By  :  Annica Baart,  Serife Demir,   Nicolaas Leten,  Machteld Van Mieghem,  Carolien Van Wauwe,  Margot Vercammen

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 Galileo Galilei

The story of a brilliant Italian scientist and mathematician.

 

BIOGRAPHY

Galileo was born in Pisa on February 15, 1564. His father, Vincenzo Galilei, played an important role in the musical revolution from medieval polyphony to harmonic modulation. Just as Vicenzo saw that rigid theory stifled new forms in music, so his oldest son came to see Aristotelian physical theology as limiting scientific inquiry.

Galileo was thought by monks at Vallombrosa and then entered the University of Pisa in 1581 to study Medicine. He soon turned to Philosophy and Mathematics, leaving the University without a degree in 1585. For a time he tutored privately and wrote on hydrostatics and natural motions, but he did not publish. In 1589 he became Professor of Mathematics at Pisa where he is reported to have shown his students the error of Aristoteles’ belief that speed of fall is proportional to weight, by dropping two objects of different weight simultaneously from the leaning tower. His contract was not renewed in 1592, probably because he contradicted Aristotelian professors. The same year, he was appointed to the chair of Mathematics at the University of Padua, where he remained until 1610. In 1609 he heard that a spyglass had been invented in Holland. In august of that year he presented a telescope, about as powerful as a modern field glass, to the doge of Venice. Its value for naval and maritime operations resulted in the doubling of his salary and his assurance of lifelong tenure as a professor.

At Padua, Galileo invented a calculating "compass" for the practical solution of mathematical prelims. He turned from speculative physics to careful measurements, invented the microscope, built a thermoscope, discovered the law of falling bodies and the parabolic path of projectiles, studied the motions of pendulums, and investigated mechanics and the strength of materials. He showed little interest in astronomy, although beginning in 1595 he prefered the Copernican theory –that the earth revolves around the sun- to the Aristotelian and Ptolemaic assumption that planets circle around the earth. Only the Copernican model supported Galileo’s theory, which was based on motions of the earth. He encountered serious opposition from the Catholic Church, who admonished, summoned, condemned and also compelled him to abjure his theory. In October 1632, Galileo was found guilty of heresy by the tribunal of the Holy Office in Rome. They sent him to exile in Siena and finally in December 1633, he was sentenced to house arrest to his villa in Arcetri where he died January 8, 1642. 

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Galileo's villa in Arcetri

ASTRONOMY

In 1609 Galileo heard of the invention of the telescope in Holland. Soon thereafter, he had built a much-improved version for himself. He used this to look at the moon and he was the first to report the "mare" (seas), the mountain ranges and other unexpected features. These and other observations, including the first observation of the Rings of Saturn and his careful observations of the positions of Saturn’s moons are described in his book "Siderius Nuncius" which he wrote in 1610. The observations of the sky, which Galileo carried out with his telescope, led to the discovery of   the satellites of Jupiter and to his increased adherence to the Copernican system. The phenomena, which were revealed little by little due to the increase possibility of larger lenses, are also described and illustrated by Galileo in his Siderius Nuncies.. He studied the periods and the frequencies of appearances of the satellites of Jupiter in order to develop a method for determining longitudes at sea.

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The Orbiter named after Galileo.

Nowadays scientists from the German Aerospace Center (DLR) in Berlin, where Galileo imaging team members from the DLR are working in collaboration with team members from the U.S.A. and Canada, strive to unveil the mysteries of the Jovian system including the enigma of whether an ocean exists on Jupiter's moon Europa or not.

Recently this team released many 'Galileo Images' made from Jupiter, Io and Europa.

 

HIS  CONTRIBUTION  TO  MECHANICS   AND  HIS   ANALYSIS  OF  PROJECTILE  MOTION

The contribution made by Galileo to mechanics are fundamental, despite the fact that his astronomical discoveries impressed more the Medici Grand Dukes. Galileo's investigations concerned the natural descent of bodies along planes of various inclinations, the formulation of the law which established the relationship between space traversed and time interval in free-fall, the isochronism of the oscillations of pendulums of equal lengths and, of particular importance : the motion of projectiles.

His work: "Discorsi e dimostrazioni matematiche intorno à due nuove scienze" (Dialogues of the Two New Sciences), published in 1638, was a through revolution. The importance of Galileo's work on the physics of motion is that it continued to apply the mathematical approach to the study of physical problems that had previously been treated in a non-mathematical way (Aristoteles' old approach).

