The Theory of Heliocentrism

Johannes Kepler’s new home of Prague was a place of uncanny magic and wonders. According to legend, it had been founded by a sorceress.

Long, long ago, so the stories went, Bohemia had been ruled by a queen named Libussa. One day as she stood on the edge of a cliff, looking down into the valley through which flowed the Vltava River, the spirit of prophecy came over her. “I see a great city,” she said to her followers. “With your help, its glory shall touch the stars. In the forest below you there is a clearing. There you will find a man making the best use of his teeth at midday. That is the place where the great city should be founded.”

So, some of her retinue made their way down into the valley. Right where their queen had pointed, they found the clearing in the forest, and found that a group of workmen were building a house there. Or rather, one workman was doing so: most of the party were sprawled on the grass eating their lunch, while one exceptionally diligent man alone persisted in sawing at a big block of wood. “What are you making?” the wanderers asked him.

“The threshold for the house,” he replied. In the Czech language, the word for “threshold” is prah. Thus the city that Queen Libussa’s people proceeded to build became known as Praha — or Prague, in its English incarnation.

A vapor of the ineffable still hung low over Prague at the turn of the seventeenth century. Its mazes of alleys seemed to promise devils or angels just on the other side of every devious angle. Here magic and science were of a piece. Around one corner might be a wild-eyed gypsy seer to whom birds foretold the future; around the next might be a medical man dissecting the corpse of a criminal for the edification of a crowd of onlookers. Merchants in stalls drew up horoscopes for their customers. Chimneys belched acrid fumes, the byproduct of alchemical laboratories where men of learning toiled day after day in the hope of discovering the philosopher’s stone that could turn base metals into gold. From open windows drifted the chants of mediums who claimed to be able to call the spirits of the dead up out of Heaven, Hell, or Purgatory, wherever they had landed.

Nestled deep within the warren of streets lay the Jewish Quarter, where the secrets of the Kabbalah were pondered with more dedication than in perhaps any other place in Europe. Here lived a rabbi named Judah Loew ben Bezalel, whose fame as a practitioner of the mystic arts was so enormous that he was occasionally invited by Holy Roman Emperor Rudolf to visit him in his palace, the only Jew ever to be accorded such an honor. It was said that Rabbi Loew could fashion figures out of clay or wood and bring them to life to do his bidding, just as God had once breathed life into Adam: “My substance was not hid from thee, when I was made in secret, and curiously wrought in the lowest parts of the Earth. Thine eyes did see my substance, yet being imperfect…”

Emperor Rudolf himself grew ever more reclusive and eccentric with each passing year. Within his “Cabinet of Curiosities” at the heart of his palace, he collected such treasures as a unicorn horn (probably a narwhal tusk in truth) and a jeweled chalice that he believed to be the Holy Grail which had been used to catch the blood of Jesus Christ. Only a privileged few were allowed to see him during these, his later years on his throne. Those who were so favored met a pale, pop-eyed scarecrow of a man, who mutely haunted the dim halls of his palace like one of Rabbi Loew’s golems, a Curiosity in his own right.

Amidst these scenes and tales of wonders, Johannes Kepler was about to forge a wonder of his own. After thousands upon thousands of years of trying by generations upon generations of his forefathers, he would devise the first ever factually correct model of the cosmos, where the mathematics lined up with the observed phenomena to form a consistent, logical whole. Nicolaus Copernicus and Tycho Brahe had each in his way begun to crack open the door to a new understanding of the cosmos. Now, it came down to Kepler to charge through it fearlessly. The decade he would spend in Prague after the death of Tycho would prove the most productive of his life — and one of the most productive and important in the entire history of science.

Yet he was not without distractions and tribulations as he sat himself down to tease out the reality hidden behind Tycho’s reams and reams of observational data. Although he was supposed to be the recipient of a comfortable stipend as Rudolf’s latest Imperial Mathematician, the payments came through for him even more sporadically than they had for Tycho, such that his family sometimes found themselves so in arrears on the rent that they were at risk of being tossed out of the house they had moved into.

