galieo

Biographical sketch

Galileo was born in Pisa, in the Tuscany region of Italy, on February 15, 1564, the first of six children of Vincenzo Galilei. Although as a young man he seriously considered the priesthood, at his father's urging he enrolled for a medical degree at the University of Pisa. He did not complete this degree, but instead studied mathematics, in 1589 being appointed to the chair of mathematics in Pisa. 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 (e.g., kinematics of motion, and astronomy) and applied science (e.g., strength of materials, improvement of the telescope).

Although a devout Roman Catholic, Galileo fathered three children out of wedlock 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, both girls were sent to the convent of San Matteo in Arcetri at early ages and remained there for the rest of their lives. Virginia (b. 1600) took the name Maria Celeste upon entering the convent. Galileo's eldest child, she was also the most beloved, and inherited her father's sharp mind. 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, Copernican theory of the universe against the dominant earth-centered Ptolemaic 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 heresy. Galileo went to Rome to defend himself against these accusations, but, in 1616, Cardinal Roberto Bellarmino personally handed Galileo an admonition enjoining him neither to advocate nor teach Copernican astronomy.[1] In 1622, Galileo wrote his first book, The Assayer (Saggiatore), which was approved and published in 1623. In 1624, he developed the first known example of the microscope. 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 Holy Office 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.) By contrast, 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 Pythagorean 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, writing that "the language of God is mathematics." 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, Galileo's adherence to experimental results, and their most honest interpretation, led to his rejection of blind allegiance to authority, both philosophical and religious, in matters of science. In broader terms, this helped separate science from both philosophy and religion, a major development in human thought.

By the standards of his own 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."'[2]

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 also attempted to measure the speed of light, wisely concluding that his measurement technique was too imprecise to accurately determine its value.

* He climbed one hill and had an assistant to climb another hill; both had lanterns with shutters, initially closed.
* He then opened the shutter of his lantern. His assistant was instructed to open his own shutter upon seeing Galileo's lantern. Galileo then measured the time interval for his assistant's shutter to open.
* Knowing the time interval and the separation between the hills, he determined the apparent speed of light.

On repeating the experiment with more distant hills, Galileo obtained the same time lapse, concluding that the time for the light to travel was much less than his and his assistant's reaction time, and therefore that the actual speed of light was beyond the sensitivity of his measurement technique.[citation needed]

Galileo showed a remarkably modern appreciation for the proper relationship between mathematics, theoretical physics, and experimental physics. For example:

* 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).
* He asserted that the parabola was the theoretically-ideal trajectory for uniformly accelerated motion, in the absence of friction and other disturbances. Further, he 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. (Two New Sciences, page 274 of the National Edition).
* He 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.

Albert Einstein, in appreciation, called Galileo the "father of modern science".

Astronomy

Contributions

Based only on sketchy descriptions of the telescope, invented in the Netherlands in 1608, during that same year Galileo made one 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 could 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 August 25, 1609, he demonstrated his first telescope to Venetian lawmakers. His work on the device made for a profitable sideline with merchants who found it useful for their shipping businesses. He published his initial telescopic astronomical observations in March 1610 in a short treatise entitled Sidereus Nuncius (Starry Messenger).
It was on this page that Galileo first noted an observation of the moons of Jupiter. 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.
It was on this page that Galileo first noted an observation of the moons of Jupiter. 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's four largest satellites (moons): Io, Europa, and Callisto. He discovered Ganymede 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 satellites. 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 exhibited a full set of 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, 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. [3]

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. 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 Sizi, 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. 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 also the first to report lunar mountains and 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 nebulous, 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 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.

Galileo made at least one major scientific error, in addition to opposing Kepler's hypothesis that the gravity of the moon is the origin of the tides. This was his view on the origin of the comets of 1618. He argued vehemently in The Assayer that they were an optical illusion, in opposition to the interpretation of the Jesuit Orazio Grassi that they were real, and quite distant from the Moon. His alienation of both Scheiner and Grazzi likely contributed to the hostile response of the Jesuit order to his publication of "Dialogue Concerning the Two Chief World Systems" in 1632, and the inquisition that followed.

Galileo, Kepler, and theories of tides

Cardinal Bellarmine had written in 1615 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" (Finocchiaro 1989:67-9). 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 1989:119-133).

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 1989:127-131; Drake 1953:432-6). 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:xvii).

Galileo dismissed as a "useless fiction" the idea, held by his contemporary Johannes Kepler, that the moon caused the tides (Finocchiaro 1989:128). Galileo also refused to accept Kepler's elliptical orbits of the planets,[4] considering the circle the "perfect" shape for planetary orbits.

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 Sir Isaac Newton. He was a pioneer, at least in the European tradition, in performing rigorous experiments and insisting on a mathematical 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 accelerated independently of their mass. (Although Galileo was the first person to demonstrate this via experiment, he was not — contrary to popular belief — the first to argue that it was true. John Philoponus had argued this centuries earlier: see also the 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-Haitham 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).
Dome of the cathedral of Pisa with the "lamp of Galileo"
Dome of the cathedral of Pisa with the "lamp of Galileo"

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 below)

In the early 1600s, Galileo and an assistant tried to measure the speed of light. They stood on different hilltops, each holding a shuttered lantern. Galileo would open his shutter, and, as soon as his assistant saw the flash, he would open his shutter. At a distance of less than a mile, Galileo could detect no delay in the round-trip time greater than when he and the assistant were only a few yards apart. While he could reach no conclusion on whether light propagated instantaneously, he recognized that the distance between the hilltops was perhaps too small for a good measurement.

