Galileo (Galilei, Galileo) (1564–1642)
In the Siderius nuncius, he noted that the Moon was "not unlike the face of the Earth," that its dark regions might be seas and its bright parts land, and that "the Moon has its own atmosphere." Although within a few years he came to doubt these conclusions, they were given wide credence by others (see Moon, life on). In particular, they immediately led to the first piece of speculation about extraterrestrial life based on instrument-derived data. Kepler wrote to Galileo with the suggestion that one of the large features he had seen on the lunar surface might have been excavated by intelligent inhabitants who "make their homes in numerous caves hewn out of that circular embankment." Galileo would not be drawn on this except to say that if there were lunar life it would be "extremely diverse and beyond all our imaginings." His defense of the Copernican system in Dialogue on the Two Chief World Systems brought severe censure from the Church and he was forced to recant before, at the age of 69, being sentenced to life imprisonment (commuted to house arrest).
Birth of a myth
Like all his fellow students throughout Europe, Galileo was fed a stale diet of Aristotelian physics. But he also lived in an age of fast receding horizons, of explorers heading into uncharted seas and returning with tales of wonder. There was a new spirit of questioning abroad, of wanting to see the truth of things for oneself. And so Galileo, who would have stood out as a genius in any century, became the first genius of experimental science. High among his priorities was to check, once and for all, Aristotle's claims about how objects move and fall.
Which brings us to a familiar tale. This short, stocky, red-haired man, now a very unconventional professor of mathematics at Pisa, who repeatedly run afoul of the authorities for refusing to wear his academic gown while teaching, climbs the winding stairs of the Leaning Tower. From an upper balcony, he reaches out and lets fall two stones of different weights. And a remarkable thing happens. To the gasps and amazement of the crowd gathered below, the stones hit the ground together. Although doubtless in part apocryphal, this story does at least have some backing from Galileo's pupil and amanuensis Viviani who reported that Galileo had done the experiment "in front of all the faculty and students assembled." Also, in his Discourses on Two New Sciences (1638), Galileo has one of his protagonists, Sagredo, say, "But I, Simplicio, who have made the test can assure you that a cannonball weighing one or two hundred pounds, or even more, will not reach the ground by as much as a span ahead of a musket ball weighing only half a pound, provided both are dropped from a height of 200 cubits." Perhaps the Tower experiment was really just a class demonstration, or perhaps it never happened at all and Galileo's description in Two New Sciences was no more than a mental exercise. Whatever the truth of the affair, it's unimportant scientifically because Galileo had already gathered all the data he needed about falling bodies from a different source: a series of beautifully crafted studies in which the pull of gravity is diluted and its effects made crystal clear.
Early doubtsIt's easy to get the impression that Galileo, a colorful, rambunctious, prickly character and one of the few scientists that everyone can name, took on Aristotle and his institutionalized worldview virtually single-handed. But voices of discontent had been raised very much earlier. Back in the 5th century AD, the Greek Christian philosopher John Philoponus, also known as John the Grammarian among other names, cast a critical eye over what Aristotle had to say in his Physus. Philoponus didn't buy Aristotle's explanation that an object in flight is nudged along by a vortex of air. Much more likely, he thought, a projectile keeps moving because of a "kinetic force" that is imparted to it by whatever sets it going, such as a hand or bow, for example, and that exhausts itself in the course of the movement. Similar ideas had been expressed even earlier, by Hipparchus in the 2nd century BC and Synesius in the 4th century AD. Although this theory of impetus, as it became known, is still flawed because it fudges the issue of how the kinetic force could work, it marks a crucial step away from Aristotelian dynamics toward a more modern theory of how things move – a theory based, as we'll see, on the concept of inertia. It also gave Philoponus a new perspective on the role of the medium through which an object travels. Far from being the means by which the projectile is kept moving, the medium is seen in the impetus theory to be something that gets in the way. This being the case, Philoponus concludes, there's nothing to prevent one from imagining motion taking place through a void, and therefore no reason to disbelieve in empty space purely on the grounds that Aristotle defended. As for the natural motion of bodies falling through a medium, Aristotle's verdict that the speed is proportional to the weight of the moving bodies and indirectly proportional to the density of the medium is undermined by Philoponus through appeal to a mind's-eye conception of the same kind of experiment that Galileo would carry out centuries later.
