The Theory of Heliocentrism

Galileo Galilei is a relative rarity in the history of science, being an important scientist who first rose to prominence only in middle-age. He was almost eight years older than Johannes Kepler, and yet it was Kepler who first made a name for himself throughout Europe. Galileo was already 46 years old when he swept in out of nowhere to set European astronomy on its head with his little book The Starry Messenger.

Then again, everyone comes from somewhere. Galileo was born in Pisa on February 15, 1564, the first son of a Florentine nobleman. Although he would spend much of the first half of his life away from Florence, he would always consider himself to be a Florentine born and bred, an heir to that city’s stupendous heritage as Ground Zero of the Renaissance. In one of those poetic perfections that history gives us sometimes, his life overlapped by exactly three days with that of Florence’s most honored son of all, the great artist Michelangelo, who died at age 88 just after Galileo was born. Galileo too would be given the gift of an unusually long life by the standards of his time, and his life too would be marked as much by Rome as by Florence. In Galileo’s case, however, the attention of popes would frequently prove less welcome and more painful.

Galileo’s father may have been of noble blood, but he wasn’t a wealthy man. An accomplished lute player, he ran a music school in Pisa, but earned the bulk of his income trading in textiles, the beating commercial heart of this part of Tuscany since long before the Renaissance came calling. Galileo did not grow up in splendor, yet he did grow up surrounded by art, literature, and philosophy, as every true son of Florence ought to. He was fluent in Latin, Greek, and Aristotelian logic before age ten, when the family moved to Florence proper, where his father had found a minor position in the government. By then, he had a younger brother — named Michelangelo after the artist — and two younger sisters.

Wealth can be a curse as well as a blessing. The fact that his family had little of it left Galileo freer than many another nobleman’s eldest son to choose his own path in life. Initially, he demonstrated no particular interest in astronomy. There was no formative event in his childhood to lead him in that direction, as there was in those of Tycho Brahe and Kepler. If he noticed the comet of 1577 at all, it didn’t leave much impression on him.

Galileo was not a socially malformed youngster in the way of Kepler; as a scion of noble blood, he was taught proper social etiquette, learned how to hold his own at a dinner party with confident aplomb. Even so, he loved most of all more secluded pursuits: reading books and working with his hands and playing music with his father. He dabbled in poetry and various other forms of artistic expression throughout his life, although the general consensus is that he was not overly accomplished at any of it. (One wag said that the best thing about his sonnets is that there are not more of them.)

As a boy, Galileo was extremely devout — so much so that he moved into a monastery on the cusp of his teenage years, only to ultimately decide not to take his vows and become a priest or a monk. His piety would slowly fade thereafter, almost linearly over the course of the ensuing decades. For Kepler, science started and to some extent remained a mystical quest for the Truth of God’s plan. Galileo evinced a soberer perspective. “He was utterly devoid of any mystical, contemplative leanings, in which the bitter passions could from time to time be resolved,” writes Arthur Koestler. “He was unable to transcend himself and find refuge, as Kepler did in his darkest hours, in the cosmic mystery. He did not stand astride the watershed; Galileo is wholly and frighteningly modern.”

In 1580, Galileo’s father scraped together the money to enroll him at the University of Pisa. There he was to study medicine, a sure path then as now to a stable, respectable, and fairly lucrative career for a bright young man. But not long after arriving at university, he discovered his lifelong hero, our old friend Archimedes, messenger of Aristarchus’s radical theory about the cosmos and so much more in his own right. Archimedes turned Galileo away from medicine and into a scientist of another stripe. Galileo found the hands-on, data-driven approaches employed by his hero to be far more congenial to his way of thinking than the abstract theorizing of Aristotle and Galen, the great ancient philosopher of medicine. “It is all too obvious that no one else has ever been nearly as clever as he was,” the young Galileo enthused about Archimedes, going on to call him “superhuman” and “divine.”

