Main Page | See live article | Alphabetical index

Galileo Galilei

Galileo Galilei (February 15, 1564 - January 8, 1642), was an Italian astronomer, philosopher, and physicist who is commonly associated with the Scientific Revolution. He has been referred to as the "father of modern astronomy" (a title to which Kepler has perhaps a stronger claim), as the "father of modern physics", and as "father of science". Along with Bacon, he pioneered the modern scientific method. Galileo was born in Pisa and his career coincided with that of Kepler. The work of Galileo is considered to be a significant break from that of Aristotle; in particular, Galileo placed emphasis on quantity, rather than quality.

Table of contents
1 Experimental science
2 Astronomy
3 Physics
4 Mathematics
5 Technology
6 Church controversy
8 Writings by Galileo
9 References
10 Other sources

Experimental science

In the pantheon of the scientific revolution Galileo occupies a high position because of his pioneering use of quantitative experiments with results analyzed mathematically. There was no tradition of such methods in European thought at that time; the great experimentalist who immediately preceded Galileo, William Gilbert, did not use a quantitative approach. (However, Galileo's father, Vincenzo Galilei, had performed experiments in which he discovered what may be the oldest known non-linear relation in physics, between the tension and the pitch of a stretched string.)

In the 20th century the reality of Galileo's experiments was challenged by some authorities, in particular the distinguished French historian of science Alexandre Koyré. The experiments reported in Two New Sciences to determine the law of acceleration of falling bodies, for instance, required accurate measurements of time, which appeared to have been impossible with the technology of 1600. According to Koyré, the law was arrived at deductively, and the experiments were merely illustrative thought experiments.

Later research, however, has validated the experiments. The experiments on falling bodies (actually rolling balls) were replicated using the methods described by Galileo (Settle, 1961), and the precision of the results was consistent with Galileo's report. Later research into Galileo's unpublished working papers from as early as 1604 clearly showed the reality of the experiments and even indicated the particular results that led to the time-squared law (Drake, 1973).


Galileo was one of the first people to use the telescope to observe the sky. Based on sketchy descriptions of existing telescopes, he made one with about 8x magnification, and then made improved models up to about 20x. He published his initial telescopic observations in March 1610 in a short treatise entitled Sidereus Nuncius (Sidereal Messenger).

Galileo Galilei’s discovery of the moons of Jupiter. This is a manuscript page, in Italian, on which Galileo first noted an observation of the moons; a full description of them appeared in Sidereus Nuncius in March 1610.
For a translation from Sidereus Nuncius click on the picture.

In 1610 Galileo discovered Jupiter's four largest satellitess (moons): Io, Europa, Ganymede, and Callisto. He determined that these moons were orbiting the planet since they would occasionally disappear; something he attributed to their movement behind Jupiter. He made additional observations of them in 1620. (Later astronomers overruled Galileo's naming of these objects, changing his Medicean stars 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.

Galileo noted that Venus exhibited a full set of phases like the Moon. Because the apparent brightness of Venus is nearly constant, Galileo reasoned that Venus could not be circling the Earth at a constant distance. By contrast, the heliocentric model of the solar system developed by Copernicus would neatly account for the steady brightness by reason of the much greater distance from the Earth at the time of "full Venus", when the two planets were on opposite sides of the sun such that Venus' illuminated hemisphere faced the Earth.

Galileo made the first European observations of sunspots, although there is evidence that Chinese astronomers had done so before him. The very existence of sunspots showed another difficulty with the 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 either the geocentric system or that of Tycho Brahe.

He was the first to report lunar mountains, whose existence he deduced from the patterns of light and shadow on the Moon's surface. He even estimated their 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", and not a perfect sphere as Aristotle had claimed.

Galileo observed Neptune in 1611, but believed it to be a star.


Galileo's theoretical and experimental work on the motions of bodies, along with the largely independent work of Kepler and 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.

