing so, he argued, observers would find evidence for his claim that “the same cause that united the material in each of the principal planets had also arranged [distribué] the smaller bodies into distinct groups.”
Le Verrier was right. The distribution of asteroids found since he proposed his idea reflects the primordial process of planet formation—the accumulation of particles of material into first smaller objects, then rocks, then “planetismals.” Out to the orbit of Mars, the sequence continued up to the accumulation of the major rocky planets. In the asteroid belt, though, Jupiter’s gravitation whipped the accreting objects up with enough violence to prevent any single large object from forming. Instead, as Le Verrier predicted, the asteroids do form into groups and families that are connected by common orbital dynamics—a clumping driven by Jupiter’s gravitational influence—though Le Verrier himself did not correctly identify Jupiter’s role in that result. But for any later correction, Le Verrier here displayed the key capacity for scientific advance: he saw past the easy similitude—who doesn’t love a wreck!—and chose not to reason backward from appearances.
Instead, he made the critical assumption: a new phenomenon does not necessarily demand its own new cause to account for its sudden appearance. Observations are essential; but, as Le Verrier argued through his analysis of the minor planets, they are not in themselves sufficient. The scientist’s duty confronting some new circumstance is to find the meaning within the flood of new data. Half a century later, his compatriot the great mathematician Henri Poincaré would put it like this: “We can not know all facts and it is necessary to choose those which are worthy of being known.”
That sounds reckless, arrogant—who are you or I to conclude some detail is “worthy”? But no, says Poincaré. There is an internal logic, a way of framing the beauty in nature that removes the scientist’s particular caprice from the process. The trick was to lay claim only to those facts that could “complete an unfinished harmony, or…make one foresee a great number of other facts.” Le Verrier confronting the asteroids found in the facts already established—twenty-six well-mapped orbits—a path to such elegant efficiency. Look for more asteroids, he said. Place them within the deeply established apparatus of Newtonian gravitation, and use that analysis to enlarge the already well-ordered taxonomy of the planets. For Poincaré, scientific thinking at its best was an artist’s performance; Le Verrier, confronting the asteroids, delivered work to please the most exacting connoisseur.
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More success didn’t mellow the man. Le Verrier turned out to be a viciously effective academic politician. By the early 1850s, he laid his sights on control of the Paris Observatory, and with it control over the most significant astronomical research program in France. Against Le Verrier stood François Arago, the incumbent director and his onetime patron. The two had fallen out in the late 1840s, when Le Verrier made his first attempt to maneuver behind the scenes to gain control of at least part of the Observatory’s resources. Arago held on, but as he grew ill in 1853, he and his allies set up a committee to review possible successors. Le Verrier hadn’t wasted his time either, and had accumulated enough influence with the French government to protect himself. The Ministry of Public Instruction ordered a halt to the search process, and instead set up a review of all facets of the observatory’s operations by a commission that included Le Verrier. The committee’s final report, with Le Verrier’s hand obvious in its recommendations, described an institution fallen behind the times, burdened with obsolete equipment, poorly located, and ineffectively led. Clearly a new approach and a new man was needed—and the report proposed the creation of a permanent directorship whose authority, it was stated, “must be absolute…not to be inhibited or compromised by the intervention of a deliberative body.” The Ministry agreed, and in an order delivered ten days after receiving the committee’s work, named the obvious candidate as the new and all-powerful leader of France’s astronomical ambitions: Urbain-Jean-Joseph Le Verrier, of course.
The Paris Observatory, as a newspaper illustrator glossed it in 1862
Those who knew him best braced for trouble. Joseph Bertrand would serve for more than two decades as the permanent secretary to the Academy of Sciences. He observed Le Verrier at close range for years, and he wrote that almost as soon as Le Verrier became Neptune’s discoverer, he played poorly with others. He remembered incidents dating back to those very first years of celebrity in which, “he showed little curiosity regarding the work of anyone else; he corrected others on occasion, and highlighted their errors, never softening the harshness of his manner in such encounters….Through each dispute, the admiration he received at first did not last.”
Rising from colleague to boss didn’t improve Le Verrier’s behavior. He fired all those he felt had been too close to the last administration—so remorselessly that one biographer suggests he drove one man to suicide. He was no kinder to the subordinates he hired himself. Camille Flammarion, an assistant who joined the Observatory staff in 1858, recalled him as “haughty, disdainful, inflexible…[an] autocrat [who] considered all the employees at the Observatory as his slaves.” Charles Aimé Joseph Daverdoing, the artist who had painted his portrait in the first glorious afterglow of Neptune, knew the private Le Verrier as “a good-natured fellow, very cheerful and good company.” But he confirmed that at work, “Le Verrier was excessively demanding…[and] did not make allowance for the age or the stamina of the workers….He was never one to bite his tongue, and once or twice laid hands on someone.” This was more than mere gossip. The personnel records from his tenure as director reveal a monstrous casualty list: during Le Verrier’s first thirteen years in the job, seventeen astronomers and forty-six assistants abandoned the Observatory.