A separate line of attack against Aristotle was taken up by Giovanni Benedetti, born in a very different era – just 34 years before Galileo. Starting his career as court mathematician to the Duke of Parma, he moved to Turin at the invitation of the Duke of Savoy to serve as philosopher in residence there. In his final and most important work, Diversarum speculationum (1585), published around the time Galileo was finishing his college education, Benedetti draws attention to a thought experiment that effectively demolishes Aristotle's theory of free fall. Imagine, says Benedetti, two equal weights connected by a gossamer thin, essentially weightless line. Thus joined they must fall at the same rate as a single body having their combined weight. Now suppose the line is cut. Intuition demands that the two equal bodies, though disconnected, must continue to fall at the same speed they had before. And so Aristotle, who insisted that bodies with different weights came to earth at different rates, was undone by a simple flourish of logic. All that remained now was for someone to expose the untruth definitively in real life.
Inclined to success
One of the difficulties of doing low-tech experiments with gravity is that objects drop vertically at a pretty brisk pace. There were no stop watches or high-speed cameras at the turn of the 17th century, so studying closely the behavior of falling bodies posed quite a problem: all the action was over before you could really tell what was going on. To this difficulty Galileo brought a brilliant and elegant solution. His realized he had to somehow slow down the rate at which an object fell so that he could accurately measure its speed. Yet he had to do this without altering the character of the motion. The trick he came up with was to replace the vertical drop of a body with a much more gradual roll down an inclined plane. This is how he describes his apparatus in Two New Sciences:
A piece of wooden molding or scantling, about 12 cubits [some 23 feet] long, half a cubit [about one foot] wide and three finger-breadths [about two inches] thick, was taken; on its edge was cut a channel a little more than one finger in breadth; having made this groove very straight, smooth, and polished, and having lined it with parchment, also as smooth and polished as possible, we rolled along it a hard, smooth, and very round bronze ball.The beauty of this setup, he pointed out, is that the speed gained in rolling down the ramp doesn't depend on its slope. A similar pattern would emerge, Galileo explained, if a ball rolled down a ramp that was smoothly connected to another steeper upward ramp: the ball would roll up the second ramp to a level essentially equal to the level it started at, even though the two ramps had different slopes. It would then continue to roll back and forth between the two ramps, before finally coming to rest because of friction. Thinking about this motion, it's clear that, if you ignore the gradual slowing down on successive passes, the ball must be going at the same speed coming off one ramp as it does coming off the other. Galileo then invites us to imagine the second ramp getting steeper and steeper until it becomes nearly vertical, at which point the ball is essentially in free fall. Thus, he concludes, for a ball rolling down a ramp, the speed at various heights is the same as the speed the ball would have reached, much sooner, by just falling vertically from its starting point to that height. This fact handed him the perfect solution: the physics of free fall could be modeled using a ball and a ramp. And by inclining the ramp at a gentle enough angle, the movement could be made sufficiently sedate to be measured. Effectively, Galileo had reduced the power of gravity so that he could watch objects descend in slow motion.
His only remaining problem was the lack of a precision timekeeper. And here, again, he showed his ingenuity by turning to an ancient device – the water clock, or klepsydra – by which he could literally weigh the moments of his experiments:
[W]e employed a large vessel of water placed in an elevated position; to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water, which we collected in a small glass during the time of each descent... The water thus collected was weighed, after each descent, on a very accurate balance; the difference and ratios of these weights gave us the differences and ratios of the times...Perhaps Galileo first acquired his skill as an empiricist while assisting his father, who carried out home experiments in the physics of sound. At any rate, Galileo was himself a very musical man with a natural sense of rhythm and this he put to good use in evolving a second strategy for time measurement. In the path of the balls that he rolled down the plane he placed little bumps. Every time a ball went over a bump it made a click. By arranging the bumps so that the clicks came in regular succession he could be sure that the time between bumps was the same.