Even when his salary did come in on time, Kepler’s marriage remained as loveless as ever. The daughter of prosperous, self-satisfied millers, Barbara Kepler just wanted her husband to be normal, to pull his nose out of his books and behave like a respectable imperial courtier. She didn’t give two hoots whether the Earth went around the Sun or the Sun went around the Earth or whether Helios dragged the yellow orb across the sky each day behind a team of horses. She refused to appreciate that it was her husband’s ideas that had brought them here to Emperor Rudolf’s doorstep in the first place.

Rudolf found his latest Imperial Mathematician almost as aggravating as the latter’s wife did. Johannes Kepler was even less equipped than Tycho Brahe had been to play the role of a fawning courtier, casting horoscope after horoscope and catering to the emperor’s every whim. His habit of telling Rudolf what he really believed rather than what the emperor wanted to hear likely contributed to his erratic salary. He was often forced to visit the imperial palace personally to beg for his wages. He found this necessity every bit as excruciating as had Tycho. He wrote in his diary of his disgust at having to “look up like a little dog to its master who used to feed it.” (Even now, when he had ostensibly become a respected man of learning, he couldn’t seem to cease writing about himself using canine metaphors.)

Kepler’s native honesty and social awkwardness — two of the least desirable traits for a courtier to possess — created an opening for Franz Tengnagel von Camp, the German nobleman who had married Tycho’s daughter. Tengnagel was never able to realize his fondest dream of displacing Kepler entirely as Imperial Mathematician, what with Kepler’s status as Tycho’s preferred successor having been stated so clearly in the deceased astronomer’s will, but he did succeed in making life in that position less congenial for Kepler in manifold ways. Tycho’s data, Tengnagel argued, rightfully belonged to the emperor, having become his by royal perquisite as soon as Tycho had agreed to become his Imperial Mathematician. Thanks to Kepler’s abject ineptness at palace intriguing, this dubious argument was allowed to carry the day almost uncontested. Tengnagel got himself appointed to the next best position to Imperial Mathematician: he was placed in charge of the publication of the data, now renamed the “Rudolphine Tables” in honor of his sovereign. Because Tengnagel knew so little about astronomy when push came to shove, and because he had every motivation to drag out his assignment as long as possible in order to stay close to the emperor, years and years went by with scant to no progress being made on the great book that Kepler had long envisioned, the ultimate fruit of Tycho’s decades of steady, methodical stargazing. This was immensely frustrating; while Kepler of course had access to all of the data himself as the current Imperial Mathematician, he was a firm believer in what we might call open-source science, who thought that a thousand minds with access to the same information was vastly preferable to just one or two. Tengnagel went so far as to demand that he be credited as co-author of any book Kepler might write that relied upon Tycho’s data, given that he, Tengnagel, was the official custodian of that data. This argument was specious on the face of it, but Rudolf’s court was not exactly bursting with voices rushing to take the introverted commoner’s side over that of Tycho’s boisterous, well-connected, blue-blooded son-in-law.

Kepler grew so frustrated that he tried to funnel his energies in other directions that wouldn’t leave him so exposed to Tengnagel’s machinations. In 1604, he published a treatise on optics that stands as his first really significant contribution to the permanent literature of science. His interest in the subject had been ignited by Tycho’s stargazing, despite his own notoriously poor eyesight. (We’ll have cause to revisit this aspect of his work a bit later in this book.)

In the autumn of the same year, yet another new star appeared suddenly in the sky over Europe, brighter than any of the others, raising all of the old uncomfortable questions that had been prompted by the heavenly spectacles of 1572 and 1577. If the Earth, Sun, and all of their companions existed within a closed sphere, like a sort of ship in a bottle, where did all of these stellar visitors keep coming from? Tycho Brahe would doubtless have been thrilled to take to his instruments again. In his absence, many others turned their eyes and their equipment toward the sky in order to learn what they could from this latest heavenly visitor. Even the myopic Kepler did so.