In 1585, he dropped out of medical school and returned to Florence, much to the dissatisfaction of his father, who all but disowned him. Galileo was undaunted: he was determined to continue the studies that Archimedes had begun almost 2000 years ago in mathematics, physics, and engineering. These subjects appealed to his increasingly non-mystical mind because they were quantifiable and provable. Such qualities set them apart not only from medicine but from astronomy as it was generally practiced in the late sixteenth century, with its airy estrangement from terrestrial physics and its co-dependent relationship with astrology. Shortly after returning to Florence, Galileo was inspired by the most enduring tale of all of them involving Archimedes to write his first proper treatise.

The king of Syracuse, so the story goes, has ordered a goldsmith to make a new crown for him, providing his subject with an ample chunk of raw gold for the purpose. But when the crown is delivered, the king grows suspicious that the man may have alloyed some of the gold with a quantity of silver before making it, keeping the rest of the more valuable metal for himself. The king asks Archimedes, who is living in Syracuse at this time, to test the truth of this proposition.

Even Archimedes’s prodigious intellect is stymied by the request for quite some time. To be sure, scales do exist that can weigh the crown with a high degree of accuracy, and these show that it does indeed weigh exactly as much as the chunk of raw gold which the king gave to the goldsmith. Yet this proves nothing in itself; if the man truly has alloyed the gold with silver, he too could have used a scale to make sure the finished crown weighs just the right amount.

Steeling himself to disappoint his king — a dangerous thing for even an acknowledged great man like himself to do — Archimedes takes a bath to calm his nerves. Sinking down into the water with a sigh, he notices how its level rises in the bathtub as part of it is displaced by his own body. And just like that, his mind is off and running again. Earlier experiments have taught him that the volume and weight of every pure metal as well as every alloy have a different ratio to one another. (This is because every substance has a different density.) Now, he realizes in a flash of insight that he can compare the volumes of the crown and of another hunk of pure gold of the exact same weight by dropping them one at a time into the same container of water and recording how much the water level rises as a result. Legend says that Archimedes was so excited that he jumped out of his bathtub to run naked through the streets of Syracuse, shouting “Eureka! Eureka!”: “I’ve got it! I’ve got it!”

His method soon proved that the goldsmith really had attempted to cheat the king; the crown displaced more water than it ought to because of the silver with which its gold had been alloyed. The fate of the crooked goldsmith is not recorded in the legend, but we can assume that it was an unpleasant one.

Galileo questioned one part of this story. He had learned from his own experiments that measuring a rise in the water level of a basin was annoyingly hard to do with precision. Yes, you could put markings on the side of it as a means of doing so, but that could yield only a rather crude approximation; you couldn’t make the markings fine-grained enough to satisfy the needs of an experiment like Archimedes’s. Likewise, if you tried to quantify the change in depth using a measuring stick, you mucked up the data as soon as you dipped it into the basin, since the stick would itself displace a volume of water. You might try to fix that mathematically, changing the numbers to account for the additional volume of the measuring stick, but that was a tricky calculation to pull off, so much so that Galileo didn’t trust his own reckoning.

Luckily, Archimedes himself had already provided a better solution elsewhere, in the form of Archimedes’s Principle. It states that, thanks to the buoyancy of water, any object that sinks rather than floats when immersed in it will, if weighed underwater, see its registered weight decreased by the weight of the amount of water that it displaces. This provides a way of calculating its density, and by extension its material composition. The modern metric system makes the necessary calculations easy, in that it defines one liter of water as weighing precisely one kilogram: water, we therefore say, has a specific gravity of 1.00. Now, let us imagine that we start with a chunk of silver that weighs one kilogram when dry, then immerse it in water and weigh it again; it now registers a weight of .9048 kilograms. We can determine the specific gravity of silver by dividing its weight out of water (1 kilogram)  by the weight of the water that was displaced (1 – .9048, or .0952 kilograms). Thus we learn that silver is 10.5 times as dense as water — or that it has a specific gravity of 10.50. One kilogram of gold weighs .9482 kilograms underwater. Thus we learn (1 / (1 – .9482)) that gold has a specific gravity of 19.31.