In hundreds of different ways Galileo conducted his inclined plane experiments to penetrate the mysteries of motion and fall. He varied the height of the plane and the angle it made with the horizontal. He varied the size and weight of the balls. In some trials, the ball left the end of the ramp, which sat on a table, and descended directly in an arc to the floor. In other, related experiments, a horizontal shelf was placed at the end of the ramp, and the ball would travel along this shelf before making its final plunge. Diligently he measured the times and distances traveled, both horizontally and vertically, during each descent.
For Galileo, it wasn't enough to show beyond the shadow of a doubt, as he did, that objects of different weight fall at the same rate. He longed to know the precise law that governed falling bodies – the mathematics of unhindered descent. And in this quest his ear for tempo served him well. Listening for the clicks as each bronze ball rolled down the plane, he uncovered a wonderful secret of nature. In the first second of descent, the ball covered a distance of one unit. In the next second it traveled three times this distance, and in the next second, five times the initial distance. This sequence spoke of uniform acceleration – the ball speeding up by equal amounts in equal times. Repeated tests, with the plane at different angles, always gave the same result: from one second to the next, as the ball rolled down the inclined plane, the ratios of the distances covered increased by odd numbers, that is, by intervals of 1, 3, 5, 7, 9 and so. After one second the ball had covered a distance of one unit. In the next second, it covered three more units, so that at the end of the first two seconds it had traveled four units in total. In the third second, it covered five more units, for a total distance after three seconds of nine units. One, four, nine – the next in the sequence would be 16, then 25: these are, Galileo realized, the square numbers, 12, 22, 32,... Here was the intimate connection between time and distance for everything that descends under gravity: the distance an object falls varies as the square of the elapsed time. The precise formula took many years for Galileo to establish and verify and appears in public for the first time in his Two New Sciences, more than three decades after the first inclined experiments were carried out. We can write it in the form s = ½at 2, where s is distance, t is time, and a is a constant – the uniform acceleration due to gravity.
One of Galileo's greatest insights was to realize that a body's motion has two completely different and separate components. Movement in the vertical direction, if you ignore air resistance, is dictated by gravity and follows the time-squared rule just described. Horizontal motion, however, isn't affected by gravity at all. Aristotle claimed that it took some kind of push to keep going. But even in ancient times this idea was refuted by Philoponus with his theory of impetus. Galileo's close contemporary Bennedetti then advanced the anti-Aristotelian argument further in a couple of ways: first by claiming that the medium hinders, rather than aids, the motion, and second, by portraying impetus as a quality transferred to a body which enables it to stay motion. The longer the body is impressed with impetus, he said, the more it acquires. In Galileo's hands, this concept became still more refined. Impetus, Galileo explained, has similarities to both heat and sound. Once you transfer heat to a body, for example, it is hot and remains so until the heat has dissipated. If you strike a bell, it acquires a sonorous quality that continues even when the bell is no longer being disturbed. In the same way, motion imparted to an object remains until the medium resists and drains away the impetus.
Galileo explored impetus by thinking again in terms of a rolling ball and inclined planes. To begin with, a ball is rolling back and forth between two identical inclines. Suppose the ball and surfaces are so smooth that there's no friction and therefore no loss of impetus over time. Whatever height the ball starts out from on the left incline, it climbs back up to on the right incline before reversing its motion. Now suppose the right incline isn't so steep. The ball again rises to the same height from which it was released, but now it has to roll a greater distance up the right incline before coming to a halt for an instant at the top of its journey. Therefore, it takes more time for the ball to roll to a stop on the right incline before it turns around. This time grows longer and longer as the slope of the right incline decreases. Finally, the right incline becomes flat. In this case, Galileo realized, the ball would take an infinitely long time to stop; in other words, it would carry on moving forever without any change in speed or course – unless something else, such as friction, affected it.
