Also at this time, he began to think about percussive force. For many years, he thought that the correct science of these phenomena should describe how bodies change according to where they are on their paths. Specifically, it seemed that height is crucial. Since they generally work by establishing static equilibrium, time is not a feature of their action one would normally attend to. In discussing a balance, for instance, one does not normally think about how fast an arm of the balance descends, nor how fast a body on the opposite arm is rising though Galileo does in his Postils to Rocco circa —45; see Palmieri The converse is also true.
It is difficult to model dynamic phenomena that involve rates of change as balance arms moving upwards or downwards because of differential weights.
Throughout his life, he could not find systematic relations among specific gravities, heights of fall, and percussive forces. In the period —9, Galileo experimented with inclined planes and, most importantly, pendulums. These studies again exhibited to Galileo that acceleration and, therefore, time is a crucial variable. Moreover, the isochrony of the pendulum—the period depends only on the length of the cord, regardless of the weight of the bob—went some way towards showing that time is a possible term in the equilibrium or ratio that needs to be made explicit to represent motion.
It also shows that, in at least one case, time can displace weight as a crucial variable. The law of free fall—i. At first, Galileo attempted to represent this phenomenon with a velocity-distance relation, and the equivalent mean proportional relation.
Yet Galileo would not publish anything making time central to his analysis of motion until , in the Two New Sciences. In , Galileo began his work with the telescope.
However, they are remarkable insofar as they are his start at dismantling the celestial-terrestrial distinction entrenched in Aristotelian cosmology Feyerabend Perhaps the most unequivocal case of this is when he analogizes the mountains on the moon to mountains in Bohemia in the Starry Messenger. Also crucial was his discovery of the four moons circling Jupiter, which lent credence to the Copernican system since it meant that a planet-moon arrangement was not unique to the Earth.
The abandonment of the dichotomy between heavens and earth implied that all matter, whether celestial or terrestrial, is of the same kind. Further, if there is only one kind of matter, there can be only one kind of natural motion—one kind of motion that this matter has by nature. So it has to be that one law of motion will hold throughout the terrestrial and celestial realms. This is a far stronger claim than he had made in , which concerned only the terrestrial elements.
A few years later, in his Letters on Sunspots , Galileo offered new telescopic evidence that supported the Copernican theory. But these observations also served as additional reasons for dissolving the celestial-terrestrial distinction. One was that the sun is not an immutable aetherial sphere, but has changing spots maculae on its surface.
Another was that the sun rotates circularly around its axis, like the Earth. A third was the discovery that Venus undergoes a full sequence of phases like the moon , which entails that Venus revolves around the sun, and suggests that the Earth is likewise a celestial body moving around the sun. Certainly the phases of Venus contradicted the Ptolemaic ordering of the planets. Later, in , Galileo argued for a quite mistaken material thesis. In The Assayer , he tried to show that comets are sublunary phenomena and that their properties could be explained by optical refraction.
While this work stands as a masterpiece of scientific rhetoric, it is somewhat strange that Galileo should have argued against the superlunary nature of comets, which the great Danish astronomer Tycho Brahe had demonstrated earlier. Yet even with all these developments, Galileo still needed to work out general principles concerning the nature of motion for this newly unified matter.
For Galileo, by contrast, Copernicanism was also a commitment to a physically realizable cosmography. Consequently, he needed to work out, at least qualitatively, a way of thinking about the actual motions of matter. He had to devise or shall we say, discover principles of local motion that would fit a central sun, planets moving around that sun, a whirling Earth, and everything on it. This he did by introducing two new principles. In Day One of his Dialogue Concerning the Two Chief World Systems , Galileo argues that matter will move naturally along circular trajectories, neither speeding up nor slowing down.
Then, in Day Two, he introduces his version of the famous principle of the relativity of observed motion. This latter holds that observers cannot detect uniform motions they share with objects under observation; only differential motion can be seen. Of course, neither of these principles was entirely original with Galileo. They had predecessors. But no one needed them for the reasons that he did, namely that they were necessitated by a unified cosmological matter.
One key effect of these principles is that the diurnal terrestrial rotation asserted by the Copernican system is unobservable. We only notice departures from shared rotation, such as bodies falling or rising. This blunted standard objections to Copernicanism on the grounds that there is no evidence of terrestrial motion.