Galileo was convinced that this was the true way that Archimedes had conducted his most famous experiment; after all,  it wasn’t known as Archimedes’s Principle for nothing. After establishing the specific gravity of pure silver and gold by this method, the ancient scientist would have weighed the dubious crown that had been given to him, first out of the water and then underwater. We can assume that his measurements and calculations yielded a specific gravity somewhere between 10.50 and 19.31, indicating that it contained a combination of gold and silver. Archimedes would even have been able to tell his king with some degree of confidence what percentage of the crown’s gold the goldsmith had replaced with silver. Off with his head!

Galileo wrote up his own conclusions in a treatise called The Little Balance, which included the first table of the specific gravities of common substances ever to have been publicly distributed. Yet he devoted most of the text to instructions for the construction of a beam balance capable of making these sorts of measurements efficiently and accurately; this is the “little balance” of the title. For, like Tycho Brahe but unlike Nicolaus Copernicus and Johannes Kepler, Galileo Galilei was an inveterate tinkerer, a man intrigued not just by the mysteries of nature but by whatever gadgetry he could find or devise to help him clarify them.

The Little Balance has still more to tell us about the man who wrote it. It was never printed, but rather made its way around Tuscany in hand-copied versions only. Further, Galileo chose to write it in his native Tuscan dialect of Italian rather than Latin, the language of “serious” European scholarship. If Tuscan had been good enough for Dante and Petrarch, Galileo must have thought, it was good enough for him. Still, his decision not to write his texts in the lingua franca of the era resulted in his name being absent from the conversations going on in natural philosophy in a broader European context. Galileo was not a man who shunned the spotlight in the way of Copernicus; this makes his failure to reach for a wider readership early on all the more head-scratching. It may have had something to do with old ideas about the dignity of nobility, which were still not considered compatible with the scribbling of texts in some quarters. Galileo, in other words, may not have been quite as modern as Arthur Koestler posits.

His nobility notwithstanding, practical problems of a sort that are all too familiar to most of us untitled moderns were pressing Galileo from every side at the time he wrote The Little Balance. His father didn’t have the means to support him even if he had been inclined to. Galileo found work as a teacher of mathematics in Florence while he contemplated his next step  in life. He dearly wanted to secure a position at some university or other, but this was complicated by the fact that he hadn’t managed to secure his own degree. So, just as a young and hungry Michelangelo had done 91 years earlier, he turned his gaze to Rome, the city to which all roads in Italy seemed to lead all of the ambitious young men who lived there sooner or later.

It was in the fall of 1587, at the age of 23, that Galileo went to Rome for the first time. The city that he encountered was a dramatically different place from the half-ruined warren of crooked alleyways that Michelangelo had seen on his own first pilgrimage from Florence. Thanks to a large extent to Michelangelo and the string of popes who had funded his efforts, the Rome of 1587 was well on its way to becoming the shining city on seven hills that tourists and pilgrims of today visit in the millions upon millions every year. The new strictures and standards introduced by the Council of Trent did not prescribe any embrace of Protestant modesty when it came to the architecture of the Catholic faith. The current Pope Sixtus V was carrying out urban renewal on a scale that dwarfed even that of his immediate predecessors, moving obelisks and statues and streets and entire neighborhoods around like a child looming over a Lego set. The great dome of the new Saint Peter’s Basilica, planned but unfinished at the time of Michelangelo’s death, was finally on the verge of being set in place, to create the largest single church in the world in terms of interior volume, then as it still is today. The Rome which Sixtus would bequeath to his successors was in all respects grander than it had been since ancient times. It was also healthier than ever, what with the aqueducts he ordered built to bring in clean water and the surrounding pestilential swamps he ordered drained. Galileo was duly awed by the spectacle of the city, a self-conscious embodiment in stone of the power of the Catholic Church — constructed, as such things so often are, just as that power was being attacked in unprecedented ways. With almost half of Western Europe having slipped through its grasp, the Church was more determined than ever to display and wield its might in the half that remained to it. Thankfully, Galileo — still a good, orthodox Catholic at this stage of his life in most respects, among them an unquestioning acceptance of geocentrism — had no reason as yet to fear that the ire of the Church might be turned against him.

