Galileo Galilei (1564-1642), often referred to simply as Galileo, was an Italian physicist and astronomer who used the telescope to study the heavens, contributed to the field of mechanical physics, proposed the heliocentric model of Copernicus as the accurate universal model, and later in life had a famous dispute with the Catholic Church in which they labeled him a heretic. The backdrop was the Reformation. Despite the Church being in a divided state, on this issue the Catholic Church spoke for all of Christianity. Protestants Martin Luther and John Calvin had also both disputed the heliocentric model.
Galileo first came to prominence when, in 1604, he demonstrated that a supernova was further away from the earth than the moon. At the time that was shocking as it was not expected within the earth-centered framework that existed at that time. It was also around this time that he invented a geometric and military compass. Galileo sought a patron, and made overtures to the Cosimo family, but had to supplement his income by selling his compass to students along with a handbook on how to use it. He also invented a primitive thermometer and a barometer.
Galileo was born on February 15, 1564 in Pisa, Italy. His father was a Florentine, a member of a noble family, but impoverished; to make ends meet he was a merchant in cloth. He was also reputed for his skill in mathematics and music, and these traits he passed on to his son. At the age of 13 Galileo was sent to the monastery at Vallombrosa, where he studied Greek and Latin for a short period of time.
At the age of 17 he entered the University of Pisa, where he studied medicine, ostensibly to prevent a career in math or music by his father. His advice was sought out in the world of art; he had become a respected critic during his time there, but is was in math where he excelled. In his first year he discovered the isochronism in the swing of the pendulum, and developed formulas related to the function of various machines. His stay at the university was not long - he was compelled to leave due to lack of funding - but he continued his investigative work in mathematics; he wrote and published for the Florentine Academy several papers on the center of gravity in solids, the hydrostatic balance, and the place and overall dimensions of Dante's Inferno.
As Galileo became more well known, he was commissioned by the city father's of Florence to find a way to cast a new bell for the town. The local artisans had been unsuccessful, as the wooden mold for the bell's inner surface kept rising when molten metal was poured between it and the mold for the outer surface. Using Archimedes as his guide, Galileo explained that bodies must be heavier than the volume of liquid they displace or they will float to the surface. This view went against Aristotle who had claimed that objects floated when they "pierced" the skin of a liquid and escaped from it. Based on what Galileo told them, the Florence bell-casters succeeded in their task by increasing the pressure on the inner mold. Since Galileo had also recently shown that Aristotle was wrong about falling objects, he was walking on sensitive ground.
Despite his growing fame, Galileo found it difficult to find employment; he applied for teaching positions and had even thought of seeking fortune by heading east into Asia. But he did gain a position as a lecturer on mathematics at the University of Pisa in 1589, where during the next two years he also conducted experiments on falling bodies, including the famous experiment from the Leaning Tower; the theory that heavy objects fall faster than light ones was found to be a consequence of air resistance, not gravity. His discoveries would cause a rift between him and the Aristotelian faculty; a paper he wrote ridiculing the the university's rules made matters worse and would cause his resignation in 1591. He would assume the chair of mathematics at the University of Padua a short time later.
It was there he taught and lectured for the next eighteen years, on subjects as diverse as the sphere, mechanics, accelerated motion, military architecture, and gnomonics. He invented a machine for raising water, an air thermometer, and the geometrical compass. He had during his time in Padua become so well-known that his lecture hall seated two thousand people, which included many highly-learned and respected individuals from all parts of Europe, who took back with them the treatises which he wrote prolifically.
His telescope and astronomical discoveries
His most famous discovery came in June or July of 1609, when he had learned that the Dutchman Hans Lippershey and several others had taken magnifying glasses and constructed the first working telescope. Without knowing the technical details of the construction of the device, he was able to design and create one for himself, and he is credited in being the first to train the new device towards the heavens. Over time he continued to upgrade it. He found mountains on the Moon, viewed Venus and Jupiter, and with some protection located sunspots.
In 1610 while observing Jupiter he discovered four smaller bodies - the Galilean moons of Io, Europa, Ganymede, Callisto - revolving around it, which eventually became one of Galileo's most well-known and important discoveries: heliocentrism. Galileo's two main evidences in this respect both came from the ability of his telescope to carefully examine the heavens, and his observations of Jupiter and Venus provided strong evidence against geocentrism (at the time this doctrine was not simply limited to the earth's being the center of the universe, but also that no extraterrestrial orbits existed). 
