Astronomical Games: May 2014

Seek and Ye Shall Find!

Skill and luck combined to find the last known gas giant

To be taken into account were some years of schooling, where I studied with diligence Neptune's laws, and these laws I tried to obey when I sailed overseas; it was worth the while.

—Joshua Slocum, Canadian explorer (1844–1909), first person to sail solo around the world

SOME TIME ago, I found myself in need of a technical paper in my office. Now my office, you should know, is best characterized as being continually in a state of well-constrained chaos. Which is to say that most objects in my office have a logical and stable place, but a small fraction exist in a kind of quantum haze in which their exact location cannot be identified (or, I suspect, even defined) until I have actually laid eyes on them.

This system works well for me because the fraction really is small and I am pretty good at recognizing the papers I'm looking for. In this particular instance, I was even more fortunate, because I have a special stack, a reasonably small one, consisting solely of papers on probability and statistics. I went through the stack and in less than a minute had found exactly the paper I was looking for and I triumphantly returned to my desk to focus on the work at hand.

I had only gotten a little ways back into my technical work when I was suddenly seized by misgiving: My subconscious had succeeded in calling my attention to the fact that the paper I was holding in my hand had not in fact been surrounded by its like, but rather by various and sundry personal documents (billing statements to file, and so forth). After a few seconds of pondering, I realized that what had happened was that I had taken a pile of my probability papers home to read. There, they'd been covered up again with my personal documents. The next day, I had, in a hurry, noticed that I had to submit some of those documents at the office for reimbursement, so I picked up the whole stack. Finally, in a burst of procrastination, I had set them down in a convenient pile so that I could return to them at a more convenient time. (I hope that explains the quantum haze.) To put it in a nub, the speed with which I had found the paper had little to do with my system of organization—such as it is—and much more to do with pure happenstance.

I sat there a few seconds more in some disappointment, but I resolved not to get too upset about it (and I did eventually take care of the offending documents). After all, far more important objects have been found through such a mixture of preparation and serendipity.

Like a planet, for instance.

The ancients (since I am forever beginning with the ancients) were familiar with six of what we consider planets today: Mercury, Venus, the Earth, Mars, Jupiter, and Saturn.

To be sure, those ancients did not consider the Earth to be a planet, since it was clearly distinct from those lights that moved amongst the constant stars. They also considered the Moon and the Sun to be planets, since they did wander amongst the stars, although it must have taken some time to realize the Sun did so, on account of its glare.

Setting aside the Moon and Sun, Venus is the brightest of the "genuine" planets, at about magnitude –4. (In the stellar magnitude system, brighter objects have lower magnitudes, and dimmer objects higher ones. The dimmest objects visible to the unaided eye have magnitude 6 or 7, depending on that eye's sensitivity and acuity.) But all of the classical planets known in antiquity are easily visible, at magnitude 0 or lower.

In addition to these six, there was one further planet that the ancients could have discovered, if they had only known where to look, and that was Uranus. Uranus has the misfortune, however, of being both relatively dim—at magnitude 5.7, it is a percent or so as bright as Saturn and therefore barely visible, even in a dark sky—and slow-moving, so that its motion against the stellar background is easy to miss. I'm sure that Uranus was seen from time to time before the invention of the telescope, but it was, as far as we know, never recognized for what it was.

Even after the invention of the telescope, further planets did not pop out of the celestial woodwork. In retrospect, this may seem surprising, but it is not so difficult to explain. In the first place, astronomers weren't expecting any further planets. There had been six planets for as long as anyone could remember. If there were any more to be found, surely they would have been bright enough to see with reasonable ease. Jupiter, at magnitude –2 or so, was brighter than any of the nighttime stars, and Saturn, the next and last of the planets, was still brighter than the vast majority of stars, at magnitude 0. It was expected that had any further planets existed, they would have shone at magnitude 2 or 3 at worst, and been easy to detect.

Secondly, although the telescope made it possible to see dimmer objects—even Galileo's crude first astronomical telescope enabled him to see stars of magnitude 8—the trade-off was a correspondingly small field of view, like looking through a long soda straw. Identifying which anonymous point of light had shifted ever so slightly (Uranus moves perhaps a third of a degree—less than the width of the Full Moon—in a single month) would have been a significant challenge, even if one was looking.

