Galileo

Warning: mkdir() [function.mkdir]: Permission denied in /home/webs/affiliatelib2/CacheManager.php on line 12

Warning: mkdir() [function.mkdir]: No such file or directory in /home/webs/affiliatelib2/CacheManager.php on line 12

Warning: fopen(/home/templatecore2cache//*cluesnet.com/e9/e910db872560457336208ac6b62d4515ab15feb0.tc2cache) [function.fopen]: failed to open stream: No such file or directory in /home/webs/affiliatelib2/CacheManager.php on line 130

Warning: fwrite(): supplied argument is not a valid stream resource in /home/webs/affiliatelib2/CacheManager.php on line 131

Warning: fclose(): supplied argument is not a valid stream resource in /home/webs/affiliatelib2/CacheManager.php on line 132

{{Infobox_Scientist|name = Galileo Galilei|image = Galileo.arp.300pix.jpg|200px|image_width = 200px|caption = Portrait of Galileo Galilei by Giusto Sustermans, [Tuscany - Italy|death_date = |death_place = [Arcetri, Tuscany - Italy, [Physics and Mathematics|alma_mater = [University of Pisa
[Telescope
Solar System|footnotes =-->Galileo Galilei ([15 February 1564 – 8 January 1642) by John Gerard. Retrieved 11 August 2007 was a Tuscany (Italian people) physicist, mathematician, astronomer, and philosopher who played a major role in the scientific revolution. His achievements include the first systematic studies of uniformly accelerated motion, improvements to the telescope and consequent astronomical observations, and support for Nicolaus Copernicus. Galileo's empirical work was a significant break from the abstract Aristotelian approach of his time.

Galileo has been called the "father of modern observational astronomy", (page 217) the "father of modern physics", the "father of science", and “the Father of Modern Science.”Maurice A. Finocchiaro, “Review of The Person of the Millennium: The Unique Impact of Galileo on World History,” The Historian 69.3 (Fall, 2007): 602. The motion of uniformly accelerated objects, taught in nearly all high school and introductory college physics courses, was studied by Galileo as the subject of kinematics. His contributions to observational astronomy include the discovery of the four largest satellites of Jupiter, named the Galilean moons in his honour, and the observation and analysis of sunspots. Galileo also worked in applied science and technology, improving compass design.

Galileo's championing of Copernicanism was controversial within his lifetime. The geocentric view had been dominant since the time of Aristotle, and the controversy engendered by Galileo's opposition to this view resulted in the Catholic Church prohibiting the advocacy of heliocentrism as potentially factual, because that theory had no decisive proof and was contrary to the literal meaning of Scripture.#Reference-Sharratt-1996, #Reference-McMullin-2005a. Galileo was eventually forced to recant his heliocentrism and spent the last years of his life under house arrest on orders of the Inquisition.

Life Galileo was born in Pisa (then part of the Grand Duchy of Tuscany), the first of six children of Vincenzo Galilei, a famous lutenist and music theory, and Giulia Ammannati. Although he seriously considered the priesthood as a young man, he enrolled for a medical degree at the University of Pisa at his father's urging. He did not complete this degree, but instead studied mathematics and in 1589 was appointed to the chair of mathematics in Pisa. In 1591 his father died and he was entrusted with the care of his younger brother Michelagnolo Galilei. In 1592 he moved to the University of Padua, teaching geometry, mechanics, and astronomy until 1610. During this period Galileo made significant discoveries in both pure science (for example, kinematics of motion, and astronomy) and applied science (for example, strength of materials, improvement of the telescope). His multiple interests included the study of astrology, which in premodern disciplinary practice was seen as correlated to the studies of mathematics and astronomy.H. Darrel Rutkin. Galileo, Astrology, and the Scientific Revolution: Another Look. Program in History & Philosophy of Science & Technology, Stanford University. Retrieved on 2007-04-15.

Although a devout Roman Catholic, Galileo fathered three children illegitimacy with Marina Gamba. They had two daughters (Virginia in 1600 and Livia in 1601) and one son (Vincenzio, in 1606). Because of their illegitimate birth, their father considered the girls unmarriageable. Their only worthy alternative was the religious life. Both girls were sent to the convent of San Matteo in Arcetri and remained there for the rest of their lives.#Reference-Sobel-2000 Chapter 1. Retrieved on August 26, 2007. "But because he never married Virginia's mother, he deemed the girl herself unmarriageable. Soon after her thirteenth birthday, he placed her at the Convent of San Matteo in Arcetri." Virginia (b. 1600) took the name Maria Celeste upon entering the convent. She died on April 2 1634, and is buried with Galileo at the Basilica di Santa Croce di Firenze. Livia (b. 1601) took the name Suor Arcangela and was ill for most of her life. Vincenzio (b. 1606) was later legitimized and married Sestilia Bocchineri.