Aristotelian physicists believed that only one kind of motion can take place at one time in an object and not two simultaneous motions as Galileo conceived and modern scientists have conceived until the time of Einstein. In Aristotles' theory of motion, projectiles were pushed along by an external force which was transmitted through the air. His medieval successors internalized this force in the projectile itself and called it "impetus." This impetus caused the object to move in a straight line until it was expended, at which point the object fell straight to the ground. It becomes clear that projectiles do not behave in this manner : the path of a projectile did not consist of two consecutive straight line components but was instead a smooth curve.

It was another essential insight that led Galileo, finally, to his most remarkable conclusion about projectile motion. First of all, he reasoned that a projectile shot from a cannon is not influenced by only one motion, but by two -- the motion that acts vertically is the force of gravity, and this pulls the projectile down by the times-squared law. But while gravity is pulling the object down, the projectile is also moving forward, horizontally at the same time. And this horizontal motion is uniform and constant according to his principle of inertia.

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What would happen if, instead of rolling along the horizontal plane, the ball were now allowed to simply fall freely once it got to the bottom of the plane? If Galileo were correct about the horizontal and vertical motions being independent, it would still continue to move horizontally with a uniform, constant speed, but gravity would now begin to pull it down vertically at the same time, the vertical distance increasing porportionally to the square of the time... and this is exactly what Galileo  could demonstrate.

Using an inclined plane, Galileo had performed experiments on uniformly accelerated motion, and he now used the same apparatus to study projectile motion. He placed an inclined plane on a table and provided it with a curved piece at the bottom which deflected an inked bronze ball into a horizontal direction. The ball thus accelerated rolled over the table-top with uniform motion and then fell off the edge of the table Where it hit the floor, it left a small mark. The mark allowed the horizontal and vertical distances traveled by the ball to be measured. By increasing the ball's horizontal velocity, the mark was made farther(horizontal distance) but the ball hit the ground(vertical distance) in the same time.

Galileo's extraordinary conclusion, explained in his book on the Two New Sciences, determined that the path that any projectile follows is a curve that has a  mathematical shape -- it is one the Greeks had already studied and called the parabola. Galileo brought all of the mathematical properties of parabolas to bear upon the physical problems of projectile motion and he drew exact consequences from this discovery which, as he said, could only have been achieved by the sort of exacting analysis that mathematics made possible.

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Traettorie a forma di parabola di proiettili sparati in orizzontale con velocità iniziali differenti. Il moto complessivo deriva dalla composizione di due moti distinti e indipendenti : un moto uniformemente accelerato in verticale e un moto uniforme in orizzontale. Maggiore è la velocità iniziale, più la parabola è piatta e più il proiettile alterra lontano.

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In ogni punto della traiettoria la velocità istantanea del proiettile si ottiene sommando vettorialmente la sua velocità istantanea in orrizzontale e quella in verticale.
A causa dell'accelerazione di gravità, che ogni secondo aggiunge 10 m/s alla velocità verticale, quest'ultima velocità del proiettili totale aumenta man mano che cade e diventa sempre più obliqua.

At the end of the 16th century, Galileï used an inclined plane to demonstrate that the horizontal and vertical motion of the projectile were independent and that the described curve was a parabola. Now 400 years later we can calculate and see (f.e. with the TI-83) that his great thoughts were really true ...   

HIS  CONTRIBUTION  TO  MICROSCOPY,  THERMOMETRY   AND  MAGNETISM

In the early years of the seventeenth century Galileo adapted a telescope for the viewing of extremely small objects. Between 1619 and 1624 he began to produce microscopes or "occhialini" as he called them. The Galileian microscope is made up of the tube of a telescope, of reduced size, furnished with two lenses. Galileo gave his "occhialino" to various people. He sent a letter to Federigo Cesi, accompanying the instrument, in which he explained the means by which it was focussed and the arrangement of objects for observation.

Already Galileo discovered that the density of liquid is changed by varying temperatures. The Galileo thermometers are manufactured on this principle. The temperature can be read from the lead discs hanging from the coloured spheres. The weight differential of the spheres is only 2/1000 grams and ensures an accuracy of 1°C. The spheres descend slowly when the temperatures increases and rise when the temperature falls. The temperature and can be read from the lowest lead disc of the high floating spheres.
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Between 1600 and 1609 Galileo devoted himself to studying magnetism, inspired by William Gilbert's De Magnete. He attempted to increase the strength of loadstones by means of special armatures. One of these was given to Grand Duke Ferdinand II by Galileo.