One of the most famous stories about Galileo is that he dropped balls of different masses from the Leaning Tower of Pisa to demonstrate that their velocity 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. Though the story of the tower first appeared in a biography by Galileo's pupil Viviani, it is now not generally believed to be true. However, Galileo did do experiments involving balls rolling down inclined planes, which showed the same thing. He determined the correct mathematical law for acceleration: the total distance covered, starting from rest, is proportional to the square of the time. He concluded that falling objects are accelerated independently of their mass, and that objects retain their velocity unless a force acts upon them.

Galileo also noted that a pendulum's swings always take the same amount of time, independently of the amplitude. While Galileo believed this equality of period to be exact, it is only approximate, applying to small swings. It is good enough to regulate a clock, however, as Galileo may have been the first to realize. (See Technology.)

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, he could detect no delay greater than when he and the assistant were a few yards apart. While he could reach no conclusion on whether light propagated instantaneously, he recognized that the distance over which he had made the measurement was small.


While Galileo's application of mathematics to experimental physics was innovative, his mathematical methods were the standard ones of the day. The analyses 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, which a modern finds incomparably easier to follow.

Galileo produced one piece of original and even prophetic work in mathematics: Galileo's paradox, which shows that there are as many odd numbers as there are whole numbers including both even and odd. Such seeming contradictions were brought under control 250 years later in the work of Georg Cantor.


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 Tartaglia and Guidobaldo. For gunners, it offered, in addition to a new and safer way of elevating cannon 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 1606 - 1607 (or possibly earlier) Galileo made a thermometer, using the expansion and contraction of air in a bulb to move water in an attached tube.

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 rest of his life; but the practical problems were insurmountable, and it was another century before John Harrison mastered longitude with his chronometer.

In his last year, when totally blind, he designed an escapement mechanism for a pendulum clock. The first fully operational pendulum clock was made by 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.

Galileo wrote several books which were circulated outside of Italy. In fact, his final book, the Two New Sciences, was published by Elzevir in the Netherlands and was not publicly circulated in Italy, where the Inquisition's ban against publishing anything whatever by Galileo was in force.

Church controversy

Galileo was a devout Catholic, yet his writings on Copernican heliocentrism disturbed the Catholic Church, which believed in a geocentric model of the solar system. The church argued that heliocentrism was in direct contradiction of the Bible and the highly revered ancient writings of Aristotle and Plato. For his insights, Galileo was threatened with death at the stake and would eventually face lifelong house arrest after recanting his claims.

The geocentric model was generally accepted at the time not only for scriptural reasons. By the time of the controversy, the Catholic Church had in fact abandoned the Ptolemaic model for the Tychonian model in which the Earth was at the centre of the Universe, the Sun revolved around the Earth and the other planets revolved around the Sun. This model is geometrically equivalent to the Copernican model and had the extra advantage that it predicted no parallax of the stars, an effect that we now know was impossible to detect with the instruments of the time.

An understanding of the controversies, if it is even possible, requires attention not only to the politics of religious organizations but to those of academic philosophy. Before Galileo had trouble with the Jesuits and before the Dominican friar Caccini denounced him from the pulpit, his employer heard him accused of contradicting Scripture by a professor of philosophy, Cosimo Boscaglia, who was neither a theologian nor a priest. The first to defend Galileo was a Benedictine abbot, Benedetto Castelli, who was also a professor of mathematics and a former student of Galileo's. It was this exchange that led Galileo to write the Letter to Grand Duchess Christina. (Castelli remained Galileo's friend, visiting him at Arcetri near the end of Galileo's life, after months of effort to get permission from the Inquisition to do so.)

However, real power lay with the Church, and Galileo's arguments were most fiercely fought on the religious level. The late nineteenth and early twentieth century historian Andrew Dickson White wrote from an anti-clerical perspective:

The war became more and more bitter. The Dominican Father Caccini preached a sermon from the text, "Ye men of Galilee, why stand ye gazing up into heaven?" and this wretched pun upon the great astronomer's name ushered in sharper weapons; for, before Caccini ended, he insisted that "geometry is of the devil," and that "mathematicians should be banished as the authors of all heresies." The Church authorities gave Caccini promotion.