In 1610 Galileo published an account of his telescopic observations of the moons of Jupiter, using this observation to argue in favor of the sun-centered, Copernicus theory of the universe against the dominant earth-centered Geocentric_model#Ptolemaic_system and Aristotelian theories. The next year Galileo visited Rome in order to demonstrate his telescope to the influential philosophers and mathematicians of the Jesuit Collegio Romano, and to let them see with their own eyes the reality of the four moons of Jupiter. While in Rome he was also made a member of the Accademia dei Lincei. In 1612, opposition arose to the Sun-centered solar system which Galileo supported. In 1614, from the pulpit of Santa Maria Novella, Father Tommaso Caccini (1574–1648) denounced Galileo's opinions on the motion of the Earth, judging them dangerous and close to Christian heresy. Galileo went to Rome to defend himself against these accusations, but, in 1616, Robert Bellarmine personally handed Galileo an admonition enjoining him neither to advocate nor teach Copernican astronomy.There are contradictory documents describing the nature of this admonition and the circumstances of its delivery. Finocchiaro, The Galileo Affair, pp.147–149, 153 During 1621 and 1622 Galileo wrote his first book, The Assayer (Il Saggiatore), which was approved and published in 1623. In 1630, he returned to Rome to apply for a license to print the Dialogue Concerning the Two Chief World Systems, published in Florence in 1632. In October of that year, however, he was ordered to appear before the Congregation for the Doctrine of the Faith in Rome.

Scientific methods Galileo Galilei pioneered the use of quantitative experiments whose results could be analyzed with mathematical precision (More typical of science at the time were the qualitative studies of William Gilbert, on magnetism and electricity). Galileo's father, Vincenzo Galilei, a lutenist and music theorist, had performed experiments establishing perhaps the oldest known non-linear relation in physics: for a stretched string, the pitch varies as the square root of the tension. These observations lay within the framework of the Pythagoras#Musical theories and investigations tradition of music, well-known to instrument makers, which included the fact that subdividing a string by a whole number produces a harmonious scale. 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 is perhaps the first 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; ...".In #Reference-Drake-1957 His mathematical analyses are a further development of a tradition employed by late scholastic natural philosophers, which Galileo learned when he studied philosophy. Wallace, (1984) Although he tried to remain loyal to the Catholic Church, his adherence to experimental results, and their most honest interpretation, led to a rejection of blind allegiance to authority, both philosophical and religious, in matters of science. In broader terms, this aided to separate science from both philosophy and religion; a major development in human thought.

By the standards of his time, Galileo was often willing to change his views in accordance with observation. Philosopher of science Paul Feyerabend also noted the supposedly improper aspects of Galileo's methodology, but he argued that Galileo's methods could be justified retroactively by their results. The bulk of Feyerabend's major work, Against Method (1975), was devoted to an analysis of Galileo, using his astronomical research as a case study to support Feyerabend's own anarchistic theory of scientific method. As he put it: 'Aristotelians demanded strong empirical support while the Galileans were content with far-reaching, unsupported and partially refuted theories. I do not criticize them for that; on the contrary, I favour Niels Bohr's "this is not crazy enough."'Paul Feyerabend, Against Method (third edition, London: Verso, 1993), p. 129. 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. For measurements of particularly short intervals of time, Galileo sang songs with whose timing he was familiar.

Galileo showed a remarkably 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 for uniformly accelerated motion, in the absence of friction and other disturbances. He also noted that there are limits to the validity of this theory, stating that it was appropriate only for laboratory-scale and battlefield-scale trajectories, and noting on theoretical grounds that the parabola could not possibly apply to a trajectory so large as to be comparable to the size of the planet. #Reference-Galileo-1954 #Reference-Favaro-1890 8:274) . Thirdly, Galilei recognized that his experimental data would never agree exactly with any theoretical or mathematical form, because of the imprecision of measurement, irreducible friction, and other factors.

According to Stephen Hawking, Galileo probably bears more of the responsibility for the birth of modern science than anybody else,#Reference-Hawking-1988. and Albert Einstein called him the father of modern science.#Reference-Einstein-1954. "Propositions arrived at by purely logical means are completely empty as regards reality. Because Galileo realised this, and particularly because he drummed it into the scientific world, he is the father of modern physics—indeed, of modern science altogether."