The star was, we now know, another supernova, coincidentally the second to light up the skies of Earth in just 32 years; none have been visible with the naked eye since. It has become known today as Kepler’s Supernova, because Kepler published a short book about it in 1606, setting hard information collected by himself and others beside a great deal of rambling astrological commentary. The mystical impulse had yet to leave Kepler; it never completely would.

Even in the midst of such distractions, however, Kepler could not hold himself back from trying to make use of Tycho’s data in the service of a better, cleaner cosmos. Betwixt and between all of the aforementioned lines of inquiry, he soldiered on across that daunting battlefield, straining to turn Tycho’s numbers to a purpose which their originator would have stridently disavowed: a heliocentric model of the universe that made actual sense. For years, he focused his energies almost exclusively on Mars, which he chose because it was simultaneously one of the two easiest planets to see and the most exasperating of them all, being far more inexplicable in its movements than the even brighter Venus. And for literally years, he too couldn’t make any sense of its motions without falling back on arbitrary kludges like Ptolemy’s epicycles and equants — kludges that, his intuition screamed to him, couldn’t reflect physical reality.

At his wit’s end, having tried everything else he could think of, Kepler turned to a possibility that had barely been considered in the history of astronomy to date: what if the orbits of the planets were not perfect circles but ellipses? It wasn’t only the need to believe in a perfect universe, sculpted in harmony and proportion by a divine hand, that had stood in the way of this idea over the centuries, although that was certainly a big part of the reluctance to pursue it. The fact was that ellipses on their own didn’t solve anything for the poor confused astronomer, that they made the observations and mathematics no easier to line up with one another, as Kepler quickly confirmed for himself. But then he had the biggest brainstorm of his life, a eureka moment that stands among the most important of all time: what if the planets were constantly speeding up and slowing down as they pursued their elliptical orbits around the Sun?

This idea of accelerating and decelerating planets was no more new in the abstract than that of ellipses. In fact, as we’ve seen, it was at the heart of Ptolemy’s theories about equants. Yet no one had ever thought to combine it with elliptical rather than perfectly circular orbits. There was a reason for this too that transcended traditions about divine perfection. The harsh truth was that nobody knew quite how to calculate such a combination of motions. Calculus, the branch of mathematics dealing with complex motion, had yet to be invented. As a heliocentrist, Kepler had to search for a model that accounted for not only the motions of Mars but those of Earth, reflecting Tycho’s earthbound observations of Mars. And he had to do it without recourse to calculus.

After exhausting every other approach he could come up with, Kepler fell back on trial and error, the mathematician’s last refuge. He plugged in relation after relation, equation after equation, groping in the dark for something that fit. And finally he succeeded in finding the genuine, consistent, repeatable relationship he had been looking for. He determined that “the radius vector joining Mars and the Sun sweeps out equal areas during equal intervals of time”; the same was true of the radius vector joining Earth and the Sun. Clear as mud, right? Never fear. In this case, a picture really is worth a thousand words.

The picture above shows a planet pursuing an elliptical orbit around the Sun. The areas the planet “sweeps out” at different stages of its orbit are shaded in blue. Notice that all of these shaded areas are equal in size; this is the key point. It takes the planet the same amount of time to cover each of the distances that produce the shaded areas. In other words, when the planet is closest to the Sun, it is moving most quickly along its orbital path; it is moving most slowly when it is farthest from the Sun. Ironically, Kepler’s formula is the polar opposite of Ptolemy’s system of equants, which proposed that objects orbiting the Earth move more slowly in linear terms the closer they are to our planet, in order to maintain a constant angular velocity from our perspective. When we consider that it comes at the same time as a shift from a stationary to a peripatetic Earth, however, the change becomes less surprising.