Having dispelled these arguments against the Copernican system, Galileo then dramatically argues in its favor. In Day Three of the Dialogue. The resulting diagram neatly corresponds to the Copernican model. In the Dialogue , things are more complicated than we have just sketched.
Galileo, as noted, argues for circular natural motion. Yet he also introduces, in places, an intrinsic tendency for rectilinear motion. For example, Galileo recognizes that a stone whirled circularly in a sling would fly off along the rectilinear tangent if released Galilei , —94; see Hooper Further, in Day Four, when he is giving his mechanical explanation of the tides, he nuances his matter theory by attributing to water an additional power of retaining an impetus for motion such that it can generate a reciprocal movement once it is sloshed against a side of a basin.
We saw it first in the De Motu around , where Galileo discusses submerged and floating bodies, but he learned much more in his dispute over floating bodies which produced the Discourse on Floating Bodies in In fact, a large part of that debate turned on the exact nature of water as matter, and what kind of mathematical proportionality could be used to correctly describe it and bodies moving in it see Palmieri ; The second science, discussed in the last two Days, deals with the principles of local motion and has been much commented upon in the Galilean literature.
But the first science, discussed in the first two Days, has been misunderstood and infrequently discussed. It has misleadingly been called the science of the strength of materials, and so seems to have found a place in history of engineering, since such a course is still taught today. However, this science is not about the strength of materials per se. Galileo realizes that, before he can work out a science of the motion of matter, he must have some way of showing that the nature of matter may be mathematically characterized.
So it is in Day One that Galileo begins to discuss how to describe mathematically or geometrically the causes of the breaking of beams. But this requires a way to reconcile mathematical description with the physical constitution of material bodies. In this vein, Galileo rejects using finite atoms as a basis for physical discussion, since they are not representable by continuously divisible mathematical magnitudes. Instead, he treats matter as composed of infinitely many indivisible—which is to say, mathematical—points.
This allows him to give mathematical accounts for various properties of matter. Among these are the density of matter, its coherence in material bodies, and the properties of the resisting media in which bodies move. The Second Day lays out the mathematical principles concerning how bodies break. Galileo does all this by reducing the problems of matter to problems of how a lever and a balance function, which renders them mathematically tractable via the law of the lever.
He had begun this back in , though this time he believes he is getting it right, showing mathematically how bits of matter solidify and stick together, and how they break into bits.
On the one hand, if Aristotle is correct, the faster fall of the heavier body will be retarded by the slower motion of the lighter body, so that the conjoined body will fall slower than the original heavy body. And yet, the conjoined body is heavier than either original body, so it should also fall faster. Hence, there is a contradiction in the Aristotelian position Gendler ; Palmieri ; Brown and Fehige This is now the motion of all matter, not just sublunary stuff, and the treatment takes the categories of time and acceleration as basic.
In the projected Fifth Day, Galileo would have treated the power of moving matter to act by impact, which he calls the force of percussion. Ultimately, Galileo was unable to give mathematical principles of this kind of interaction, but this problem subsequently became an important locus of interest.
He offered a new science of matter, a new physical cosmography, and a new science of local motion. It is in this way that Galileo developed the categories of the mechanical new science, the science of matter and motion. His new categories utilized some of the basic principles of traditional mechanics, to which he added the category of time and so emphasized acceleration. But throughout, he was working out the details about the nature of matter so that it could be understood as uniform and universal, and treated in a way that allowed for coherent discussion of the principles of motion.
It was due to Galileo that a unified matter became accepted and its nature became one of the problems for the new science that followed. After him, matter really mattered. The end of the affair is simply stated. In late , in the aftermath of the publication of the Dialogue Concerning the Two Chief World Systems , Galileo was ordered to appear in Rome to be examined by the Congregation of the Holy Office; i.
In January , a very ill Galileo made an arduous journey to Rome. From April, Galileo was called four times to hearings; the last was on June The next day, June 22, , Galileo was taken to the church of Santa Maria sopra Minerva, and ordered to kneel while his condemnation was read. I have been judged vehemently suspect of heresy, that is, of having held and believed that the sun in the center of the universe and immoveable, and that the Earth is not at the center of same, and that it does move.
Wishing however, to remove from the minds of your Eminences and all faithful Christians this vehement suspicion reasonably conceived against me, I abjure with a sincere heart and unfeigned faith, I curse and detest the said errors and heresies, and generally all and every error, heresy, and sect contrary to the Holy Catholic Church. Quoted in Shea and Artigas , When he later finished his last book, the Two New Sciences which does not mention Copernicanism at all , it had to be printed in Holland, and Galileo professed amazement at how it could have been published.
