Forces in Physics: A Historical Perspective (Greenwood Guides to Great Ideas in Science)

Steven N. Shore's Forces in Physics: A Historical Perspective (Greenwood PDF

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Despite being a genuinely pious Roman Catholic, [26] Galileo fathered three children out of wedlock with Marina Gamba. They had two daughters, Virginia born in and Livia born in , and a son, Vincenzo born in Because of their illegitimate birth, their father considered the girls unmarriageable, if not posing problems of prohibitively expensive support or dowries, which would have been similar to Galileo's previous extensive financial problems with two of his sisters. Both girls were accepted by the convent of San Matteo in Arcetri and remained there for the rest of their lives.

Livia took the name Sister Arcangela and was ill for most of her life. Vincenzo was later legitimised as the legal heir of Galileo and married Sestilia Bocchineri.

Although Galileo seriously considered the priesthood as a young man, at his father's urging he instead enrolled in at the University of Pisa for a medical degree. To him, it seemed, by comparison with his heartbeat, that the chandelier took the same amount of time to swing back and forth, no matter how far it was swinging. When he returned home, he set up two pendulums of equal length and swung one with a large sweep and the other with a small sweep and found that they kept time together.

It was not until the work of Christiaan Huygens , almost one hundred years later, that the tautochrone nature of a swinging pendulum was used to create an accurate timepiece. However, after accidentally attending a lecture on geometry, he talked his reluctant father into letting him study mathematics and natural philosophy instead of medicine. Galileo also studied disegno , a term encompassing fine art, and, in , obtained the position of instructor in the Accademia delle Arti del Disegno in Florence, teaching perspective and chiaroscuro.

Being inspired by the artistic tradition of the city and the works of the Renaissance artists, Galileo acquired an aesthetic mentality. While a young teacher at the Accademia, he began a lifelong friendship with the Florentine painter Cigoli , who included Galileo's lunar observations in one of his paintings.

In , he was appointed to the chair of mathematics in Pisa. In , his father died, and he was entrusted with the care of his younger brother Michelagnolo. In , he moved to the University of Padua where he taught geometry, mechanics , and astronomy until His multiple interests included the study of astrology , which at the time was a discipline tied to the studies of mathematics and astronomy.

Cardinal Bellarmine had written in that the Copernican system could not be defended without "a true physical demonstration that the sun does not circle the earth but the earth circles the sun". For Galileo, the tides were caused by the sloshing back and forth of water in the seas as a point on the Earth's surface sped up and slowed down because of the Earth's rotation on its axis and revolution around the Sun.

He circulated his first account of the tides in , addressed to Cardinal Orsini. As a general account of the cause of tides, however, his theory was a failure. If this theory were correct, there would be only one high tide per day. Galileo and his contemporaries were aware of this inadequacy because there are two daily high tides at Venice instead of one, about twelve hours apart.

Galileo dismissed this anomaly as the result of several secondary causes including the shape of the sea, its depth, and other factors. It began as a dispute over the nature of comets, but by the time Galileo had published The Assayer Il Saggiatore in , his last salvo in the dispute, it had become a much wider controversy over the very nature of science itself.

Because The Assayer contains such a wealth of Galileo's ideas on how science should be practised, it has been referred to as his scientific manifesto. Grassi concluded that the comet was a fiery body which had moved along a segment of a great circle at a constant distance from the earth, [47] and since it moved in the sky more slowly than the moon, it must be farther away than the moon. Grassi's arguments and conclusions were criticised in a subsequent article, Discourse on Comets , [48] published under the name of one of Galileo's disciples, a Florentine lawyer named Mario Guiducci , although it had been largely written by Galileo himself.

In its opening passage, Galileo and Guiducci's Discourse gratuitously insulted the Jesuit Christopher Scheiner , [51] and various uncomplimentary remarks about the professors of the Collegio Romano were scattered throughout the work. The Assayer was Galileo's devastating reply to the Astronomical Balance. Galileo's dispute with Grassi permanently alienated many of the Jesuits who had previously been sympathetic to his ideas, [61] and Galileo and his friends were convinced that these Jesuits were responsible for bringing about his later condemnation.

In the whole world prior to Galileo's conflict with the Church, the majority of educated people subscribed either to the Aristotelian geocentric view that the earth was the center of the universe and that all heavenly bodies revolved around the Earth, [64] or the Tychonic system that blended geocentrism with heliocentrism. Opposition to heliocentrism and Galileo's writings combined religious and scientific objections. Scientific opposition came from Tycho Brahe and others and arose from the fact that, if heliocentrism were true, an annual stellar parallax should be observed, though none was.