Astronomy Contributions Based only on sketchy descriptions of the telescope, invented in the Netherlands in 1608, during that same year Galileo made a telescope with about 3x magnification, and later made others with up to about 32x magnification. With this improved device he could see magnified, upright images on the earth - it was what is now known as a terrestrial telescope, or spyglass. He could also use it to observe the sky; for a time he was one of very few who could construct telescopes good enough for that purpose. On 25 August 1609, he demonstrated his first telescope to Venice lawmakers. His work on the device made for a profitable sideline with merchants who found it useful for their shipping businesses and trading issues. He published his initial telescopic astronomical observations in March 1610 in a short treatise entitled Sidereus Nuncius (Starry Messenger). of Jupiter (planet). This observation upset the notion that all celestial bodies must revolve around the Earth. Galileo published a full description in Sidereus Nuncius in March 1610

In the week of January 7 1610 Galileo discovered three of Jupiter (planet)'s four largest natural satellite (moons): Io (moon), Europa (moon), and Callisto (moon). He discovered Ganymede (moon) four nights later. He noted that the moons would appear and disappear periodically, an observation which he attributed to their movement behind Jupiter, and concluded that they were orbiting the planet. He made additional observations of them in 1620. Later astronomers overruled Galileo's naming of these objects, changing his originally named Medicean stars (after his patrons, the Medici) to Galilean moons. The demonstration that a planet had smaller planets orbiting it was problematic for the orderly, comprehensive picture of the geocentric model of the universe, in which everything circled around the Earth.

From September 1610, Galileo observed that Venus (planet) exhibited a full set of Lunar phases similar to that of the Moon. The heliocentric model of the solar system developed by 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. In contrast, the geocentric model of Ptolemy predicted that only crescent and new phases would be seen, since Venus was thought to remain between the Sun and Earth during its orbit around the Earth. Galileo's observations of the phases of Venus proved that it orbited the Sun and lent support to (but did not prove) the heliocentric model.

Galileo also observed the planet Saturn (planet), 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 1616, further confusing him.Baalke, Ron. Historical Background of Saturn's Rings. Jet Propulsion Laboratory, California Institute of Technology, NASA. Retrieved on 2007-03-11

Galileo was one of the first Europeans to observe sunspots. He also reinterpreted a sunspot observation from the time of Charlemagne, which formerly had been attributed (impossibly) to a transit of Mercury (planet). The very existence of sunspots showed another difficulty with the unchanging perfection of the heavens as assumed in the older philosophy. And the annual variations in their motions, first noticed by Francesco Sizzi, presented great difficulties for both the geocentric system and that of Tycho Brahe. A dispute over priority in the discovery of sunspots, and in their interpretation, led Galileo to a long and bitter feud with the Jesuit Christoph Scheiner; in fact, there is little doubt that both of them were beaten by David Fabricius and his son Johannes Fabricius. Scheiner quickly adopted Kepler's 1615 proposal of the modern telescope design, which gave larger magnification at the cost of inverted images; Galileo apparently never changed to Kepler's design.

Galileo was the first to report lunar mountains and impact craters, whose existence he deduced from the patterns of light and shadow on the Moon's surface. He even estimated the mountains' heights from these observations. This led him to the conclusion that the Moon was "rough and uneven, and just like the surface of the Earth itself," rather than a perfect sphere as Aristotle had claimed. Galileo observed the Milky Way, previously believed to be Nebula, and found it to be a multitude of stars packed so densely that they appeared to be clouds from Earth. He located many other stars too distant to be visible with the naked eye. Galileo also observed the planet Neptune (planet) in 1612, but did not realize that it was a planet and took no particular notice of it. It appears in his notebooks as one of many unremarkable dim stars.

Controversy over comets and The Assayer In 1619 Galileo became embroiled in a controversy with Father Horatio Grassi, the professor of mathematics at the Jesuit Collegio Romano. It began as a dispute over the nature of comets, but by the time Galileo had published The Assayer (Il Saggiatore) in 1623, his last salvo in the dispute, it had become a much wider argument 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.#Reference-Drake-1960 , #Reference-Sharratt-1996.

Early in 1619 Father Grassi had anonymously published a pamphlet, The_Assayer#disputatio,#Reference-Grassi-1960a . which discussed the nature of a comet that had appeared late in November of the previous year. 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,#Reference-Drake-1978 , #Reference-Grassi-1960a . and that it had been located well beyond the moon.

Grassi's arguments and conclusions were criticised in a subsequent article, The Assayer#Discourse_on_Comets,#Reference-Galileo&Guiducci-1960 . 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.#Reference-Drake-1960 . Galileo and Guiducci offered no definitive theory of their own on the nature of comets, #Reference-Drake-1957 , #Reference-Drake-1960 . although they did present some tentative conjectures which we now know to be mistaken.