But even if Le Verrier failed the test of power, his own abilities were never in question. Once he had completed his initial coup at the Observatory, he set out to make good on his earlier promise to complete a full theory of the solar system. He still had some preliminary work to do—most significantly analyzing several thousand measurements of the sun’s (relative) motion across the sky. In 1852, when he began tackling the problem, the prevailing best estimate of the distance between the earth and the sun was 95 million miles (about 153 million kilometers). By 1858, Le Verrier was able to correct that figure by more than 2.5 percent—a huge improvement—to yield a measurement of 92.5 million miles, impressively close to the modern number of 92.995 million miles (or 149.597 million kilometers).
There’s an air of routine in such data crunching—the kind of dry record keeping needed to fix the third or fourth decim
al places of navigational tables to keep OCD ship captains happy. Certainly the luckless and overstretched assistants who performed the in-the-trenches work likely felt they were strapped to an endless assembly line, tabulating position after position, and then powering through the endless sums to yield the precision Le Verrier required. But in fact, this analysis was absolutely crucial to the larger goal of resolving all the remaining anomalies in the tables for each of the eight planets. With his much improved account of the sun, Le Verrier next sought to recast the tables for the four inner planets, to bring them to the same level of accuracy already achieved for the giant outer planets that had (among much else) yielded up Neptune in the first place. When he did so, he found that one simple change—altering upward estimates of the mass of Earth and Mars—combined with the new solar distance, allowed him to make sense of three of the four bodies to be explained. The mathematical representations of Venus, Earth, and Mars all behaved properly. The calculated version of each planet produced a chart that matched the one formed by the observational record of the three material planets making their way around the sun.
One, though, obstinately refused to conform: Mercury.
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Mercury, of course, was an old adversary. Recall that in the 1840s, it had eluded Le Verrier in his first attempt to construct a mathematical model of its behavior. His had been the most accurate to date, but he understood the implications of its near miss on the timing of Mercury’s 1845 solar transit. Better-than was not good enough; it still wasn’t right.
Back then, Le Verrier acknowledged that there was no obvious solution to the problem. He wrote, “If the tables do not strictly agree with the group of observations, we will certainly not be tempted into charging the law of universal gravitation with inadequacy.” Why not? Neptune, of course, with its once-and-for-all demonstration of the power of Newton’s theory, or, as he put it, “these days, this principle has acquired such a degree of certainty that we would not allow it to be altered.”
Instead, Le Verrier argued, such an error must be due either to “some inaccuracy in the working [calculation] or some material cause whose existence has escaped us.” At the time he wasn’t sure where the fault lay. Given the complexity of analysis and the relative poverty of data on Mercury, “we will not be able to decide,” he wrote, whether to blame “analytical errors or…the imperfection of our knowledge of celestial physics.”
There the matter rested. It wasn’t until 1859, sixteen years after his first attempt, that he found himself free to return to the problem. He was forty-eight years old, at the height of both his fame and, by all witness testimony, his mathematical powers. He had the resources of the Paris Observatory at his disposal. Mercury’s theory should have been a straightforward task.
It was…and it wasn’t. The older Le Verrier had one absolute advantage over his younger self: better data. He reexamined the information he had used in 1843—measurements of Mercury’s motion made at the Observatory itself. To that he added the best observations it was possible to make at the current state of astronomical technology: transits, with high-quality records for Mercury extending back to 1697. With a good clock and an accurate fix on where on earth the event was being viewed, timing a planet’s entry or exit from a transit ranked among the most precise measurements available to astronomers.
Le Verrier launched his assault following his usual plan. First he mapped out Mercury’s actual orbit with all of its components of motion as described by the empirical data: direct measurements of Mercury’s behavior. Next came calculation: what do Newton’s laws predict for Mercury, given all the known gravitational contributions of the planets as well as the sun? Any discrepancies—astronomers call them “residuals”—between the empirical picture and the theoretical one must then be explained. If there were none, then the theory of the planet was complete, and the model of the solar system would be one step closer to being done.
But there was a leftover result. It was a small number—tiny, really—but the gap between theory and the data was greater than estimates of observational errors could explain, which meant the problem was real. That settled one matter: it strongly suggested that Mercury’s difficulties almost certainly lay not with flaws in Le Verrier’s analysis, but rather in something unknown out there in space.