He brought with him to Rome The Little Balance, plus a clutch of more recent, equally impressive papers on determining the center of gravity of solids. He carried these to the Roman College, where he met with Christopher Clavius, the principal architect of the Gregorian calendar that had gone into effect in Catholic Europe five years ago. Yet it appears that the calendar, and the movements of the heavenly spheres that were the ultimate cause of its years and seasons, scarcely came up on this visit. Instead the old man and the young one confined their discussions to the latter’s work in terrestrial physics and mathematics; Galileo was still keeping his eyes fixed firmly to the ground, not to the heavens above. On that basis, he won the admiration of Clavius, who promised he would use his influence to try to find him an academic posting that was worthy of his talents.

Clavius’s patronage paid off for Galileo, although it did take some time. In the autumn of 1589, he was invited to join the faculty of the University of Pisa — the same institution from which he had dropped out four years before — as a professor of mathematics and physics. Wishing to understand how weight and density affect motion, Galileo promptly launched into a series of experiments that involved dropping various objects from the top of the Leaning Tower of Pisa. (It is a delicious scene to picture, is it not?)

Imagine that you drop a cannonball and a musket ball from the tower, as Galileo did. Which hits the ground first? You might incline toward a seemingly commonsense assumption that was also advocated by Aristotle: that the heavier cannonball will do so well before the much lighter musket ball. Indeed, Aristotle claimed that the relationship between weight and speed of falling is linear, meaning that a 100-pound object will reach the ground 100 times faster than a one-pound object. But in reality this is not the case at all. Both will fall at almost the same speed, as Galileo discovered. (The “almost” in that sentence has to do with air resistance; in our planet’s atmosphere, a hammer falls much faster than a feather not because it is heavier but because it is denser — i.e., it has a higher specific gravity — and because it has less surface area facing in the direction of its fall in proportion to its overall size. In 1971, the American astronaut David Scott famously dropped a hammer and a feather at the same time from an equal height whilst standing on the surface of the Moon, a vacuum where air resistance cannot become a factor. As had been predicted by physicists, both hit the ground simultaneously.)

In an indication that he had already traveled far from the knee-jerk reverence for the infallible ancients that had been inculcated in him as a child, Galileo didn’t hesitate to pronounce Aristotle’s position “ridiculous.” He was as scathing toward that hallowed philosopher as he was toward a fellow member of the University of Pisa faculty who repeated his experiments with the express goal of invalidating them, an endeavor from which he emerged with a litany of small discrepancies to point to. Galileo was having none of it.

Aristotle says that a 100-pound ball falling from a height of 100 braccia [a measure of length about equal to that of an average man’s arm] hits the ground before a one-pound ball has fallen one braccio. I say they arrive at the same time. You find, on making the test, that the larger ball beats the smaller one by two inches. Behind those two inches, you want to hide Aristotle’s 99 braccia and, speaking only of my tiny error, remain silent about his enormous mistake.

Galileo was developing into a rapier-witted debater, one whom other men learned to steer clear of almost regardless of the merits of their case. His rhetorical style combined logic with a flair for drollery and drama that he had picked up from his artistic studies and his early exposure to the chattering classes of Florence. This was another thing that set him apart from Kepler, even though the two men’s modes of argumentation could be equally devastating in their own ways. Whereas Kepler tried to bludgeon his opponents to death, Galileo was a master of the surgical strike. “He never takes his adversary by abrupt frontal attack, but after a courteous greeting stands back to await the first blow,” wrote a colleague. “Going on the defense, he entices his opponent to advance. Suddenly he strikes where least expected, and, profiting from the surprise, presses in, pushes back, knocks out his adversary, and withdraws without taking any further notice of the combat.” For all his skill in a verbal joust, however, Galileo would prove less willing than Kepler to press his case to the utmost if it meant risking his reputation or livelihood, as we shall soon see.