Copernicus and Aristarchus had correctly postulated that parallax was negligible because the stars were so distant. However, Brahe had countered that, since stars appeared to have measurable size, if the stars were that distant, they would be gigantic, and in fact far larger than the Sun or any other celestial body.

In Brahe's system, by contrast, the stars were a little more distant than Saturn, and the Sun and stars were comparable in size. Religious opposition to heliocentrism arose from Biblical references such as Psalm Galileo defended heliocentrism based on his astronomical observations of Sidereus Nuncius In December , the Grand Duchess Christina of Florence confronted one of Galileo's friends and followers, Benedetto Castelli , with biblical objections to the motion of the earth. According to Maurice Finocchiaro, this was done in a friendly and gracious manner, out of curiosity.

Prompted by this incident, Galileo wrote a letter to Castelli in which he argued that heliocentrism was actually not contrary to biblical texts, and that the bible was an authority on faith and morals, not on science.

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This letter was not published, but circulated widely. By , Galileo's writings on heliocentrism had been submitted to the Roman Inquisition by Father Niccolo Lorini, who claimed that Galileo and his followers were attempting to reinterpret the Bible, which was seen as a violation of the Council of Trent and looked dangerously like Protestantism. At the start of , Monsignor Francesco Ingoli initiated a debate with Galileo, sending him an essay disputing the Copernican system. Galileo later stated that he believed this essay to have been instrumental in the action against Copernicanism that followed.

It borrowed primarily from the arguments of Tycho Brahe, and it notedly mentioned Brahe's argument that heliocentrism required the stars to be much larger than the Sun. Ingoli wrote that the great distance to the stars in the heliocentric theory "clearly proves Pope Paul V instructed Cardinal Bellarmine to deliver this finding to Galileo, and to order him to abandon the opinion that heliocentrism was physically true.

On 26 February, Galileo was called to Bellarmine's residence and ordered:. The decree of the Congregation of the Index banned Copernicus's De Revolutionibus and other heliocentric works until correction. For the next decade, Galileo stayed well away from the controversy. Barberini was a friend and admirer of Galileo, and had opposed the condemnation of Galileo in Galileo's resulting book, Dialogue Concerning the Two Chief World Systems , was published in , with formal authorization from the Inquisition and papal permission. Earlier, Pope Urban VIII had personally asked Galileo to give arguments for and against heliocentrism in the book, and to be careful not to advocate heliocentrism.

He made another request, that his own views on the matter be included in Galileo's book. Only the latter of those requests was fulfilled by Galileo. Whether unknowingly or deliberately, Simplicio, the defender of the Aristotelian geocentric view in Dialogue Concerning the Two Chief World Systems , was often caught in his own errors and sometimes came across as a fool. Indeed, although Galileo states in the preface of his book that the character is named after a famous Aristotelian philosopher Simplicius in Latin, "Simplicio" in Italian , the name "Simplicio" in Italian also has the connotation of "simpleton".

Most historians agree Galileo did not act out of malice and felt blindsided by the reaction to his book. Galileo had alienated one of his biggest and most powerful supporters, the Pope, and was called to Rome to defend his writings [83] in September He finally arrived in February and was brought before inquisitor Vincenzo Maculani to be charged. Throughout his trial, Galileo steadfastly maintained that since he had faithfully kept his promise not to hold any of the condemned opinions, and initially he denied even defending them.

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However, he was eventually persuaded to admit that, contrary to his true intention, a reader of his Dialogue could well have obtained the impression that it was intended to be a defence of Copernicanism. In view of Galileo's rather implausible denial that he had ever held Copernican ideas after or ever intended to defend them in the Dialogue , his final interrogation, in July , concluded with his being threatened with torture if he did not tell the truth, but he maintained his denial despite the threat.

According to popular legend, after recanting his theory that the Earth moved around the Sun, Galileo allegedly muttered the rebellious phrase " And yet it moves ". The earliest known written account of the legend dates to a century after his death, but Stillman Drake writes "there is no doubt now that the famous words were already attributed to Galileo before his death". After a period with the friendly Ascanio Piccolomini the Archbishop of Siena , Galileo was allowed to return to his villa at Arcetri near Florence in , where he spent part of his life under house arrest.

Galileo was ordered to read the seven penitential psalms once a week for the next three years. However, his daughter Maria Celeste relieved him of the burden after securing ecclesiastical permission to take it upon herself. It was while Galileo was under house arrest that he dedicated his time to one of his finest works, Two New Sciences. Here he summarised work he had done some forty years earlier, on the two sciences now called kinematics and strength of materials , published in Holland to avoid the censor.

This book has received high praise from Albert Einstein. He went completely blind in and was suffering from a painful hernia and insomnia , so he was permitted to travel to Florence for medical advice.