In point of fact, Uranus was found, and even named, by the first British Astronomer Royal, John Flamsteed (1646–1719). The only problem was that he was focused on compiling a comprehensive star atlas and catalogue, and was not particularly checking to see if any of the stars he ticked off were moving anomalously. Accordingly, in 1690, he recorded Uranus as 34 Tauri—that is, the 34th star, counting west to east, in the constellation of Taurus the Bull—no fewer than six times. And consequently moved on, none the wiser.

Half a century later, the French astronomer Pierre LeMonnier (1715–1799) observed Uranus a dozen or so times over a period of almost two decades, from 1750 to 1767. In spite of the on-again, off-again strife between the countries on opposite sides of the English Channel, LeMonnier was a champion of British astronomical methods, and worked extensively, importing them in an effort to improve French astronomy. He was even, at the tender age of 23, admitted into the Royal Society, which had recently seen such a luminary as Isaac Newton. But he too failed to recognize Uranus as a planet.

It wasn't until the arrival of the German-born, English musician/astronomer William Herschel (1738–1822) that Uranus was finally recorded as a planet, in 1781. Even then, Herschel was not at first sure what he had found. He had been looking for comets—like most other astronomers, he discounted the possibility of finding planets—but in his telescope, straining at the magnification limits imposed by the unsteady atmosphere, Uranus seemed round and unfuzzy, utterly unlike any other comet he had seen. It also moved slowly and steadily against the background stars, unlike other comets. Eventually, it was decided that Herschel had in fact discovered a planet, the first since ancient times, almost one and three-quarters centuries after the invention of the telescope.

But perhaps even more astonishing than this series of pre-discovery sightings of Uranus was an observation of Neptune, made by none other than Galileo himself. This observation was a stroke of luck, for Galileo in the winter of 1612–13 was intent on observing the satellites of Jupiter, and anything else was just a reference point. It so happened that Jupiter and its satellite had wandered near Neptune in the night sky, and Neptune, at magnitude 8 or so, was just within the capabilities of Galileo's telescope.

If luck had worked to put Neptune in Galileo's sights, however, it now conspired to rob him of its discovery, for Neptune was just then rounding into retrograde. At that point, both the Earth and Neptune were moving in more or less the same direction, and as a result, Neptune appeared to stand still for a period of weeks (and then even to move backward for a few months), and Galileo missed out on an even more amazing discovery than would await Herschel 170 years later.

Uranus was a glory for British astronomy. No other modern country could lay claim to an entirely new planet, and Herschel was feted and supported beyond his imaginings. Some even insisted that the new planet should be named Herschel. Herschel, for his own part, proposed that it should be called Georgium Sidus (Latin for "George's Star") in honor of his patron, King George III (the one who had lately lost hold of the American colonies). Fortunately for posterity, more sedate heads prevailed and the planet was named Uranus, after the Roman god of the heavens. (Johann Bayer, in 1603, had called his star map the Uranometria.)

It had eluded identification as a planet in part because it moved so slowly (the word "planet" comes from Greek planetes, meaning "wanderers"), and partly because it was dim. It was dim, in turn, in part because it was far away, but also because it was significantly smaller than both Jupiter and Saturn, the most distant of the planets of antiquity. Uranus orbits the Sun at about twice the distance of Saturn, so if Uranus had been the same size as Saturn, it would have appeared to Herschel and his contemporaries as about half the width of Saturn in the telescope.

But in actuality, Uranus never appears more than about a fifth of the width of Saturn. Even accounting for its greater distance, this meant that Uranus's diameter was no more than about two-fifths that of Saturn. Even at the 300x magnification a steady atmosphere will usually permit, Uranus looks no larger through a telescope than a pea held up at arm's length.

Not that there was much to look at in the case of Uranus. Jupiter has its colorful belts and the Great Red Spot. The surface of Saturn is blander than that of Jupiter, but it has, in compensation, its brilliant set of rings. Uranus, further from the Sun and generating less internal heat than either of them, exhibits essentially no turbulence in its atmosphere, and so its surface is remarkably plain. And it has no rings that could be seen with any telescopes of the 18th century.

But it does have that name, which has given no shortage of pleasure to twelve-year-old children around the English-speaking world. So there's that.