Galileo’s work on the physics of motion, which he would elucidate more fully much later in life, would become an essential steppingstone to Isaac Newton’s full theory of gravity. But in the here and now of circa 1590, the experiments weren’t completely satisfying, a reality which is not entirely disguised by the merciless counterattack on his hapless fellow professor which I’ve quoted above. Despite his skill in working with his hands, Galileo still lacked the instruments to carry out his experiments with the rigorousness they demanded; he could put no hard-and-fast numbers on his findings, could only report the subjective impressions of a ground-based observer watching the two objects fall. His plight was the same as that of budding European science as a whole. It was beginning to realize that ancient wisdom was sometimes lacking, sometimes outright wrong. Yet it still lacked many of the tools — both physical and intellectual — to reliably produce new knowledge about the world.

At some level, Galileo himself may have sensed this. It was his original intention to create a definitive textbook on the physics of motion, archetypally entitled simply On Motion. He even deigned to write it in Latin, indicating that he may have envisioned it as his version of Tycho Brahe’s De Nova Stella, his ticket to general European fame as a natural philosopher of the new school. But in the end, after a long period of struggle, he abandoned the text. He just couldn’t produce the consistent results he needed to draw firm conclusions with the tools he had to hand — and he was too much of an empiricist not to admit it.

Galileo’s experiments with motion did at least garner him considerable recognition in northern Italy. In the summer of 1592, he accepted a position at the University of Padua, the same place where the young Copernicus had studied for two years and where Giordano Bruno had recently presented his blasphemous ideas about an infinite universe and much else besides, only to be arrested by the Inquisition in nearby Venice just weeks before Galileo arrived. The corridors of the university must have still been abuzz with the news of Bruno’s downfall. It would be fascinating to know what Galileo made of the controversy, but he contributed nothing about it to the public record — neither now nor at any other point in his long life.

An older Galileo does tell us, however, that he came to look back on the eighteen years he spent in Padua as the very best of his life. To his biographers, by contrast, the same period is a source of immense frustration. He wrote almost nothing that has survived for stretches of whole years, giving them only context and supposition to go on when trying to reconstruct his life and thought in Padua. Still, it does seem clear enough that, not that long after arriving in his new posting, he turned his attention seriously for the first time to astronomy, read Copernicus’s On the Revolutions of the Heavenly Spheres, and became a convert to heliocentrism despite that volume’s manifest deficiencies.

We know that Galileo encountered Johannes Kepler’s rather underwhelming first book as well, because he wrote him a letter about it in August of 1597. It’s an amazing document just for being the first communication between these two giants in the history of astronomy, who would never meet one another in person, but it’s even more amazing for the insight it provides into Galileo’s state of mind. After confessing that he has as yet “only perused the preface,” he tells Kepler that he too has been a Copernican for several years. Then he goes on to say that he has chosen to keep his views to himself, “terrified as I am by the fortune of our teacher Copernicus himself, who, although he earned immortal fame among some, nevertheless among a vast number (for such is the number of fools) appeared fit to be ridiculed and hissed off the stage. I would certainly dare to publish my reflections at once if more people like you existed. As they don’t, I shall refrain from doing so.” It is the first indelible hint that Galileo knows that to challenge orthodoxy is to play with fire; if it did nothing else, the fate of Bruno would have provided ample evidence of that fact. At the same time, it shows the pragmatism of the man. Galileo is not prepared to become a martyr for the cause of heliocentrism, even in a figurative sense. He would prefer to charge the ramparts of geocentrism as a soldier in the second rank, not in the vanguard. He isn’t prepared to risk his career for the cause — much less his life.