Having discovered this relationship to apply to the orbits of Mars and the Earth, Kepler turned his attention to the other planets. He found that their observed motions as well could all be captured using the same relationship. There must be, he concluded, some sort of a “moving spirit” that emanated from the Sun and grew weaker with distance from it, thus causing the planets to change speed as they pursued their elliptical paths. He was groping toward a theory of gravity, although a full treatment of that phenomenon would have to wait for Isaac Newton much later in the century. In the meantime, the mere fact of his groping was hugely significant in itself. For time immemorial, astronomy had been kept separate from terrestrial physics. The heavenly bodies, it was believed, were governed by their own system of rules that had nothing to do with the ones that held sway on Terra firma. Now, Kepler was taking the first tentative steps toward a unified physics that applied to the heavens and the Earth equally, the point of origin of a journey that would be continued by Newton and eventually Albert Einstein. He was even prescient enough to guess that the same force that kept the planets moving around the Sun might be responsible for the tides of the terrestrial oceans.

Setting physics aside, Kepler had a clockwork system of the cosmos that was quite easy to apply mathematically after he had done the heavy lifting of providing the necessary governing relationship. This wouldn’t have prevented Claudius Ptolemy, Nicolaus Copernicus, and Tycho Brahe alike from hating it for its inharmonious arbitrariness. Yet it seemed to Kepler undeniable that it was the first model of the cosmos that made real empirical sense. Having been lucky enough to finally see the truth, he pitied every astronomer who had come before him, who had “wasted his valuable time and ingenuity on the construction of spirals, loops, helixes, vortices, and a whole labyrinth of convolutions in order to represent that which exists only in the mind, and which Nature entirely refuses to accept as her likeness.”

Still, Kepler himself was a rather pitiable character in another way. It was a lonely labor for him, this reinventing of the cosmos. His prestigious title notwithstanding, few others who purported to study the heavens seriously showed much interest in his project. He tried to renew his friendship with his first mentor Michael Mästlin, but received only perfunctory replies to the letters he sent. That friendship, it was now clear, had been irreparably shattered by the argument over the calendar, of which the Gregorian date which Kepler wrote at the top of each of his letters served as a constant reminder.

Perhaps as a hedge against loneliness, Kepler composed the book he was preparing on his fresh take on heliocentrism as a narrative of his long struggle to make a consistent, believable cosmos out of Tycho Brahe’s mass of data points. He poured out his soul to it in lieu of the friend he lacked, often in florid, vaguely tortured prose. (As the reader has surely noticed by now, Kepler had a strong taste for the melodramatic.) When it was finished, Astronomia Nova (“The New Astronomy”), as he called his book, had become a baggy monstrosity of some 650 pages. It is a deeply human and personal work. It reads almost like a mystery novel, telling how Kepler cracked the cosmic case one clue at a time, complete with all of the red herrings and blind allies on which he wasted days, weeks, or months in the course of his journey to the truth.

Alas, another, all too familiar difficulty presented itself when Kepler began to think about his book’s publication: Franz Tengnagel von Camp continued to demand a co-author credit. The two men wrangled for weeks on end. At last, Kepler girded his loins and begged for help from Emperor Rudolf, who was more of an absence than a presence at the center of his oft-squabbling court. The emperor emerged from his Cabinet of Curiosities long enough to broker a hasty compromise: Kepler could publish his book under his name alone, but he would have to pay lavish tribute in its pages to the generosity of Tengnagel for allowing him to use Tycho’s data, and would also have have to give his antagonist the opportunity to provide some thoughts of his own in the form of a preface.

Thus given free rein to vent, Tengnagel would surely have loved to present a point-by-point refutation of Kepler’s theories, but he wasn’t enough of an astronomer or mathematician to even start upon such a task. Instead, just before Kepler took the manuscript to Protestant Germany to have it printed, he scribbled a petty, mean-spirited little note in very bad Latin, a note which made Andreas Osiander’s much-debated preface to Copernicus’s magnum opus seem like a model of erudition and moderation. In it, Tengnagel cast Kepler’s work as no more than a stray carbuncle upon Tycho’s prodigious corpus, even had the temerity to blame him for his own tardiness in producing a proper published edition of all of Tycho’s data.