One of the first things that astronomers did when Uranus was discovered was to plot its orbit. Uranus is far too distant for astronomers to make a direct measurement of its distance, but by this time, Newton's law of universal gravitation had become well established, and Uranus's slow sojourn amongst the distant stars, in conjunction with constraints on its motion imposed by Newton, permitted astronomers to determine Uranus's location in the three dimensions of space. In relatively quick order, for instance, they were able to determine that Uranus takes 84 Earth years to orbit the Sun, that its orbit was very nearly in the same plane as the Earth's orbit, and so forth. Very neatly done!

Before too long, however, cracks began to appear in the foundation. If Uranus were alone in the solar system, it would move at a steady pace in accordance with Kepler's and Newton's laws. It was, to be sure, subject to the gravitational pulls of massive Jupiter and Saturn, so there were occasional irregularities in its motion to be expected, but these could be accounted for. (The pulls of the Earth and the smaller planets and asteroids were thought too small to have any measurable impact.) For instance, in 1821, the French astronomer Alexis Bouvard (1767–1843) published a set of positions for Uranus that incorporated the then known gravitational perturbations.

Bouvard was a careful observer and mathematician. He had published similar sets of positions for Jupiter and Saturn, and these had been highly successful. But his positions for Uranus failed to match their accuracy. At first, this could have been attributed to observational error, but as the years passed and the discrepancies began to accumulate, it became clear that something else was responsible. That could have been a new wrinkle in Newton's law of gravitation, but astronomers were not especially eager to find fault with a formula so elegant and so generally accurate. So Bouvard suggested that another planet, an eighth planet still further out and as yet unseen, was responsible for the variations in the motion of Uranus.

Bouvard died in 1843 before he was able to make anything substantial of his hypothesis, but shortly before then, the British astronomer John Couch Adams (1819–1892) took up the task. Adams had been named after his mother's uncle, John Couch, who was born in Cornwall where his name was pronounced "Cooch." She had inherited a small library of books from him, and these books the young Adams consulted avidly. He found the astronomy books particularly engaging.

The Adams family was fairly poor, and Adams himself received a somewhat spotty education. (In those days, to be sure, a spotty education still included algebra and ancient Greek.) He ended up teaching himself higher mathematics, reading from the local university library books on general science and calculus.

When he was about 17, his mother secured a small inheritance that made the family a bit more comfortable and which also made it possible, a few years later, to send Adams to Cambridge to study mathematics. He entered as a sizar, as Newton had done almost two centuries ago, which meant that his education, room, and board were partially subsidized in exchange for various tasks, such as tutoring or manual labor.

It was while he was at Cambridge that Adams first learned of the irregularities in Uranus's motion. Adams was galvanized into action; on July 3, 1841, in fact, he specifically made mention of his intention to decipher the discrepancies. What Adams had in mind was not trivial. It was tedious, but rather straightforward, to work from known positions of known objects, and numerically compute what should happen to their motions. What Adams proposed to do was the reverse problem: to take the motions of a set of objects, and determine from them the position, mass, and velocity of an entirely unseen interloper.

By the time Adams finally completed his coursework and began working on the problem in 1843, astronomers had accumulated about sixty years' worth of solid observations of Uranus (plus a handful of less solid pre-discovery observations), but Adams's task was still imposing. If the interloper were the size of Uranus, but (let's say) twice as far away, it would appear only half as wide and cover only a quarter the area in the telescope's field of view as Uranus does. What's more, this more distant planet would receive only a quarter as much light as Uranus. It would be around magnitude 8 at its brightest, and there would be little besides its very slow motion (which would appear only a half to a third as fast as Uranus's already slow crawl) to distinguish it from all of the tens of thousands of other stars of similar brightness.

Adams's task was akin to determining the location of a magnet, pulling at a BB at a distance of several yards while moving almost imperceptibly through a field of 30,000 counterfeit magnets. All this while observing the BB from the moving platform of the Earth! It seemed too difficult to approach.

In fact, it was too difficult to approach with the technology of the day. With today's computers, it is a routine task, but the uncertainty in the observations, although they were small enough to permit Uranus's deviations to be detected, were still large enough to allow for multiple possible orbits. Some way of narrowing the field was needed.