A question of curvatureThese innovative ideas about vertical and horizontal motions, Galileo brought to bear on the old puzzle of determining the path of a projectile. Tartaglia had shown the way with his, albeit hazy, recognition that the path was everywhere curved, not mostly made of straight lines as Aristotle had taught. But Galileo was able to nail the actual curve – its precise shape and mathematical signature – by applying the theoretical and applied knowledge he'd gained from his inclined plane experiments. If a cannonball falls vertically under gravity obeying the time-squared law while, simultaneously, it travels horizontally at constant speed because of its impetus, its combined motions (ignoring air resistance and all other factors) will make it describe that most graceful of curves, the parabola.
The parabola is the curve that all projectiles trace out under the influence of gravity, providing that the effects of the medium are negligible. Galileo understood that air affects the path of an object, but he thought its influence could be safely ignored. As it happens, it can if the projectile is massive enough and moving fairly slowly. This explains why Galileo's calculated trajectories work so well for cannonballs and their ilk. Ballisticians eventually went to all sorts of lengths to try to figure out the much more complicated paths of lighter, faster objects, such as bullets and artillery shells, for which drag is vastly more influential. But that's a different story. Galileo had put mathematics into the heart of science, or natural philosophy as it was then still known. He'd begun to uncover the laws by which things moved and fell. And, through painstaking experiment and analysis, he'd begun to dispel the mystery of gravity. Galileo's great genius lay in his ability to observe the world at hand, to understand the behavior of its parts, and, most tellingly, to describe what he found in terms of mathematical proportions. For these achievements, Albert Einstein dubbed him "the father of modern physics – indeed of modern science altogether."
And perhaps if he had stopped there, with his studies of movement, gravity and other terrestrial science, he would have brought less trouble on himself. But Galileo's vision wasn't confined to phenomena on or near the Earth. He dared to raise his eyes to the Heavens and question what lay there – and that would put his very life at risk.
What is and what should never beIn 1600 the renegade Dominican friar Giordano Bruno was burned at the stake in Rome for offering views that differed rather too markedly from those of the Vatican. Among his heresies were to insist that the Earth didn't sit motionless at the center of the universe, but instead traveled around the sun, and that – madness upon madness – "innumerable suns exist; innumerable Earths revolve about these suns... Living beings inhabit these worlds." Few modern astrobiologists would disagree.
In the same year that Bruno's life was abruptly curtailed, that of Galileo's first child began. As Jacob Bronowski wrote in The Ascent of Man, Galileo "had rather more children than a bachelor should." His two daughters and one son were all born of his long illicit liaison with the beautiful Marina Gamba of Venice. The eldest offspring, christened Virginia, later became Sister Maria Celeste – the subject of Dava Sobel's best-selling book, Galileo's Daughter – after entering the convent at San Matteo. Her sister, Livia, also took the veil and vows at San Matteo, while their brother, Vincenzio, youngest progeny of Galileo and Marina, was eventually legitimized in a fiat by the grand duke of Tuscany and went to study law at his father's old alma mater in Pisa.
Maria and the three children were living in Padua, and Galileo teaching mathematics at the university there, having moved from Pisa, when the course of scientific history changed. In July 1609, Galileo learned of the invention of the telescope in Holland. Not knowing the exact details, he began working out the principles involved for himself and by the beginning of 1610 had built his first simple "optik tube." Immediately he set it up in the garden behind his house, pointed it at objects in the night sky – the Moon, the planets, the Milky Way – and was astounded by what he saw.
A bewildering number of stars leapt out at him, "more than ten times as many" as were visible to the naked eye. The Pleiades showed not merely the seven "sisters," long sung of by the poets, but thirty-six glittering members, while the faint haze of the Milky Way resolved into a breathtaking stellar host. The Moon, far from appearing as the smooth orb the Scholastics supposed it to be, was "rough and uneven, covered everywhere, just like the Earth's surface, with huge prominences, deep valleys, and chasms." It was another world, in some ways resembling our own. With his primitive scope trained on Jupiter, Galileo spied four attendant pinpoints of light. As he watched, from hour to hour, and night to night, the lights changed position; they were, Galileo realized, satellites moving around their large parent, the whole comprising a planetary system in miniature.