Father Lorini proved that Galileo's doctrine was not only heretical but "atheistic," and besought the Inquisition to intervene. The Bishop of Fiesole screamed in rage against the Copernican system, publicly insulted Galileo, and denounced him to the Grand-Duke. The Archbishop of Pisa secretly sought to entrap Galileo and deliver him to the Inquisition at Rome. The Archbishop of Florence solemnly condemned the new doctrines as unscriptural; and Paul V, while petting Galileo, and inviting him as the greatest astronomer of the world to visit Rome, was secretly moving the Archbishop of Pisa to pick up evidence against the astronomer.

But by far the most terrible champion who now appeared was Cardinal Bellarmin, one of the greatest theologians the world has known. He was earnest, sincere, and learned, but insisted on making science conform to Scripture. The weapons which men of Bellarmin's stamp used were purely theological. They held up before the world the dreadful consequences which must result to Christian theology were the heavenly bodies proved to revolve about the Sun and not about the Earth. Their most tremendous dogmatic engine was the statement that "his pretended discovery vitiates the whole Christian plan of salvation." Father Lecazre declared "it casts suspicion on the doctrine of the incarnation." Others declared, "It upsets the whole basis of theology. If the Earth is a planet, and only one among several planets, it can not be that any such great things have been done specially for it as the Christian doctrine teaches. If there are other planets, since God makes nothing in vain, they must be inhabited; but how can their inhabitants be descended from Adam? How can they trace back their origin to Noah's ark? How can they have been redeemed by the Saviour?" Nor was this argument confined to the theologians of the Roman Church; Melanchthon, Protestant as he was, had already used it in his attacks on Copernicus and his school. (White, 1898; online text)

In 1616, the Inquisition warned Galileo not to hold or defend the hypothesis asserted in Copernicus's On the Revolutions, though it has been debated whether he was admonished not to "teach in any way" the heliocentric theory. When Galileo was tried in 1633, the Inquisition was proceeding on the premise that he had been ordered not to teach it at all, based on a paper in the records from 1616; but Galileo produced a letter from Cardinal Bellarmine that showed only the "hold or defend" order. The latter is in Bellarmine's own hand and of unquestioned authenticity; the former is an unsigned copy, violating the Inquisition's own rule that the record of such an admonition had to be signed by all parties and notarized. Leaving aside technical rules of evidence, what can one conclude as to the real events? There are two schools of thought. According to Stillman Drake, the order not to teach was delivered unofficially and improperly; Bellarmine would not allow a formal record to be made, and assured Galileo in writing that the only order in effect was not to "defend or hold". According to Giorgio di Santillana, however, the unsigned minute was simply a fabrication by the Inquisition.

Despite his continued insistence that his work in the area was purely theoretical, despite his strict following of the church protocol for publication of works (which required prior examination by church censors and subsequent permission), and despite his close friendship with Maffeo Barberini who later became Pope Urban VIII and presided throughout the ordeal, Galileo was forced to recant his views repeatedly, and was put under life-long house arrest from 1633 to 1642.

The Inquisition had rejected earlier pleas by Galileo to postpone or relocate the trial because of his ill health. At a meeting presided by Pope Urban VIII, the Inquisition decided to notify Galileo that he either had to come to Rome or that he would be arrested and brought there in chains. Galileo arrived in Rome for his trial before the Inquisition on February 13, 1633. After two weeks in quarantine, Galileo was detained at the comfortable residence of the Tuscan ambassador, as a favor to the influential Grand Duke Ferdinand II de' Medici. In April 1633, he was formally interrogated by the Inquisition. He was not imprisoned in a dungeon cell, but detained in a room in the offices of the Inquisition for 22 days.