Adams found it in a statistical oddity called Bode's Law, named after the German astronomer Johann Elert Bode (1747–1826), but was originally proposed by Johann Daniel Titius (1729–1796) in 1766. Titius had observed that a simple mathematical rule appeared to govern the distances of the various planets from the Sun. If you take the sequence 0, 3, 6, 12, 24, 48, 96, in which all of the numbers (except the second) is twice the preceding number, add 4 to each one, and divide by 10, you end up with

0.4, 0.7, 1.0, 1.6, 2.8, 5.6, 10.0

Titius noticed that except for 2.8, the remaining numbers matched up well: Mercury is 0.4 astronomical units (1 AU = 150 million km, the mean distance between the Sun and Earth), Venus is 0.7 AU, Earth of course is 1 AU, Mars is 1.5 AU, Jupiter is 5.2 AU, and Saturn is 9.5 AU. Titius published his observation in 1766, before Uranus was discovered, but only in a translation of someone else's scientific work, and it passed almost unnoticed.

Bode, however, did notice it. He then incorporated the rule, in 1772, into an astronomical text he was writing, where it gained additional notice (Bode was a rising star in German astronomy, whereas Titius was a university professor of relatively little moment). For the next decade or so, however, it remained mostly a curiosity.

And then Uranus was discovered to be orbiting the Sun in a nearly circular orbit at a distance of 19.2 AU. Extend the Titius-Bode Law, and you find that it predicts a distance of 19.6 AU for the next planet after Saturn. Almost overnight, the law gained substantial credence. Bode naturally urged astronomers to look for a heretofore unknown planet in the fifth slot, at an approximate distance of 2.8 AU. Such a planet was found in 1801 by the Italian astronomer Giuseppe Piazzi (1746–1826), and named Ceres, after the Roman goddess of agriculture. Ceres is much smaller than any of the other planets, and it was eventually found to be only the largest of a class of small bodies, mostly scattered between Mars and Jupiter, which Herschel proposed to call asteroids, after a Greek word for "starlike."

None of this dimmed the enthusiasm for the Titius-Bode Law, though, and Adams chose to use it as his initial sieve. The law predicted an eighth planet (not counting the asteroidal rubble), at a distance of 38.8 AU. He also noticed that Uranus appeared to be speeding up in its orbit prior to about 1820 (as though something were pulling forward on it), and afterward appeared to be slowing down (as though something were pulling back on it). He decided, as a first guess, to assume that the unseen planet (which we might call Planet X) was more or less directly behind Uranus in 1820, at a distance of 38.8 AU (give or take a few AU).

Adams was not so confident in the law as to let that first guess hold sway, however. He decided upon a program of successive refinement: He would first calculate how Planet X would influence Uranus, given his initial guess. This predicted influence would, he presumed, differ from the actual motion of Uranus. Based on these difference, he would make a second and hopefully improved guess of Planet X's orbit, and calculate again. Over time, this iterative process ought to yield a reasonably accurate orbit for Planet X.

It was hard work. Adams spent much of 1843 calculating just the first iteration of Planet X's gravitational perturbation of Uranus. Early in 1844, he sent word to James Challis (1803–1882), director of the Cambridge Observatory, asking for the latest observations of Uranus. Challis, in turn, relayed the request to George Biddell Airy (1801–1892), Britain's Astronomer Royal at Greenwich Observatory.

By September 1845, Adams felt reasonably confident in his calculations and apparently relayed them to Challis. How he did so, exactly, is unclear, for scant documentation remains of their exchange. He appears to have wanted to be respectfully diffident, however, and offered no detailed calculations to back up his prediction. Challis, perhaps understandably, was reluctant to devote substantial resources to a search that he expected to be fruitless (Adams was still relatively unknown), and thus matters sat for the time being.

Meanwhile, a couple of months later, on the opposite side of the Channel, the French astronomer Urbain Le Verrier (1811–1877), presented a report on Uranus to the French Academy of Sciences, in which he also reported on the discrepancies in Uranus's motion. Unaware of Adams's efforts, he embarked on a similar program, and the following June presented a second report in which he predicted the position of Planet X, in very nearly the same location as Adams had.

With this additional corroboration, Airy and Challis reassessed the situation and began a desperate program to locate Planet X—for they recognized that their counterparts in France would surely be embarking on a similar hunt. Their progress was hampered by the fact that Adams was continuing to calculate away and relaying supposed refinements to Challis, occasionally sending them to widely disparate parts of the sky (and far from where Neptune would eventually turn out to be). Even so, Challis's team managed to observe Planet X on August 8, and again on August 12—but because they lacked a good star map down to magnitude 8 (which Planet X was predicted to be), they did not recognize it as their quarry.