The details and interpretations of these proceedings have long been debated, and it seems that each year we learn more about what actually happened. One point of controversy is the legitimacy of the charges against Galileo, both in terms of their content and the judicial procedure.
Galileo was charged with teaching and defending the Copernican doctrine that holds the sun is at the center of the universe and the Earth moves. The status of this doctrine was cloudy. In , an internal commission of the Inquisition had determined that it was heretical, but this was not publicly proclaimed.
In , at the same time that the Inquisition was evaluating Copernicanism, they were also investigating Galileo personally—a separate proceeding of which Galileo himself was not likely aware. To confound issues further, the case against Galileo transpired in a fraught political context. Galileo was a creature of the powerful Medici and a personal friend of Pope Urban VIII, connections that significantly modulated developments Biagioli But he insisted that he did not do so because he himself believed in heliocentrism, Kelly said.
Rather, he claimed he was simply showing off his debating skills. Galileo was never tortured, however. The pope decreed that the interrogation should stop short with the mere threat of torture. He died in In his later years Galileo insisted on the truth of the geocentric solar system, Kelly said.
Jessica Wolf December 22, Today virtually every child grows up learning that the earth orbits the sun. The Dutch telescopes magnified images by 3 times; Galileo's telescopes magnified them by 8 to 30 times. At the time, astronomy, like much of science, remained under the spell of Aristotle. Almost 2, years after his death, the giant of Greek philosophy was held in such high regard that even his most suspect pronouncements were considered unimpeachable.
Aristotle had maintained that all celestial objects were perfect and immutable spheres, and that the stars made a dizzying daily journey around the center of the universe, our stationary Earth.
Why scrutinize the sky? The system had already been neatly laid out in books. Astronomers "wish never to raise their eyes from those pages," Galileo wrote in frustration, "as if this great book of the universe had been written to be read by nobody but Aristotle, and his eyes had been destined to see for all posterity.
In Galileo's day, the study of astronomy was used to maintain and reform the calendar. Sufficiently advanced students of astronomy made horoscopes; the alignment of the stars was believed to influence everything from politics to health. Certain pursuits were not in an astronomer's job description, says Dava Sobel, author of the best-selling historical memoir Galileo's Daughter So when Galileo, then 45 years old, turned his telescope to the heavens in the fall of , it was a small act of dissent.
He saw that the Milky Way was in fact "a congeries of innumberable stars," more even than his tired hand could draw. He saw the pockmarked surface of the moon, which, far from being perfectly spherical, was in fact "full of cavities and prominences, being not unlike the face of the Earth. He later saw imperfections in the Sun.
Each discovery drew Aristotle's system further into question and lent ever more support to the dangerously revolutionary view that Galileo had privately come to hold—set out just a half-century earlier by a Polish astronomer named Nicolaus Copernicus—that Earth traveled around the Sun. Like many figures whose names have endured, Galileo wasn't shy about seeking fame. His genius for astronomy was matched by a genius for self-promotion, and soon, by virtue of several canny decisions, Galileo's own star was rising.
In Tuscany, the name Medici had been synonymous with power for centuries. The Medici family acquired and wielded it through various means—public office, predatory banking and alliances with the powerful Catholic Church. Conquest of territory was a method favored in the late 16th century, when the head of the family, Cosimo I, seized many regions neighboring Florence. The family took a keen interest in science and its potential military applications.
The Medicis may have needed scientists, but scientists—and especially Galileo—needed the Medicis even more. With a mistress, three children and an extended family to support, and knowing that his questioning of Aristotelian science was controversial, Galileo shrewdly decided to court the family's favor.
In , he dedicated a book about a geometric and military compass to his student Cosimo II, the family's year-old heir apparent. Then, in , on the occasion of his publication of The Starry Messenger , which detailed his telescopic findings, Galileo dedicated to Cosimo II something far greater than a book: the very moons of Jupiter. Indeed it appears that the Maker of the Stars himself, by clear arguments, admonished me to call these new planets by the illustrious name of Your Highness before all others.
He could hardly have hoped for better patrons, as the Franklin exhibit made clear. It included scores of intricately wrought instruments from the family's collection.
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