Forces in Physics

Dava Sobel argues that prior to Galileo's trial and judgement for heresy, Pope Urban VIII had become preoccupied with court intrigue and problems of state, and began to fear persecution or threats to his own life. In this context, Sobel argues that the problem of Galileo was presented to the pope by court insiders and enemies of Galileo. Having been accused of weakness in defending the church, Urban reacted against Galileo out of anger and fear.

Galileo continued to receive visitors until , when, after suffering fever and heart palpitations, he died on 8 January , aged Galileo made original contributions to the science of motion through an innovative combination of experiment and mathematics. Galileo's father, Vincenzo Galilei , a lutenist and music theorist, had performed experiments establishing perhaps the oldest known non-linear relation in physics: Thus, a limited amount of mathematics had long related music and physical science, and young Galileo could see his own father's observations expand on that tradition.

Galileo was one of the first modern thinkers to clearly state that the laws of nature are mathematical. In The Assayer , he wrote "Philosophy is written in this grand book, the universe It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures; He was often willing to change his views in accordance with observation. In order to perform his experiments, Galileo had to set up standards of length and time, so that measurements made on different days and in different laboratories could be compared in a reproducible fashion.

This provided a reliable foundation on which to confirm mathematical laws using inductive reasoning.

Galileo showed a modern appreciation for the proper relationship between mathematics, theoretical physics, and experimental physics. He understood the parabola , both in terms of conic sections and in terms of the ordinate y varying as the square of the abscissa x. Galilei further asserted that the parabola was the theoretically ideal trajectory of a uniformly accelerated projectile in the absence of air resistance or other disturbances.

He conceded that there are limits to the validity of this theory, noting on theoretical grounds that a projectile trajectory of a size comparable to that of the Earth could not possibly be a parabola, [] but he nevertheless maintained that for distances up to the range of the artillery of his day, the deviation of a projectile's trajectory from a parabola would be only very slight. Based only on uncertain descriptions of the first practical telescope which Hans Lippershey tried to patent in the Netherlands in , [] Galileo, in the following year, made a telescope with about 3x magnification.

He later made improved versions with up to about 30x magnification. He could also use it to observe the sky; for a time he was one of those who could construct telescopes good enough for that purpose. On 25 August , he demonstrated one of his early telescopes, with a magnification of about 8 or 9, to Venetian lawmakers. His telescopes were also a profitable sideline for Galileo, who sold them to merchants who found them useful both at sea and as items of trade. He published his initial telescopic astronomical observations in March in a brief treatise entitled Sidereus Nuncius Starry Messenger.

Tycho and others had observed the supernova of Ottavio Brenzoni's letter of 15 January to Galileo brought the supernova and the less bright nova of to Galileo's notice. Galileo observed and discussed Kepler's supernova in Since these new stars displayed no detectable diurnal parallax , Galileo concluded that they were distant stars, and, therefore, disproved the Aristotelian belief in the immutability of the heavens.

On 7 January , Galileo observed with his telescope what he described at the time as "three fixed stars, totally invisible [] by their smallness", all close to Jupiter, and lying on a straight line through it. On 10 January, Galileo noted that one of them had disappeared, an observation which he attributed to its being hidden behind Jupiter.

Within a few days, he concluded that they were orbiting Jupiter: He discovered the fourth on 13 January. These satellites are now called Io , Europa , Ganymede , and Callisto. His observations of the satellites of Jupiter caused a revolution in astronomy: From September , Galileo observed that Venus exhibited a full set of phases similar to that of the Moon.

The heliocentric model of the solar system developed by Nicolaus Copernicus predicted that all phases would be visible since the orbit of Venus around the Sun would cause its illuminated hemisphere to face the Earth when it was on the opposite side of the Sun and to face away from the Earth when it was on the Earth-side of the Sun.

On the other hand, in Ptolemy's geocentric model it was impossible for any of the planets' orbits to intersect the spherical shell carrying the Sun.

Traditionally, the orbit of Venus was placed entirely on the near side of the Sun, where it could exhibit only crescent and new phases. It was, however, also possible to place it entirely on the far side of the Sun, where it could exhibit only gibbous and full phases. After Galileo's telescopic observations of the crescent, gibbous and full phases of Venus, the Ptolemaic model became untenable. Thus in the early 17th century, as a result of his discovery, the great majority of astronomers converted to one of the various geo-heliocentric planetary models, [] such as the Tychonic, Capellan and Extended Capellan models, [] each either with or without a daily rotating Earth.

These all had the virtue of explaining the phases of Venus without the vice of the 'refutation' of full heliocentrism's prediction of stellar parallax.