In its opening passage, Galileo and Guiducci's Discourse gratuitously insulted the Jesuit Christopher Scheiner, #Reference-Sharratt-1996, #Reference-Drake-1960 , #Reference-Galileo&Guiducci-1960 . and various uncomplimentary remarks about the professors of the Collegio Romano were scattered throughout the work.#Reference-Sharratt-1996. The Jesuits were offended,#Reference-Sharratt-1996, #Reference-Drake-1960 . and Grassi soon replied with a polemical tract of his own, The Assayer#astronomical balance,#Reference-Grassi-1960b. under the pseudonym Lothario Sarsi, purporting to be one of his own pupils.

The Assayer,#Reference-Galileo-1960. was Galileo's devastating reply to the Astronomical Balance. It has been widely regarded as a masterpiece of polemical literature,#Reference-Sharratt-1996, #Reference-Drake-1957 . in which "Sarsi's" arguments are subjected to withering scorn.#Reference-Sharratt-1996. It was greeted with wide acclaim, and particularly pleased the new pope, Urban VIII, to whom it had been dedicated.#Reference-Drake-1960 .

Galileo's dispute with Grassi permanently alienated many of the Jesuits who had previously been sympathetic to his ideas,#Reference-Drake-1960 . and Galileo and his friends were convinced that these Jesuits were responsible for bringing about his later condemnation.#Reference-Sharratt-1996. The evidence for this is at best equivocal, however.#Reference-Sharratt-1996.

Galileo, Kepler and theories of tides Cardinal Bellarmine had written in 1615 that the Copernican system could not be defended without "a true demonstration that the sun does not circle the earth but the earth circles the sun".Finocchiaro (1989), pp. 67–9. Galileo considered his theory of the tides to provide the required physical proof of the motion of the earth. This theory was so important to Galileo that he originally intended to entitle his Dialogue on the Two Chief World Systems the Dialogue on the Ebb and Flow of the Sea.Finocchiaro (1989), p. 354, n. 52 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 speeded up and slowed down because of the Earth's rotation on its axis and revolution around the Sun. Galileo circulated his first account of the tides in 1616, addressed to Cardinal Orsini.Finocchiaro (1989), pp.119–133

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.Finocchiaro (1989), pp.127–131 and Drake (1953), pp. 432–6 Against the assertion that Galileo was deceptive in making these arguments, Albert Einstein expressed the opinion that Galileo developed his "fascinating arguments" and accepted them uncritically out of a desire for physical proof of the motion of the Earth.Einstein (1952) p. xvii

Galileo dismissed as a "useless fiction" the idea, held by his contemporary Johannes Kepler, that the moon caused the tides.Finocchiaro (1989), p. 128 Galileo also refused to accept Johannes Kepler elliptical orbits of the planets,Sachiko Kusukawa. Starry Messenger. The Telescope, Department of History and Philosophy of Science of the University of Cambridge. Retrieved on 2007-03-10 considering the circle the "perfect" shape for planetary orbits.

Technology

Galileo made a number of contributions to what is now known as technology, as distinct from pure physics, and suggested others. This is not the same distinction as made by Aristotle, who would have considered all Galileo's physics as techne or useful knowledge, as opposed to episteme, or philosophical investigation into the causes of things. Between 1595–1598, Galileo devised and improved a Geometric and Military Compass suitable for use by artillery and surveying. This expanded on earlier instruments designed by Niccolò Tartaglia and Guidobaldo del Monte. 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 Round shots 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. About Timeline of temperature and pressure measurement technology, Galileo constructed a thermometer, using the expansion and contraction of air in a bulb to move water in an attached tube.

In 1609, Galileo was among the first to use a refracting telescope as an instrument to observe stars, planets or moons. In 1610, he used a telescope at close range to magnify the parts of insects,#Reference-Drake-1978, #Reference-Favaro-1890 (1892, 3:163- 164). and by 1624 he had perfectedProbably in 1623, according to #Reference-Drake-1978. a compound microscope. He gave one of these instruments to Cardinal Zollern in May of that year for presentation to the Duke of Bavaria, #Reference-Drake-1978, #Reference-Favaro-1890 (1903, 13:177) . and in September he sent another to Federico Cesi, the founder of the Linceans.#Reference-Drake-1978, #Reference-Favaro-1890 (1903, 13:208). The inventors of the telescope and microscope remain debatable. A general view on this can be found in Hans Lippershey (last updated 2003-08-01), © 1995-2007 by Davidson, Michael W. and the Florida State University. Retrieved 2007-08-28Van Helden, Al. Galileo Timeline (last updated 1995), The Galileo Project. Retrieved 2007-08-28. See also Timeline of microscope technology. Illustrations of insects made using one of Galileo's microscopes, and published in 1625, appear to have been the Timeline of microscope technology clear documentation of the use of a compound microscope. #Reference-Drake-1978.