On June 22, 1633, the Roman Inquisition started its trial against Galileo, who was then 69 years old and pleaded for mercy, pointing to his "regrettable state of physical unwellness". Threatening him with torture, imprisonment, and death on the stake, the show trial forced Galileo to "abjure, curse and detest" his work and to promise to denounce others who held his prior viewpoint. Galileo did everything the church requested him to do. That the threat of torture and death Galileo was facing was a real one had been proven by the church in the earlier trial against Giordano Bruno, who was burned at the stake in 1600 for holding a naturalistic view of the Universe.

The tale that Galileo, rising from his knees after recanting, said "Eppur si muove!" (But it does move!) cannot possibly be true; to say any such thing in the offices of the Inquisition would have been a ticket to follow Bruno to the stake. But the widespread belief that the whole incident is an 18th-century invention is also false. A Spanish painting, dated 1643 or possibly 1645, shows Galileo writing the phrase on the wall of a dungeon cell. Here we have a second version of the story, which also cannot be true, because Galileo was never imprisoned in a dungeon; but the painting shows that some story of "Eppur si muove" was circulating in Galileo's time. In the months immediately after his condemnation, Galileo resided with Archbishop Ascanio Piccolomini of Siena, a learned man and a sympathetic host; the fact that Piccolomini's brother was a military attaché in Madrid, where the painting was made some years later, suggests that the Archbishop may have related a story to his family, and it later became garbled in oral tradition.

Galileo was sentenced to prison, but because of his advanced age (and/or Church politics) the sentence was commuted to house arrest at his villas in Arcetri and Florence[1]. Because of a painful hernia, he requested permission to consult physicians in Florence, which was denied by Rome, which warned that further such requests would lead to imprisonment. Under arrest, he was forced to recite penitentiary psalms regularly, and his social contacts were at times highly restricted, but he was allowed to continue his less controversial research.

Publication was another matter. His Dialogue had been put on the Index Librorum Prohibitorum, the official black list of banned books, where it stayed until 1822 (Hellman, 1998). Though the sentence announced against Galileo mentioned no other works, Galileo found out two years later that publication of anything he might ever write had been quietly banned. The ban was effective in France, Poland, and German states, but not in the Netherlands.

He went totally blind in 1638 (his petition to the Inquisition to be released was rejected, but he was allowed to move to his house in Florence where he was closer to his physicians).

According to Andrew Dickson White and many of his colleagues, Galileo's experiences demonstrate a classic case of a scholar forced to recant a scientific insight because it offended powerful, conservative forces in society: for the church at the time, it was not the scientific method that should be used to find truth -- especially in certain areas -- but the doctrine as interpreted and defined by church scholars, and this doctrine was defended with torture, murder, deprivation of freedom, and censorship.

More recently, the viewpoints of White and his colleagues have become less generally accepted by the academic community, partially because White wrote from a perspective that Christianity is a destructive force. This attitude can also be seen in the works of Bertolt Brecht, whose play about Galileo is one of the chief sources for popular ideas about the scientist. Moreover, deeper examination of the primary sources for Galileo and his trial shows that claims of torture and deprivation were likely exaggerated. Dava Sobel's Galileo's Daughter offers a different set of insights into Galileo and his world, in large part through the private correspondence of Maria Celeste, the daughter of the title, and her father.

In 1992, 359 years after the Galileo trial, Pope John Paul II issued an apology, lifting the edict of Inquisition against Galileo: "Galileo sensed in his scientific research the presence of the Creator who, stirring in the depths of his spirit, stimulated him, anticipating and assisting his intuitions." After the release of this report, the Pope said further that "... Galileo, a sincere believer, showed himself to be more perceptive in this regard [the relation of scientific and Biblical truths] than the theologians who opposed him."


Writings by Galileo

See also: Galilean transformation, Lorentz transformation equations


Other sources