Hastily, Galileo published his findings in a booklet called Siderius nuncius (The Starry Messenger) in March 1610. "I render infinite thanks to God," wrote Galileo after his wondrous nights at the eyepiece, "for being so kind as to make me alone the first observer of marvels kept hidden in obscurity for all previous centuries." Those marvels caused a sensation, were the talk of intellectuals and high society throughout Europe, and transformed Galileo's life. In no time he was appointed chief mathematician and philosopher to the grand duke of Florence, and moved there to assume his position at the court of Cosimo de' Medici. But even as his fame and prosperity grew, he attracted enmity and suspicion.
The planets went around the Earth, Aristotle and the Church maintained, so how could Jupiter have four private worlds of its own? The Heavens were perfect and immutable, orthodoxy taught. Why then did the moon look rough and changeable, disturbingly familiar? Worse was to come.
Hardly had Galileo's first wave of cosmic revelations broken upon an astonished population before there was a new spate. Galileo followed the progress of Venus, "the mother of loves" as he described it, week by week, and found something utterly astonishing. Venus cycled through phases from full to crescent, just as the moon did. And horror of horrors, the Sun was blemished, marked by what Galileo called macchie solari – sunspots – that crawled continuously across its face. The perfect sun, the emblem of divinity, was speckled and despoiled.
Galileo was now sailing into dangerous waters, not just because of what he'd seen with his optically enhanced vision, but because of how he interpreted those sights. For Galileo believed in the theory, espoused ages ago by Aristarchus but much more recently revived by the Polish cleric and amateur astronomer Nicolaus Copernicus, that the Earth trekked around the Sun.
RevolutionsCopernicus, born in Torun in 1473 and educated at Cracow University, had traveled to Italy in his youth, learned medicine and law there, and been infected with the new spirit of inquiry and free thinking that he encountered. Soon he found himself questioning the cosmological worldview of his Church superiors. There was something strange, he knew, about the motion of the planets: they didn't take part in the regular east-west procession of the other heavenly bodies. Mars, for example, after traveling east to west as expected, would pause in its motion for several nights and then mysteriously begin to travel backward from west to east, swimming against the heavenly tide. Several nights later, after this enigmatic excursion, it would resume its normal course from east to west. It was a puzzle that had troubled astronomers since antiquity: Why did the Red Planet trace out a loop in its journey across the sky?
Aristotle and, later, Ptolemy, had tried to account for the sometimes aberrant motions of the planets in their geocentric scheme by calling on an elaborate hierarchy of circular orbits. In the final, full-blown Ptolemaic model, each planet moves not only on a circular path around the Earth but also travels around a little "epicycle," designed to explain the occasional strange retrograde movements. Even this complicated arrangement doesn't work very well, but Copernicus realized that it works better if the object around which everything else revolves isn't the Earth but the sun. By the time he became canon of Frauenburg Cathedral in 1512, having succeeded his uncle in that post, Copernicus had abandoned the Ptolemaic system and begun to formulate a new vision of the cosmos with the sun at its heart. He first discussed his ideas in Commentariolus, a brief tract completed sometime before 1514 and circulated in manuscript form to interested scholars. Thereafter he fleshed out the details of his new system in De revolutionibus orbium coelestium (On the Revolution of the Celestial Sphere). Although the manuscript for this was written by 1530, Copernicus seems, probably for fear of Papal retribution, to have been reluctant to publish it. In fact, it was a decade later before he was persuaded to go ahead, by the Austrian mystic and mathematician Rheticus who was one of Copernicus's most outspoken advocates. The work finally appeared in 1543 just in time, according to popular legend, for it to be shown to Copernicus on his deathbed.