In 1612, having determined the orbital periods of Jupiter's satellites, Galileo proposed that with sufficiently accurate knowledge of their orbits one could use their positions as a universal clock, and this would make possible the determination of longitude. He worked on this problem from time to time during the remainder of his life; but the practical problems were severe. The method was first successfully applied by Giovanni Domenico Cassini in 1681 and was later used extensively for large land surveys; this method, for example, was used by Lewis and Clark. For sea navigation, where delicate telescopic observations were more difficult, the longitude problem eventually required development of a practical portable marine chronometer, such as that of John Harrison.

In his last year, when totally blind, he designed an escapement mechanism for a pendulum clock, a vectorial model of which may be seen Galileo's escapement. The first fully operational pendulum clock was made by Christiaan Huygens in the 1650s. Galilei created sketches of various inventions, such as a candle and mirror combination to reflect light throughout a building, an automatic tomato picker, a pocket comb that doubled as an eating utensil, and what appears to be a ballpoint pen.

Physics Galileo's theoretical and experimental work on the motions of bodies, along with the largely independent work of Kepler and René Descartes, was a precursor of the classical mechanics developed by Isaac Newton. He was a pioneer, at least in the European tradition, in performing rigorous experiments and insisting on a mathematics description of the laws of nature.

Galileo is said to have dropped balls of different masses from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass (excluding the limited effect of air resistance). This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight. Although the story of the tower first appeared in a biography by Galileo's pupil Vincenzo Viviani, it is not now generally accepted as true. Moreover, Giambattista Benedetti had reached the same scientific conclusion years before, in 1553. However, Galileo did perform experiments involving rolling balls down inclined planes, one of which is in Florence, called the bell and ball experiment, which proved the same thing: falling or rolling objects (rolling is a slower version of falling, as long as the distribution of mass in the objects is the same) are acceleration independently of their mass. Galileo was the first person to demonstrate this via experiment, but he was not—contrary to popular belief—the first to argue that it was true. John Philoponus had argued this Oxford Calculators.

Galileo determined the correct mathematical law for acceleration: the total distance covered, starting from rest, is proportional to the square of the time (d \propto t^2). He expressed this law using geometrical constructions and mathematically-precise words, adhering to the standards of the day. (It remained for others to re-express the law in algebraic terms). He also concluded that objects retain their velocity unless a force—often friction—acts upon them, refuting the generally accepted Aristotelian hypothesis that objects "naturally" slow down and stop unless a force acts upon them (again this was not a new idea: Ibn al-Haytham had proposed it centuries earlier, as had Jean Buridan, and according to Joseph Needham, Mo Tzu had proposed it centuries before either of them, but this was the first time that it had been mathematically expressed). Galileo's Principle of Inertia stated: "A body moving on a level surface will continue in the same direction at constant speed unless disturbed." This principle was incorporated into Newton's laws of motion (first law).

Galileo also noted that a pendulum's swings always take the same amount of time, independently of the amplitude. The story goes that he came to this conclusion by watching the swings of the bronze chandelier in the cathedral of Pisa, using his pulse to time it. While Galileo believed this equality of period to be exact, it is only an approximation appropriate to small amplitudes. It is good enough to regulate a clock, however, as Galileo may have been the first to realize. (See #Technology above)

In 1638 Galileo described an experimental method to measure the speed of light by arranging that two observers, each having lanterns equipped with shutters, observe each other's lanterns at some distance. The first observer opens the shutter of his lamp, and, the second, upon seeing the light, immediately opens the shutter of his own lantern. The time between the first observer's opening his shutter and seeing the light from the second observer's lamp indicates the time it takes light to travel back and forth between the two observers. Galileo reported that when he tried this at a distance of less than a mile, he was unable to determine whether or not the light appeared instantaneously.Galileo Galilei, Two New Sciences, (Madison: Univ. of Wisconsin Pr., 1974) p. 50. Sometime between Galileo's death and 1667, the members of the Florentine Accademia del Cimento repeated the experiment over a distance of about a mile and obtained a similarly inconclusive result.I. Bernard Cohen, "Roemer and the First Determination of the Velocity of Light (1676)," Isis, 31 (1940): 327–379, see pp. 332–333

Galileo is lesser known for, yet still credited with, being one of the first to understand sound frequency. By scraping a chisel at different speeds, he linked the pitch of the sound produced to the spacing of the chisel's skips, a measure of frequency.