At the end of the month, Le Verrier released yet another report, this time giving his predictions on Planet X's mass and orbit. Counter to Airy and Challis's fears, Le Verrier had in fact failed to muster much enthusiasm for locating Planet X in France, so he contacted his friend, the German astronomer Johann Gottfried Galle (1812–1910), at the Berlin Observatory, to see if he would look.

Galle received Le Verrier's note on September 23, 1846. A student of his suggested that Galle use a recent map of the area, deeper and better drawn than the map Challis used, to compare with what they observed through the telescope. They began shortly after 11:00 p.m., with Galle calling out the locations of the stars he observed, and his assistant checking them off on the map. It was a laborious process that they expected could take some time.

In reality, it was less than an hour. Just after midnight, on September 24, Galle called out a star location that was not on the map. The astronomers checked their results in an agitation of excitement, and confirmed the find: Planet X had been discovered, and less than a degree from Le Verrier's predicted location. As in 1781, with the discovery of Uranus, there were not wanting those who wished to name the planet after Le Verrier or Galle, but again, cooler heads prevailed and the planet was named Neptune, after the Roman god of the sea.

The scientific world was abuzz at this second great discovery in an ordinary lifetime, and at the resounding victory for Newton's law of universal gravitation. There was also the question of priority. Almost before the ink on Galle's announcement was dry, British astronomical luminaries, headed by Herschel and Challis, insisted that Adams had already calculated Planet X's orbital parameters. This did little to convince the French, who stood firmly behind Le Verrier. Rather to the detriment of Adams's case was that his initial prediction of September 1845 had in fact been quite close already to the location of the eventual find—not as close as Le Verrier was, but close—but his subsequent calculations yielded various locations spanning 35 degrees of the sky. Little wonder that Challis was not able to verify a find!

For his own part, Adams was conciliatory. For the rest of his life, he graciously yielded the credit to Le Verrier, and did not fault either Challis or Airy for their delay in looking for Planet X. By contrast, Le Verrier himself was brash and arrogant, with the ironic result that while the French took pride in Le Verrier's prediction, they could not quite take pride in Le Verrier himself, while Adams was, thirty years later, elected president of the Royal Astronomical Society. During his term, in fact, Adams presented Le Verrier with a gold medal for his labors.

After Neptune was observed for some time, and its orbit better understood, pre-discovery observations came to light. Between Galileo's early observation, and Challis's late ones, there were also observations by the French astronomer Jerome Lalande (1732–1807) in 1795, and William Herschel's son John (1792–1871) in 1830, but until Galle's find, none of them ever knew what they saw.

It also became apparent that Neptune's orbit was not at all similar to the orbit predicted by either Adams or Le Verrier. One convenient aspect of the search for Neptune was that although knowing Neptune's distance was vital to correctly assessing its gravitational impact on Uranus's orbit, it was hardly vital at all to finding Neptune itself. So long as Adams and Le Verrier gave the proper location in the sky to look for Neptune, it made little difference whether Neptune was 10 AU closer than expected, or 10 AU further, so long as it was close enough to shine by the Sun's reflected light. And in fact, although both astronomers had assumed they would find Neptune lurking at a distance of 38.8 AU from the Sun, in accordance with the Titius-Bode Law, Neptune was actually much closer, at only 30.1 AU. It was later shown that had astronomers used the orbital parameters determined by either Adams or Le Verrier to search for Neptune either decades earlier or decades later than that fateful year of 1846, they would not have found it.

Near the end of the 19th century, astronomers began to notice what appeared to be discrepancies in Neptune's orbit, and made plans to look for a ninth planet—the new Planet X. One of the leading lights in this search was the wealthy Bostonian and astronomer Percival Lowell (1855–1916), who had earlier fueled speculation about Martian canals. Pluto was actually found, in 1930, by Clyde Tombaugh (1906–1997), based on Lowell's predictions, but this turned on even more luck than had accounted for Neptune's discovery, for the discrepancies in Neptune's motion disappeared entirely with later re-analysis.

That ended the Newtonian-informed hunt for further planets—for the time being.

Copyright (c) 2014 Brian Tung