Although De revolutionibus was banned by the Church, copies and word of it got around and began to shape the views of independent thinkers across Europe. A convert to Copernican theory, Galileo saw his startling telescopic observations as offering it powerful support. How else to explain, for example, the shifting phases of Venus other than by assuming that it was in orbit close to the Sun and showing us various aspects of itself illuminated as it went around the central fire? Galileo began to broadcast his ideas with great gusto – in bawdy humorous writings, loudly at dinner parties and forcefully in staged debates. He became the leading spokesman for the new heliocentric alternative. And that was a hazardous role to play. A committee of consultants declared to the Inquisition that the Copernican proposition that the sun is the center of the universe was a heresy. Because Galileo supported the Copernican system, he was warned by Cardinal Bellarmine, under order of Pope Paul V, that he shouldn't discuss or defend that theory any further. Galileo knew the consequences if he failed to comply, and fell silent on the subject. For seven cautious years he channeled his efforts into less perilous pursuits, such as harnessing his Jovian satellites in the service of navigation, to help sailors discover their longitude at sea. He studied poetry and wrote literary criticism. Modifying his telescope, he developed a compound microscope. "I have observed many tiny animals with great admiration," he reported, "among which the flea is quite horrible, the gnat and the moth very beautiful; and with great satisfaction I have seen how flies and other little animals can walk attached to mirrors, upside down."
But the siren of the new cosmos continued to call to Galileo and, in the summer of 1623, shortly after his sister's death, he found reason to turn his attention back to the Sun-centered universe. The old pope had died and a friend of Galileo's, Cardinal Maffeo Barberini, had ascended the throne of Saint Peter to become the Supreme Pontiff Urban VIII. Years earlier, Galileo had demonstrated his telescope to him and the two had even taken the same side one night in a debate on the nature of buoyancy at the Florentine court. Urban, for his part, had shown his admiration for Galileo by writing a poem for him, mentioning the sights revealed by "Galileo's glass." He brought an intellectualism and an interest in scientific inquiry to the papacy not shared by his immediate predecessors, and he gave Galileo vague permission to write a book about how the planetary motions appear to be. At the same time, it was made clear that any treatment of Copernican theory was to be in terms of a mathematical proposition only. In the final analysis, there could be doubting that the Earth stood at the center of the universe, just as the Church stood at the center of the world.
However, the temptation to speak his mind freely was too much for Galileo. In his Dialogo sopra i due massimi sistemi del mondo (Dialogues on the Two Chief Systems of the World), published in 1632, he pokes fun at the Church for its antiquated outlook. As in the case of his Two New Sciences, which came out six years later, the book is presented as a conversation between three men: the dull-witted Simplicio, who represents Church opinion and supports the Earth-centered hypothesis, Salviati, an intelligent man who stands for Galileo's views, and Sagredo, a wise and pragmatic man who is persuaded that Salviati's (Galileo's) views are correct. Simplicio's arguments in support of the Aristotelian worldview are invariably demolished by the other two, leaving the Copernican model effectively unchallenged.
Galileo had gone too far for his own good. Aged 70 and infirm, he was summoned to Rome to face the Inquisition. Accused of heresy, he explained that his dialogue was merely trying to present all sides in the debate. But given his overt portrayal of Simplicio as an out-of-touch halfwit, that was scarcely a credible defense. His trial lasted two months, at the end of which the book was banned and Galileo, under threat of torture, was forced to recant. "I abjure, curse and detest the aforesaid errors and heresies," he declared, "and I swear that in future I will never again say or assert, verbally or in writing, anything that might furnish occasion for a similar suspicion regarding me." Thus Galileo avoided Bruno's fate, but at what cost. One of the greatest minds of the Renaissance was put under house arrest for the remainder of his life. Italian science was cowed and crippled. And the Church itself suffered grievously in the long run for its ruthless condemnation of a worldview that turned out to be correct.
Well, it was correct in one essential – that the Sun, not the Earth, occupied the center of the planetary system. But, in another sense, the Copernican theory was flawed. Its weakness, like that of the Aristotelian theory it opposed, lay in its insistence that the planets moved in circles, a combination of circular orbits and Ptolemaic epicycles. But just as a new curve had been introduced by Galileo to an understanding of projectiles, so another type of curve was needed to make sense of the planetary motions.
Galileo correctly envisioned the experimental, mathematical analysis of nature as the wave of the future: "There will be opened a gateway and a road to a large and excellent science," he predicted, "into which minds more piercing than mine shall penetrate to recesses still deeper." Among the first to bear out this prophecy was a man born within a year of Galileo's death. This was Isaac Newton, an unparalleled genius who codified the laws of motion and brought gravity to the universe.
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