In his 1632 Dialogue Concerning the Two Chief World Systems Galileo presented a physical theory to account for tides, based on the motion of the Earth. If correct, this would have been a strong argument for the reality of the Earth's motion. In fact, the original title for the book described it as a dialogue on the tides; the reference to tides was removed by order of the Inquisition. His theory gave the first insight into the importance of the shapes of ocean basins in the size and timing of tides; he correctly accounted, for instance, for the negligible tides halfway along the Adriatic Sea compared to those at the ends. As a general account of the cause of tides, however, his theory was a failure. Kepler and others correctly associated the Moon with an influence over the tides, based on empirical data; a proper physical theory of the tides, however, was not available until Newton.

Galileo also put forward Galilean invariance, that the laws of physics are the same in any system that is moving at a constant speed in a straight line, regardless of its particular speed or direction. Hence, there is no absolute motion or absolute rest. This principle provided the basic framework for Newton's laws of motion and is central to Albert Einstein's special theory of relativity.

Mathematics While Galileo's application of mathematics to experimental physics was innovative, his mathematical methods were the standard ones of the day. The analysis and proofs relied heavily on the Eudoxus of Cnidus theory of proportion, as set forth in the fifth book of Euclid's Elements. This theory had become available only a century before, thanks to accurate translations by Niccolò Tartaglia and others; but by the end of Galileo's life it was being superseded by the algebraic methods of René Descartes.

Galileo produced one piece of original and even prophetic work in mathematics: Galileo's paradox, which shows that there are as many perfect squares as there are whole numbers, even though most numbers are not perfect squares. Such seeming contradictions were brought under control 250 years later in the work of Georg Cantor.

Church controversy

Western Christian biblical references "Psalm 93:1", "Psalm 96:10", and "Chronicles 16:30" include text stating that "the world is firmly established, it cannot be moved." In the same tradition, "Psalm 104:5" says, " LORD set the earth on its foundations; it can never be moved." Further, "Ecclesiastes 1:5" states that "And the sun rises and sets and returns to its place, etc."#Reference-Brodrick-1965 quoting Cardinal Bellarmine's letter to Foscarini, dated April 12, 1615. Translated from #Reference-Favaro-1890 (1902, 12:171–172) .

Galileo defended heliocentrism, and claimed it was not contrary to those Scripture passages. He took Augustine of Hippo position on Scripture: not to take every passage literally, particularly when the scripture in question is a book of poetry and songs, not a book of instructions or history. The writers of the Scripture wrote from the perspective of the terrestrial world, and from that vantage point the sun does rise and set. In fact, it is the earth's rotation which gives the impression of the sun in motion across the sky.

By 1616 the attacks on Galileo had reached a head, and he went to Rome to try to persuade the Church authorities not to ban his ideas. In the end, Cardinal Bellarmine, acting on directives from the Inquisition, delivered him an order not to "hold or defend" the idea that the Earth moves and the Sun stands still at the centre. The decree did not prevent Galileo from discussing heliocentrism hypothetically. For the next several years Galileo stayed well away from the controversy. He revived his project of writing a book on the subject, encouraged by the election of Cardinal Barberini as Pope Urban VIII in 1623. Barberini was a friend and admirer of Galileo, and had opposed the condemnation of Galileo in 1616. The book, Dialogue Concerning the Two Chief World Systems, was published in 1632, with formal authorization from the Inquisition and papal permission.

Pope Urban VIII 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 deliberate, Simplicius, 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. This fact made Dialogue Concerning the Two Chief World Systems appear as an advocacy book; an attack on Aristotelian geocentrism and defense of the Copernican theory. To add insult to injury, Galileo put the words of Pope Urban VIII into the mouth of Simplicius. Most historians agree Galileo did not act out of malice and felt blindsided by the reaction to his book. However, the Pope did not take the public ridicule lightly, nor the blatant bias. Galileo had alienated one of his biggest and most powerful supporters, the Pope, and was called to Rome to defend his writings.

With the loss of many of his defenders in Rome because of Dialogue Concerning the Two Chief World Systems, Galileo was ordered to stand trial on suspicion of heresy in 1633. The sentence of the Inquisition was in three essential parts:

Galileo was required to recant his heliocentric ideas; the idea that the Sun is stationary was condemned as "formally heretical." However, while there is no doubt that Pope Urban VIII and the vast majority of Church officials did not believe in heliocentrism, heliocentrism was never formally or officially condemned by the Catholic Church, except insofar as it held (for instance, in the formal condemnation of Galileo) that "The proposition that the sun is in the center of the world and immovable from its place is absurd, philosophically false, and formally heretical; because it is expressly contrary to Holy Scriptures", and the converse as to the Sun's not revolving around the Earth.
He was ordered imprisoned; the sentence was later commuted to house arrest.
His offending Dialogue was banned; and in an action not announced at the trial, publication of any of his works was forbidden, including any he might write in the future.#Reference-Drake-1978 #Reference-Sharratt-1996 #Reference-Favaro-1890 (1905, 16:209, 230). See Galileo affair# note-publication-ban for further details.