NASA scientist Ron Baalke wrote
|“||Galileo first observed the moons of Jupiter on January 7, 1610 through a homemade telescope. He originally thought he saw three stars near Jupiter, strung out in a line through the planet. The next evening, these stars seemed to have moved the wrong way, which caught his attention. Galileo continued to observe the stars and Jupiter for the next week. On January 13, a fourth star appeared. After a few weeks, Galileo had observed that the four stars never left the vicinity of Jupiter and appeared to be carried along with the planet, and that they changed their position with respect to each other and Jupiter. Finally, Galileo determined that what he was observing were not stars, but planetary bodies that were in orbit around Jupiter. ||”|
He published his finding in a paper titled "The Starry Messenger" which he dedicated to Grand Duke Cosimo II. His discoveries and publication led him to be appointed as Grand Duke court mathematician, a position he had coveted.
Until the sixteenth century, the prevailing view was that the Sun, Moon, stars and planets circled the Earth (the geocentric system, based on the second century work of Ptolemy). Puzzled astronomers noticed that Mars, Jupiter and Saturn sometimes seemed to move backwards, but their motions were well within the predictions of Ptolemy's theory. The moon was considered to have more freedom of movement.
A Polish astronomer, Nicolaus Copernicus (1473-1543), published a model of the solar system De Revolutionibus in 1543, in which the earth and other planets circled the sun. The Catholic Church endorsed the book.[note 1] The book’s preface (which was not written by Copernicus) argued that astronomical models have merit if they correctly predict observations, even if the underlying hypotheses cannot be proved. The scientific evidence was inconclusive.However, ancient Greek thought was idolized since it was re-discovered several hundred years before, being viewed almost on par with the Bible itself. The Ptolemaic system was the prevailing view at the time. Initially it was not the theologians who balked at Galileo's ideas, but rather mathematicians at the University of Pisa who were so outraged that he challenged Aristotle that they refused to even look through his telescope at the stars. Galileo wrote a privately-circulated pamphlet which argued that the Bible should be interpreted in the light of increasing knowledge, and warning that scientific opinion should not be treated as an article of faith. In this way he matched the great church father Saint Augustine. Quoting another of the early church fathers Galileo wrote
The intention of the Holy Ghost is to teach us how one goes to heaven, not how heaven goes.
In 1613 a Dominican friar, Tommaso Caccini, got a hold of Galileo's writing and preached a sermon against him. A mangled version of Galileo's writing was sent to Rome. Galileo heard of this and sent the full version. He was not terribly alarmed, knowing that many of the best minds in Italy, including the Vatican's mathematicians, were convinced on the heliocentric universe that his works had help to substantiate. Caccini's Dominican superior was so embarrassed that he sent a letter of apology to Galileo.
Caccini wasn't through, however, and gave an unsolicited deposition to the Inquisition about Galileo's views, which largely demonstrated his own ignorance on the subject. Nevertheless, the theologians who were given the case ruled in a manner that was not pleasing to Galileo when it was handed down. Galileo was told by the Inquisition that he must only use Copernican concepts as a hypothesis for the sake of calculation, without claiming that they had been literally proven true. Because Galileo had overstated the scientific case for the heliocentric theory and given some dubious theological arguments, the Inquisition ruling decided that: 1) the immobility of the Sun at the center of the universe was absurd in philosophy and formally heretical, and that 2) the mobility of Earth was absurd in philosophy and at least erroneous in theology.  The following month the Church’s Index of Forbidden Books required that nine sentences in Copernicus's book be corrected.
Galileo got approval from Rome to write his book Dialogue on the Tides, which discussed both the Ptolemaic and Copernican hypotheses, as long as it discussed both systems and did not draw a conclusion that would make the heliocentric world view be viewed as fact instead of theory. Rome changed the title to Dialogue on the Two Chief World Systems and it was published in Florence in 1632. Unfortunately for Galileo, the work was not made to be evenhanded. Indeed, the Ptolemaic character, called 'Simplicius' often stumbled over his own errors and seemed quite foolish. Galileo had moved out of bounds and even his name 'Simplicius' seemed designed to embarrass the Church. The Church felt they had made themselves clear. At a different time, the reaction might have been different, but it was in the middle of the 30 years war, the most deadly war in Europe ever fought between Catholics and Protestants, and embarrassing one side could result in the loss in life. Galileo claimed approval by the Church for his entire work, and that was simply false. It would be analogous today to someone speaking in the name of an organization in a way that embarrasses it, and the result is typically the same: the person is promptly fired and, if the harm is serious, often prosecuted. Put another way, Galileo's act was treasonous at a time of war. The Catholic Church felt compelled at a time of crisis to clarify its authority. At no time was there any claim of papal infallibility; this was a matter of misrepresentation of the Church's position.