Just as intriguingly, Galileo alludes in his letter to having disproved many of the traditional arguments against a peripatetic Earth in the course of his studies of motion. It was still often said that, if the Earth really was moving, objects dropped from a high place — like, say, the Leaning Tower of Pisa — should not hit the ground at a point directly below where they were released, because the planet should have moved under them in the meantime. Galileo, however, believed he knew enough about circular inertia to know that the object would continue moving along with the planet until it struck the ground. It was also said that, if the Earth really was moving, we would all be physically flung off of it into space. Galileo may not have had a full theory of gravity, but he did know that a strong attractive force pulled objects and people toward the surface of the planet, and believed this gravity was more than strong enough to overcome any centrifugal forces that might come into play here.

Typically, Kepler replied to Galileo that he ought to let go of his fears and join him in the front rank of the heliocentric revolution. “Have confidence, Galileo, and step forward,” ran his call for solidarity. “If I guess correctly, few of Europe’s principal mathematicians will want to distance themselves from us. So great a force is truth.” Galileo did not heed this clumsy exhortation, and may even have found the cajoling tone offensive; he never replied to Kepler’s letter with the deeper thoughts on the latter’s book that he had promised in his own first missive. If he really was offended, it certainly wouldn’t be the the first time Kepler had rubbed someone the wrong way, damaging his own cause in the process. Of course, it’s equally possible that Galileo merely found the muddled mystical conjectures that constituted the bulk of Kepler’s first book unconvincing, and thought discussing them further with their source not worth the effort. At any rate, the two men would not correspond again for almost thirteen years, and even then only briefly.

After having lived from hand to mouth since disappointing his father by failing to become a medical doctor, Galileo managed gradually to make a stable, comfortable life for himself in Padua; if he was reluctant to risk it by speaking out too boldly on controversial subjects like heliocentrism, that is only understandable. Being a tinkerer as well as a thinker, he set up a profitable side trade as an inventor and seller of measuring and calculating instruments, from which he may have earned more than he did from his university position some years. He cast horoscopes as well from time to time, as most scholars with any knowledge of astronomy did, whatever their opinion on the veracity of the ancient craft. And he took on practical assignments from the government of Venice, one of which resulted in one of his few substantial written works of these years, a study of fortifications in the era of gunpowder. With his earnings from all of the above, he was able to buy a fairly large house, which came complete with the requisite retinue of servants. He sometimes took his students on as boarders there. He also started a relationship with a woman named Marina Gamba, whom he refused or was prevented from marrying because she was a commoner of no particular breeding. (Shades of Tycho Brahe and his mistress Kirsten Jørgensdatter…) The couple had three children together between 1600 and 1606.

The new star of 1604 prompted Galileo to set aside the emphasis on mathematical theory that had marked his studies in astronomy to this point and begin to treat them more like his studies of physics. Now that he set his mind to it, he was well-equipped to design and build the instruments he needed to become a stargazer in his own right. Thus he learned, not entirely to his satisfaction, that no parallax could be detected in relation to the star; this was disappointing in that the presence of parallax would have represented compelling evidence that the Earth was indeed moving through space, evidence which might even have been sufficient to overcome his reluctance to out himself as a Copernican. Nonetheless, he delivered a series of public lectures on the new star in Padua, his first to deal primarily with astronomy.

And yet these investigations seemed to be revealed as more of a passing distraction than an enduring interest for Galileo after the new star faded from view again in 1605. With public interest fading as quickly as the star itself, he never officially published his findings related to it, leaving it to go down in history as “Kepler’s Supernova” rather than his own.

Galileo Galilei was now 41 years old, and seemed unlikely to ever become anything other than what he currently was: a regionally respected but far from eminent professor who spent his time tinkering with his experiments and inventions and enjoying the domestic bliss provided by his house and mistress when he wasn’t passing on his knowledge to his students. Instead, a new invention that came to Italy from the Netherlands was about to upend everything, elevating this heretofore obscure figure to heights of approbation and infamy the likes of which he could never have imagined.

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