After a period with the friendly Ascanio Piccolomini (the Archbishop of Siena), Galileo was allowed to return to his villa at Arcetri near Florence, where he spent the remainder of his life under house arrest, going blind and dying from natural causes on January 8, 1642. It was while Galileo was under house arrest that he dedicated his time to one of his finest works, Two New Sciences. Here he summarized work he had done some forty years earlier, on the two sciences now called kinematics and strength of materials. This book has received high praise from both Sir Isaac Newton and Albert Einstein. As a result of this work, Galileo is often called, the "father of modern physics."

Galileo died on January 8, 1642, and was buried the next day in his family grave in the Basilica di Santa Croce di Firenze basilica of Firenze. He was reburied on sacred ground after a monument was erected in his honor at Basilica di Santa Croce di Firenze in 1737. He was formally rehabilitated in 1741, when Pope Benedict XIV authorized the publication of Galileo's complete scientific works (a censored edition had been published in 1718), and in 1758 the general prohibition against heliocentrism was removed from the Index Librorum Prohibitorum. On 31 October 1992, Pope John Paul II expressed regret for how the Galileo affair was handled, as the result of a study conducted by the Pontifical Council for Culture. Vatican admits Galileo was right. New Scientist 07 November 1992. Retrieved on 09 August 2007.

Galileo's writings , Florence

The Little Balance (1586)
Sidereus Nuncius (1610; in Latin, Sidereus Nuncius)
Letters on Sunspots (1613)
Letter to Grand Duchess Christina (1615)
The Assayer (1623; in Italian, Il Saggiatore)
Dialogue Concerning the Two Chief World Systems (1632, in Italian Dialogo dei due massimi sistemi del mondo)
Two New Sciences (1638; in Italian Language, Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze)

Notes References

Allan-Olney, Mary. The private Life of Galileo: Compiled primarily from his correspondence and that of his eldest daughter, Sister Maria Celeste, (nun in the Franciscan convent of St. Matthew, in Arcetri), 1870, Boston : Nichols and Noyes. - Google Books: The private Life of Galileo - The Internet Archive
Biagioli, Mario (1993). Galileo, Courtier: The Practice of Science in the Culture of Absolutism. Chicago: University of Chicago Press.
Consolmagno, Guy; Schaefer, Marta (1994). Worlds Apart, A Textbook in Planetary Science. Englewood, New Jersey: Prentice-Hall, Inc. ISBN 0-13-964131-9
{{cite book | title= Galileo : the man, his work, his misfortunes

Drake, Stillman (1953), trans. Dialogue Concerning the Two Chief World Systems. Berkeley: University of California Press.
{{cite book | title= Introduction to the Controversy on the Comets of 1618

| author= Drake, Stillman | others= In [#Reference-Drake&O'Malley-1960 | year= 1960 | ref=Reference-Drake-1960-->

Drake, Stillman (1973). "Galileo's Discovery of the Law of Free Fall". Scientific American v. 228, #5, pp. 84–92.
{{cite book | title= The Controversy on the Comets of 1618

Einstein, Albert (1952). Foreword to (Drake, 1953)
{{cite book | title= Ideas and Opinions

Fantoli, Annibale (2003). Galileo — For Copernicanism and the Church, third English edition. Vatican Observatory Publications. ISBN 88-209-7427-4
. (The Works of Galileo Galilei, National Edition, 20 vols.), Florence: Barbera, 1890–1909; reprinted 1929–1939 and 1964–1966. ISBN 88-09-20881-1.--> Searchable online copy from the Institute and Museum of the History of Science, Florence . Brief overview of "Le Opere" @ Finns Fine Books, and here
Fillmore, Charles (1931, 17th printing July 2004). Metaphysical Bible Dictionary. Unity Village, Missouri: Unity House. ISBN 0-87159-067-0
Finocchiaro, Maurice A. (1989). The Galileo Affair: A Documentary History. Berkeley: University of California Press. ISBN 0-520-06662-6
{{cite book | title= The Assayer

{{cite book | title= Discourse on the Coments

Gebler, Karl von. Galileo Galilei and the Roman Curia : from authentic sources, London, C.K. Paul & co., 1879; Merrick, N.Y. : Richwood Pub. Co., 1977. - Google Books ISBN 0-915172-11-9
Geymonat, Ludovico (1965), Galileo Galilei, A biography and inquiry into his philosophy and science, translation of the 1957 Italian edition, with notes and appendix by Stillman Drake, McGraw-Hill
{{cite book | title= On the Three Comets of the Year MDCXIII