The Church officials, who felt Galileo had embarrassed them, found that Galileo had erred by advocating in the name of the Church that heliocentrism was scientifically proven. This was not compatible with the Inquisition's 1616 ruling and what Galileo had recently been told. In 1633 Galileo was ordered to stand trial in Rome. Galileo could have left the Church but instead chose to submit voluntarily its authority and decision. According to the terms of his sentence, renounced his thesis of his book. At first he was sentenced to life imprisonment, but this was immediately commuted to luxurious house arrest. His book was burned, and the sentence against him was read aloud in public in every university.  Galileo went back to studying motion and mechanics in his private villa. He received the Pope's personal blessing before he died, which is a rare honor.
Dialogues Concerning Two New Sciences
Galileo’s last book, the 1638 work Dialogues Concerning Two New Sciences, dealt with motion and mechanics. This work helped inspire Isaac Newton to create his theory of gravity, which linked Galileo’s mathematics and physics to Kepler’s laws of planetary movement.
In Two New Sciences, Galileo revealed a sophisticated understanding of engineering and what now would be called dimensional analysis, the way in which the proportions of an engineering structure need to change as the size of the structure is scaled up. He applied this to biology, explaining why the bones of a large animal need to be thicker in proportion to their size than those of smaller animals.
In an age before stopwatches, Galileo was able to make quantitative observations of uniformly-accelerated motion, using his pulse as a time reference and watching the slow acceleration of objects moving down inclined planes.
This book contains his famous discussion and thought experiment, in which he shows both by logic and by appeal to experiment that light and heavy objects fall at the same speed (contradicting Aristotle). One of his discussants says "But I, Simplicio, who have made the test can assure you that a cannon ball 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.".
Another discussant points out that this result is logical, by positing a large stone that moves at a speed of eight and a smaller one which moves at a speed of four, and showing that this leads to a contradiction if the stones are tied together. Since the smaller stone tends to fall more slowly, it ought to retard the motion of the larger one, so the combination should fall more slowly than the large stone by itself. However, "the two stones when tied together make a stone larger than before," and hence ought to fall more quickly than the large stone by itself.
It is interesting to see how Galileo was able to obtain quantitative results in physics before algebra and calculus were invented. The book uses the methods of geometry, and lays out "proofs" of physical relationships using a style and terminology similar to Euclid's Elements.
In 1741, a century after Galileo's death in January 1642, the dispute with the Catholic Church was finally settled officially when the Church under Pope Benedict XIV bid the Holy Office grant an imprimatur to the first edition of the Complete Works of Galileo.
Charges of heresy and theological error
The Holy Tribunal in Galileo's condemnation states: "The proposition that the sun is the center of the world and does not move from its place is absurd and false philosophically and formally heretical, because it is expressly contrary to the Holy Scripture.
The proposition that the earth is not the center of the world and immovable, but that it moves, and also with a diurnal motion, is equally absurd and false philosophically, and theologically considered, at least erroneous in faith." 
- For his promotion of the Copernican view of the Solar System as though it were the Church's position, Galileo was accused by the Catholic Church of disobeying its authority and misrepresenting its position. This was a crime that was sometimes punishable by death, just as treason is so punished today. He was later cleared, but forbidden from publicly misrepresenting the Church's position..
- Galileo published a book in 1632 restating his belief in Copernicus theory. He was again called before the inquisition, this time being found guilty of publishing a book in the Church's name despite its disapproval. He was confined to house arrest, but never condemned.
- The Catholic church admitted that mistakes had been made in 1992. In a speech Pope John Paul II declared the Galileo case closed, but did not admit that the church was wrong on the charge of misrepresenting the Church view at the time he was convicted.