I had decided to say many things to you [reader], but the heap of political business, by which I am detained more than usual these days, and the over-hasty departure of our Kepler, at this very moment about to go to Frankfurt, has hardly left me even this little scrap of an occasion to write. And so I thought I should give you just three words’ warning, lest you be moved by anything of Kepler’s, but especially his liberty in disagreeing with Tycho Brahe in physical arguments, which has groundlessly complicated the work on the Rudolphine Tables. But such liberties are habitual to all philosophers from the creation of the universe to the present.

As for the rest, you will come to know from the work itself that it has been constructed upon Tycho’s foundation, that is, upon his restitution of the fixed stars and the Sun, and that all the heaped-up materials [i.e., observational data] were the works of Tycho…

The New Astronomy was published complete with this strange and off-putting preface in the summer of 1609, as it happened in Heidelberg rather than Frankfurt. Strapped for funds as always, Kepler was forced to make a highly disadvantageous deal with the printer, in which the latter was allowed to sell the book without paying him any royalty at all. It is unclear how many copies of this first edition were printed; only a few of them have survived. Based on this, the number was likely in the low hundreds at best.

We have already seen a couple of uncanny similarities between the publication histories of Copernicus’s On the Revolutions of the Heavenly Spheres and Kepler’s The New Astronomy: both reflected a rare blending of Protestant and Catholic Europe, and both sported uncongenial third-party prefaces. To this same list must now be added their initial receptions. For, like On the Revolutions, The New Astronomy produced no immediate frisson of excitement among the astronomers of Europe, who evinced no understanding of the magnitude of the paradigm shift Kepler’s heliocentrism represented. If anything, they talked about Kepler’s book even less than they had Copernicus’s, probably because it was even less widely distributed. They were so entrenched in the old ways of thinking that even those who did read it tended to miss the point entirely. “With your ellipses, you abolish the circularity and uniformity of the motions, which appears to me the more absurd the more I think about it,” wrote one reader in a letter to the author. “If you could only preserve the perfect circular orbit, and justify your elliptic orbit by another little epicycle, it would be much better.” A stickler for staying in one’s own lane complained that “Kepler introduces strange speculations which belong not in the domain of astronomy but of physics.” Such obtusely hidebound counterarguments were enough to drive even a teetotaling Lutheran to drink.

Kepler was left in a situation that just about every author of any stripe knows all too well: that of having poured his heart and soul into a work, having finally seen it through to completion… and to now be mired in the emotional swamps of an anticlimactic response, or rather lack thereof. By all indications, he fell into something of a depression back in Prague. His emperor had long since ceased to show any real interest in the theories of his Imperial Mathematician, and the polite intellectual society around him also had no use for him, having been persuaded by Franz Tengnagel that the provincial little semi-cripple in their midst had come to his title only through a fluke, a last random impulse of the dying great astronomer Tycho Brahe, whose inheritance he was unworthy of in every conceivable way.

Then, in the spring of 1610, the news came to Prague that another man, an Italian, had been examining the sky of late with an instrument which had not been a part of Tycho’s arsenal, a truly amazing instrument that could actually magnify the heavens and allow the observer to see sights that were out of reach of the naked eye alone. Indeed, this Italian claimed to have already found four heretofore unsuspected moons orbiting around the planet Jupiter in the same way as the Earth’s singular satellite. “I experienced a wonderful emotion while I listened to this curious tale,” wrote Kepler. “I felt moved in my deepest being.”

For Galileo Galilei and his telescope stood to place astronomy on an even firmer empirical footing than had Tycho Brahe, proving in the process that Kepler’s heliocentrism wasn’t just another set of mathematical fantasies contorted to conform with arbitrary data points. On the contrary: his heliocentrism was reality.

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(A full listing of print and online sources used will follow the final article in this series.)