{{cite book | title= The Astronomical and Philosophical Balance

Grisar, Hartmann, S.J., Professor of Church history at the University of Innsbruck (1882). Historisch theologische Untersuchungen über die Urtheile Römischen Congegationen im Galileiprocess (Historico-theological Discussions concerning the Decisions of the Roman Congregations in the case of Galileo), Regensburg: Pustet. - Google Books ISBN 0-7905-6229-4. (LCC # QB36 - microfiche) Reviewed here (1883), pp.211–213
{{cite book | title= A Brief History of Time

Hellman, Hal (1988). Great Feuds in Science. Ten of the Liveliest Disputes Ever. New York: Wiley
{{cite book | title= The Refusal to Accommodate. Jesuit Exegetes and the Copernican System

| author= Kelter, Irving A. | others= In [#Reference-McMullin-2005 | year= 2005 | ref=Reference-Kelter-2005-->

Arthur Koestler. The Sleepwalkers: A History of Man's Changing Vision of the Universe 1958, Penguin (Non-Classics); Reprint edition (June 5, 1990). ISBN 0-14-019246-8
Lattis, James M. (1994). Between Copernicus and Galileo: Christopher Clavius and the Collapse of Ptolemaic Cosmology, Chicago: the University of Chicago Press
Langford, Jerome, Galileo, Science and the Church, third edition, St. Augustine's Press, 1998. ISBN 1-890318-25-6
Lessl, Thomas, " The Galileo Legend". New Oxford Review, 27–33 (June 2000).
{{cite book | title= The Church and Galileo

{{cite book | title= The Church's Ban on Copernicanism, 1616

| author= McMullin, Ernan, | others= In [#Reference-McMullin-2005 | year= 2005a | ref=Reference-McMullin-2005a-->

Naylor, Ronald H. (1990). "Galileo's Method of Analysis and Synthesis," Isis, 81: 695–707
Newall, Paul (2004). "The Galileo Affair"
Remmert, Volker R. (2005). Galileo, God, and Mathematics. In: Bergmans, Luc/Koetsier, Teun (eds.): Mathematics and the Divine. A Historical Study, Amsterdam et al., 347–360
Settle, Thomas B. (1961). "An Experiment in the History of Science". Science, 133:19–23
Wallace, William A. (1984) Galileo and His Sources: The Heritage of the Collegio Romano in Galileo's Science, (Princeton: Princeton Univ. Pr.), ISBN 0-691-08355-X
White, Andrew Dickson (1898). A History of the Warfare of Science with Theology in Christendom. New York 1898.
White, Michael. (2007). Galileo: Antichrist: A Biography. Weidenfeld & Nicolson:London, ISBN 978-0-297-84868-4.
Wisan, Winifred Lovell (1984). "Galileo and the Process of Scientific Creation," Isis, 75: 269–286.
Zik Yaakov, "Science and Instruments: The telescope as a scientific instrument at the beginning of the seventeenth century", Per

Galileo Biography
Galileo (1564-1642) was the first astronomer to make full use of the telescope, observing the craters of the moon and the satellites of Jupiter.

Galileo summary
Biography, with links to related internet sites.

BBC - History - Galileo Galilei (1564-1642)
In-depth look at Galileo's life and his significance.

BBC NEWS | Science/Nature | Q&A: Europe's Galileo project
Europe is building its own satellite-navigation system called Galileo. Why does it want such a service?

The Galileo Project
An extensive resource on the life, the times, and the work of Galileo Galilei.

Together we can achieve more
Together we can achieve more. A global travel technology solutions leader, we work in ... Copyright © 2004-2008 Galileo International, L.L.C. All rights reserved.

National Theatre : Productions : The Life of Galileo
The Life of Galileo. by Bertolt Brecht in a version by David Hare. Part of the Travelex £10 Season, with two thirds of the seats at £10 for every performance.

Energy and Transport - GALILEO
Features overview of the GALILEO global satellite navigation system by the European Commission. Includes functions, performances and utilization areas.

Galileo Galilei - Wikipedia, the free encyclopedia
Galileo Galilei (15 February 1564 [2] – 8 January 1642) [1] [3] was a Tuscan (Italian) physicist, mathematician, astronomer, and philosopher who played a major role in the ...

Galileo Educational Network Association
Thank you to all school administrators who participated in the two day workshops. Dr. Friesen's presentation is now available. A Classroom Observation Rubric has been created to ...