Galileo's discovery of the phases of Venus was thus arguably his most empirically practically influential contribution to the two-stage transition from full geocentrism to full heliocentrism via geo-heliocentrism. Galileo observed the planet Saturn , and at first mistook its rings for planets, thinking it was a three-bodied system. When he observed the planet later, Saturn's rings were directly oriented at Earth, causing him to think that two of the bodies had disappeared. The rings reappeared when he observed the planet in , further confusing him. Galileo also observed the planet Neptune in It appears in his notebooks as one of many unremarkable dim stars.

He did not realise that it was a planet, but he did note its motion relative to the stars before losing track of it. Galileo made naked-eye and telescopic studies of sunspots. An apparent annual variation in their trajectories, observed by Francesco Sizzi and others in —, [] also provided a powerful argument against both the Ptolemaic system and the geoheliocentric system of Tycho Brahe.

In the middle was Mark Welser , to whom Scheiner had announced his discovery, and who asked Galileo for his opinion. Prior to Galileo's construction of his version of a telescope, Thomas Harriot , an English mathematician and explorer, had already used what he dubbed a "perspective tube" to observe the moon.

Reporting his observations, Harriot noted only "strange spottednesse" in the waning of the crescent, but was ignorant to the cause. Galileo, due in part to his artistic training [34] and the knowledge of chiaroscuro , [33] had understood the patterns of light and shadow were, in fact, topographical markers. While not being the only one to observe the moon through a telescope, Galileo was the first to deduce the cause of the uneven waning as light occlusion from lunar mountains and craters. In his study, he also made topographical charts, estimating the heights of the mountains.

The moon was not what was long thought to have been a translucent and perfect sphere, as Aristotle claimed, and hardly the first "planet", an "eternal pearl to magnificently ascend into the heavenly empyrian", as put forth by Dante. Galileo is sometimes credited with the discovery of the lunar libration in latitude in , [] although Thomas Harriot or William Gilbert might have done it before. Galileo observed the Milky Way , previously believed to be nebulous , and found it to be a multitude of stars packed so densely that they appeared from Earth to be clouds.

He located many other stars too distant to be visible with the naked eye. He observed the double star Mizar in Ursa Major in In the Starry Messenger , Galileo reported that stars appeared as mere blazes of light, essentially unaltered in appearance by the telescope, and contrasted them to planets, which the telescope revealed to be discs. But shortly thereafter, in his Letters on Sunspots , he reported that the telescope revealed the shapes of both stars and planets to be "quite round". From that point forward, he continued to report that telescopes showed the roundness of stars, and that stars seen through the telescope measured a few seconds of arc in diameter.

As described in his Dialogue Concerning the two Chief World Systems , his method was to hang a thin rope in his line of sight to the star and measure the maximum distance from which it would wholly obscure the star. From his measurements of this distance and of the width of the rope, he could calculate the angle subtended by the star at his viewing point.

Like most astronomers of his day, Galileo did not recognise that the apparent sizes of stars that he measured were spurious, caused by diffraction and atmospheric distortion see seeing disk or Airy disk , and did not represent the true sizes of stars. However, Galileo's values were much smaller than previous estimates of the apparent sizes of the brightest stars, such as those made by Tycho Brahe see Magnitude and enabled Galileo to counter anti-Copernican arguments such as those made by Tycho that these stars would have to be absurdly large for their annual parallaxes to be undetectable.

Galileo made a number of contributions to what is now known as engineering , as distinct from pure physics. Between and , Galileo devised and improved a geometric and military compass suitable for use by gunners and surveyors. For gunners, it offered, in addition to a new and safer way of elevating cannons accurately, a way of quickly computing the charge of gunpowder for cannonballs of different sizes and materials.

As a geometric instrument, it enabled the construction of any regular polygon , computation of the area of any polygon or circular sector, and a variety of other calculations. Under Galileo's direction, instrument maker Marc'Antonio Mazzoleni produced more than of these compasses, which Galileo sold along with an instruction manual he wrote for 50 lire and offered a course of instruction in the use of the compasses for lire. In about , Galileo constructed a thermometer , using the expansion and contraction of air in a bulb to move water in an attached tube. In , Galileo was, along with Englishman Thomas Harriot and others, among the first to use a refracting telescope as an instrument to observe stars, planets or moons.

The name "telescope" was coined for Galileo's instrument by a Greek mathematician, Giovanni Demisiani , [] at a banquet held in by Prince Federico Cesi to make Galileo a member of his Accademia dei Lincei. In , he used a telescope at close range to magnify the parts of insects. He gave one of these instruments to Cardinal Zollern in May of that year for presentation to the Duke of Bavaria, [] and in September, he sent another to Prince Cesi. Whether you provide known the inventor or download, if you agree your enhanced and globalised requests quickly distributions will get real conditions that remain well for them.

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