THE CONTROVERSY WITH THE CHURCH

Galileo was an advocate from the heliocentric system of Copernicus. And when he succeeded in constructing a telescope he was as much convinced again. He discovered that the planet Jupiter has satellites, thus displaying a solar system in miniature and Venus and Mercury should exhibit phases like those of the moon.

Those discoveries, which made Galileo also famous, were also the cause of his lamentable controversy with ecclesiastical authority who assumed that the doctrine of Copernicus was contrary to the Holy Scripture. Galileo didn't think this theory should contradict the doctrines of the church. As he said  "The Bible teaches how to go to heaven, not how the heavens go". At present it is assumed that the opposition which Copernicanism encoutered at the hands of the clergy was prompted by hatred of science and a desire to keep the minds of men in the darkness of ignorance. Galileo was not the only mathematician / scientist to place the sun at the center of the Solar System, but he was the first to publish his conclusions in the language of the common people(Italian) and set himself with his habitual vehemence to convince others.

At first nobody raised alarm. The great work of Copernicus was published nearly three quarters of a century ago with the permission of the pope and the protection of two distinguished Churchmen and was never condemned. Galileo, coming to Rome in 1611, was received in triumph, after he demonstrated his discoveries.

It was not until three years later that trouble arose, the ecclesiastical authorities taking alarm at the persistence with which Galileo proclaimed the truth of the Copernican doctrine.

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In 1614, Father Tommaso Caccini denounced the opinions of Galileo on the motion of the Earth from the pulpit of Santa Maria Novella, judging them to be erroneous. Galileo therefore went to Rome, where he defended himself.  In 1616, the Holy Office condamned the heliocentric system and Galileo was forbidden to defend the doctrine of Copernicus.  Cardinal Bellarmino, who had to say this decision to Galileo, told him  that he could exhibit the Copernican system as an mathematical hypothesis but not establish it as a fact. In 1624 Galileo visited again Rome, but to Galileo's dissapointment the Pope would not annul the former judgement.

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Later he attempted to evade the prohibition by composing a work namely his "Dialogue Concerning the Two Chief   Worl Systems" in which a Ptolemist is utterly routed and confounded by two Copernicans. This work was published in 1632 and was taken by the Roman authorities as a direct challenge.In October of 1632 he was summoned by the Holy Office to Rome and condamned to swear off his "mistake". Seventy years old, ill, and threatened with torture, Galileo fell to his knees and recanted the Copernican Solar System with the sworn statement : "I do abjure...the said errors and heresies...I shall never again speak...such things ". Legend has it that upon arising from his knees he muttered under his breath :
" E pur si muove! " or " Nevertheless, the earth does move!".  

He was sent to exile in Siena and finally, in December of 1633, he was allowed to retire (under house arrest) to his villa in Arcetri, the Gioiello,  until his death nine years later.

Modern research has cleared up some things. It is totally uncertain that he was - as is constantly stated - either tortured or blinded by his persecutors(though in 1637, five years before his death, he became totally blind) or that he was refused to be buried in consecrated ground.

In 1822 the church's ban on the works of Galileo was lifted. In 1979 Pope John Paul II appointed a commission, and on March 1, 1984, the Vatican newspaper L'Observatore Romano said : "The so called heresy of Galileo does not seem to have any foundation, neither theologically nor under canon law". Finally, in 1992, Pope John Paul II declared that the church was mistaken in condemning Galileo.

Sources

http://galileo.imss.firenze.it/museo/4/index.html
http://galileo.ivv.nasa.gov/
http://www.pd.astro.it/ars/arshtml/mathofmotion2.html
http://galileo.ivv.nasa.gov/sepo/atjup/newim.html, http://www.jpl.nasa.gov/galileo/sepo/atjup/newim.html
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Galileo.html
http://es.rice.edu/ES/humsoc/Galileo/Student_Work/Experiment95/paraintr.html

Wordatlas of Encarta
Classic Math, History Topics for the Classroom, Art Johnson, Dale Seymour Publications - California(USA)
Dal pendolo ai quark, 1 Meccanica, Termologia, Acustica, Ugo Amaldi, Ed. Zanichelli - Bologna(Italy)

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