- cf. Galileo Galilei:"Some years ago, as Your Serene Highness well knows, I discovered in the heavens many things that had not been seen before our own age. The novelty of these things, as well as some consequences which followed from them in contradiction to the physical notions commonly held among academic philosophers, stirred up against me no small number of professors -as if I had placed these things in the sky with my own hands in order to upset nature and overturn the sciences. They seemed to forget that the increase of known truths stimulates the investigation, establishment, and growth of the arts; not their diminution or destruction. Showing a greater fondness for their own opinions than for truth they sought to deny and disprove the new things which, if they had cared to look for themselves, their own senses would have demonstrated to them. To this end they hurled various charges and published numerous writings filled with vain arguments, and they made the grave mistake of sprinkling these with passages taken from places in the Bible which they had failed to understand properly, and which were ill-suited to their purposes. ... Possibly because they are disturbed by the known truth of other propositions of mine which differ from those commonly held, and therefore mistrusting their defense so long as they confine themselves to the field of philosophy, these men have resolved to fabricate a shield for their fallacies out of the mantle of pretended religion and the authority of the Bible. These they apply with little judgement to the refutation of arguments that they do not understand and have not even listened to. First they have endeavored to spread the opinion that such propositions in general are contrary to the Bible and are consequently damnable and heretical. ... In order to facilitate their designs, they seek so far as possible (at least among the common people) to make this opinion seem new and to belong to me alone. They pretend not to know that its author, or rather its restorer and confirmer, was Nicholas Copernicus; and that he was not only a Catholic, but a priest and a canon. He was in fact so esteemed by the church that when the Lateran Council under Leo X took up the correction of the church calendar, Copernicus was called to Rome from the most remote parts of Germany to undertake its reform. At that time the calendar was defective because the true measures of the year and the lunar month were not exactly known. The Bishop of Culm, then superintendent of this matter, assigned Copernicus to seek more light and greater certainty concerning the celestial motions by means of constant study and labor. With Herculean toil he set his admirable mind to this task, and he made such great progress in this science and brought our knowledge of the heavenly motions to such precision that he became celebrated as an astronomer. Since that time not only has the calendar been regulated by his teachings, but tables of all the motions of the planets have been calculated as well. Having reduced his system into six books, he published these at the instance of the Cardinal of Capua and the Bishop of Culm. And since he had assumed his laborious enterprise by order of the supreme pontiff, he dedicated this book On the celestial revolutions to Pope Paul III. When printed, the book was accepted by the holy Church, and it has been read and studied by everyone without the faintest hint of any objection ever being conceived against its doctrines."
- Drake, Stillman. Galileo: Pioneer Scientist. (1990). 261 pp.
- Drake, Stillman. Galileo. (1981). 100 pp.
- Fantoli, Annibale. Galileo: For Copernicanism and for the Church. (1994). 540pp
- Feldhay, Rivka. Galileo and the Church: Political Inquisition or Critical Dialogue? (1995). 303 pp.
- Finocchiaro, Maurice A., ed. The Galileo Affair: A Documentary History. (1989). 382 pp. primary sources
- Reston, James. Galileo: A Life. (1994). 319 pp., popular
- Sharratt, Michael. Galileo: Decisive Innovator. (1994). 247 pp.
- Francis S. Collins, Simon and Schuster (2006). The Language of God: A Scientist Presents Evidence for Belief, 294. ISBN 9780743286398. “page=155:"While much of the criticism came from the Catholic Church, it was not limited to that. John Calvin and Martin Luther also objected." (Note: This sentence is omitted in some editions, such as First Free Press trade paperback edition July 2007.)”
- Christian History, Issue 76, "Galileo and the Powers Above"
- David Filkin, "Stephen Hawking's Universe", David Filkin Enterprises Limited, 1997, pg.44 - 46
- Galileo Galilei. Letter to the Grand Duchess Christina of Tuscany, 1615 (Modern History Sourcebook). Fordham University. Retrieved on 16/2/2012.
- On the Revolutions - English translation.
- University of Cambridge, Department of History and Philosophy of Science - Galileo Galilei
- MSN Encarta - Galileo (p3)
- Crew, Henry and Alfonso de Salvio (1914), Dialogues Concerning Two New Sciences by Galileo Galilei, Northwestern University, 1939 reprint of 1914 Macmillan edition, p. 62
- The Galileo Affair
- Stillman Drake Collection
- Henderson, Thomas H., What were Galileo's scientific and biblical conflicts with the Church?, quoting Janelle Rohr, editor, Science & Religion--Opposing Viewpoints (Greenhaven Press, 1988), p. 24.
- Galileo Galilei - NASA bio
- Galileo Galilei, The MacTutor History of Mathematics archive. School of Mathematics and Statistics, University of St Andrews Scotland.