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 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. (The original title for the book, in fact, 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 the basic principle of relativity, 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 the infinite speed of light approximation to 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 Eudoxian 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 Tartaglia and others; but by the end of Galileo's life it was being superseded by the algebraic methods of 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.

Technology
Galileo Galilei.-portrait in crayon by Leoni
Galileo Galilei.-portrait in crayon by Leoni
A replica of the earlest surviving telescope attributed to Galileo Galilei, on display at the Griffith Observatory
A replica of the earlest surviving telescope attributed to Galileo Galilei, on display at the Griffith Observatory

Galileo made a few contributions to what we now call 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.

In 1595–1598, Galileo devised and improved a "Geometric and Military Compass" suitable for use by gunners and surveyors. This expanded on earlier instruments designed by Niccolo 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 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.

About 1593, 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 as a compound microscope, and he made improved microscopes in 1623 and after. This appears to be the first clearly documented use of the compound microscope.

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 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 here. The first fully operational pendulum clock was made by Christiaan Huygens in the 1650s.

He 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.

Church controversy

Main article: Galileo affair

Cristiano Banti's 1857 painting Galileo facing the Roman Inquisition
Cristiano Banti's 1857 painting Galileo facing the Roman Inquisition

Psalm 93:1, Psalm 96:10, and Chronicles 16:30 state that "the world is firmly established, it cannot be moved." Psalm 104:5 says, "[the LORD] set the earth on it's foundations; it can never be moved." Ecclesiastes 1:5 states that "the sun rises and the sun sets, and hurries back to where it rises."

Galileo defended heliocentrism, and claimed it was not contrary to those Scripture passages. He took Augustine's 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 (who had recently had Giordano Bruno, another recent proponent of a sun-centered world view, burned at the stake for heresy[5]), 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 explain himself.

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, Catholic doctrine is defined by the pope when he speaks ex cathedra (from the Chair of Saint Peter) in matters of faith and morals. While Church officials did condemn Galileo, heliocentrism was never formally or officially condemned by the Catholic Church.
* 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 and not enforced, publication of any of his works was forbidden, including any he might write in the future.

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, dying from natural causes on January 8, 1642. It was while Galileo was under house arrest when 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".
Tomb of Galileo Galilei, Santa Croce
Tomb of Galileo Galilei, Santa Croce

Galileo was reburied on sacred ground at Santa Croce 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.[6]

In modern scientific terms, we consider Galileo's views on heliocentricity to be no fundamental advance. Most of his discoveries were only further advances of Copernicus' views. The heliocentric model that Galileo presented was no more accurate than the Tychonic system model, the main competing theory at the time. Stellar parallax, the first evidence from outside the solar system that the Earth does indeed move, would not be observed until 1838 (Consolmagno 150-152). Today, we know the Sun is no more the center of the universe than the Earth is, as it has its own orbit in the Milky Way Galaxy, just like the Galilean moons of Jupiter have orbits around Jupiter while Jupiter orbits the Sun. He found this because he realized that the only orbit the moons could follow is that which orbits behind Jupiter.

Galileo's writings
Statue outside the Uffizi, Florence
Statue outside the Uffizi, Florence

* The Little Balance 1586
* The Starry Messenger 1610 Venice (in Latin, Sidereus Nuncius)
* Letters on Sunspots 1613
* Letter to Grand Duchess Christina 1615
* The Assayer (In Italian, Il Saggiatore) 1623
* Dialogue Concerning the Two Chief World Systems 1632 (in Italian, Dialogo dei due massimi sistemi del mondo)
* Two New Sciences 1638 Lowys Elzevir (Louis Elsevier) Leiden (in Italian, Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze Leida, Appresso gli Elsevirii 1638)

Galileo in popular culture

* Life of Galileo, a play by Bertolt Brecht, 1940
* Galileo's Daughter, a memoir by Dava Sobel, 2000
* Galileo Galilei, an opera by Philip Glass, Mary Zimmerman, and Arnold Weinstein, 2002
* Galileo is mentioned in Queen's song Bohemian Rhapsody.

Named after Galileo

* Galileo (unit of acceleration)
* Galileo positioning system
* Galileo Galilei Airport in the Italian city of Pisa
* Galilei number (fluid dynamics)
* The Galileo mission to Jupiter
* The Galilean moons of Jupiter
* Galileo Regio on Ganymede
* Galileo stadium in Miami, Florida
* Galileo High School in San Francisco, California
* Galilaei crater on the Moon
* Galilaei crater on Mars
* Asteroid 697 Galilea (named on the occasion of the 300th anniversary of the discovery of the Galilean moons)
* Galileo Commissions processing system at Sesame

While in the University, Galileo did extensive experimentation with pendulums, finding that they nearly return to the height at which they were released, that different pendulums have different periods (independent of bob weight and amplitude), and that the square of the period varies directly with the pendulum's length (and it does not depend on the arc of the swing). He later used pendulums to make a clock (1641). Galileo also found that the speed at which bodies fall does not depend on their weight. He documented these discoveries in his book called, "De Motu" (meaning "On Motion"). Galileo was appointed professor of mathematics at the University of Padua (1592-1610). In 1593, Galileo invented the thermometer. Some of his many other inventions included a revolutionary water pump and a hydrostatic balance (a device that weighed things accurately in either air or water).