The particular anomaly he found is called the precession of the perihelion of Mercury’s orbit. In the squashed circle of an elliptical orbit, the point at which a planet comes closest to its star is called its perihelion. In an idealized two-body system, that orbit is stable and the perihelion remains fixed, always coming at the same point in the annual cycle. Once you add more planets, though, that constancy evaporates. In such a system, if you were to map each year’s track onto a single sheet of paper, you would over time draw a kind of flower petal, with each oval just slightly shifted. The perihelion (and its opposite number, the aphelion, or most distant point in the orbit) would move around the sun. When that shift comes in the direction that the planet moves in its annual journey, the perihelion is said to advance. As every schoolchild confronting geometry knows, a circular (or elliptical) orbit covers 360 degrees. Each degree can be divided up into sixty minutes of arc; each minute into sixty arcseconds. Le Verrier’s analysis told him that this was happening to Mercury: its perihelion advances at a rate of 565 arcseconds every hundred years.
Next came a round of celestial bookkeeping: how much of that total could be explained by the influence of the other planets on Mercury. Venus, as Mercury’s neighbor, proved to be doing most of the work. Le Verrier’s sums revealed that it accounted for almost exactly half of the precession, 280.6 seconds of arc per century. Jupiter provided another 152.6 to the total, Earth 83.6, with the rest causing scraps of motion. The total: 526.7 arcseconds per century.
This is an exaggerated view of Mercury’s orbit. The perihelion shift, repeated over decades, produces a flower petal design around the sun.
A century and a half later, the one irreducibly extraordinary fact of this work remains how incredibly small an “error” Le Verrier uncovered. The unexplained residue of Mercury’s orbital dance came down to a perihelion that landed just .38 seconds of arc ahead of where it should every year. To put it into the form in which Le Verrier’s number became famous: every hundred years, during which Mercury travels a radial journey of 36,000 degrees, the perihelion of its orbit shifts about 1/10,000th beyond its appointed destination, an error of just 38 arcseconds per century.
Tiny, yes. But the excess perihelion advance of Mercury retained one crucial property: it wasn’t zero. Le Verrier knew what such unreconciled motion must mean. If Mercury moved where no known mass existed to push it, then there was some “imperfection of our knowledge” waiting to be repaired.
* * *
* There are a number of variations on the currently most widely accepted idea of the collision hypothesis for the formation of the moon, and there is at least one proposal that suggests no collision took place at all. But the core idea explains key issues raised by the discovery of similarities between the composition of the earth and of the Apollo moon rocks and by the dynamics of the earth-moon system. So current betting is weighted toward some version of a cosmic wreck between the early Earth and some other large body.
A DISTURBING MASS
Le Verrier was hardly infallible, to be sure, but there were some errors he simply did not commit. Mercury’s orbit does precess around the sun. It does so at a rate that cannot be fully accounted for by any combination of gravitational influences within the solar system. Le Verrier’s number for the residual motion of Mercury—38 arcseconds per century—is a little off the modern value of 43 arcseconds, but he got it as nearly right as anyone could in 1859, given the limitations of the data at his disposal. Le Verrier never doubted the work. Nor did his fellow astronomers. For them, it was in fact fantastic news: the unexplained invites discoveries.
Of all men, Le Verrier knew what came next: in his book-length report on Mercury, he said as much:
“a planet, or if one prefers a group of smaller planets circling in the vicinity of Mercury’s orbit, would be capable of producing the anomalous perturbation felt by the latter planet….According to this hypothesis, the mass sought should exist inside the orbit of Mercury.’ ”
Le Verrier then took the next step, figuring out how big an intra-Mercurian planet would have to be to drive the perihelion advance. Assuming it lay roughly halfway between Mercury and the sun, he wrote, its mass would have to be about the same as its neighbor. That posed a problem, as he well knew. If it were that big, why hadn’t anyone seen it yet? Even if a Mercury-sized planet in the predicted orbit would usually be hidden within the glare of the sun, “It must be unlikely,” he wrote, that it could avoid detection “during a total eclipse of the sun.” Thus, Le Verrier proposed an alternative: “a group of asteroids [corpuscles] orbiting between the sun and Mercury.”
That conclusion must have seemed a bit deflating to Le Verrier’s readers. Adding to the lengthening list of minor planets, even in such an exotic location, hardly stacked up to finding Neptune. But the stakes of the search were just as high in both cases. Until Mercury’s precession could be accounted for, the anomaly represented a violation of the cosmic order, unthinkable (of course) to all of Newton’s heirs. Hence Le Verrier’s urgency: “It’s likely that some of these [asteroids] will be sufficiently large to be seen on their transits across the disk of the sun. Astronomers, already engaged with all the phenomena that appear on the surface of that star will without doubt find here another reason to track any spot they may see, no matter how small.” In other words: all those sunspots you folks have been tracking? Some of them might be little planets. Go get ’em!
The Hunt for Vulcan Page 6
