Introducing Galileo Galilei
A controversial and intellectually courageous character, Galileo Galilei (1564-1642) is recognised as the founder of modern 'scientific method', which he insisted should replace the Aristotelian philosophy prevalent during his time.
He emphasised that the only valid test of hypotheses was extensive experimentation and not deductive philosophising.
Galileo's achievements remain outstanding in the history of science. He began studying medicine but soon applied himself to the realms of mathematics, physics and astronomy. His first notable observation, that a pendulum takes the same time to swing through its arc no matter how large or small this is (isochronism), led to the application of the pendulum in accurately measuring time.
Born at Pisa into a relatively poor family. He showed considerable talent at an early age, and when he was 17 his father sent him to study medicine at the University of Pisa. There his scientific curiosity and originality began to show themselves, and he abandoned medicine in order to study science and mathematics.
He is said to have derived his basic law about the motion of the pendulum from his observations of a swinging lamp in the Cathedral of Pisa. As a teacher of mathematics at the University of Pisa and from 1592 on at the University of Padua, he pursued his experiments on the acceleration of moving bodies and also gained a reputation as a spirited lecturer.
In 1581 he went to the university of that city to study medicine, but soon began to take an interest in mathematics, and became lecturer in that subject at his university. He demonstrated by experiment that bodies fall with equal velocity, irrespective of weight. He also showed that the path of a projectile is a parabola. Owing to the influence of his opponents he was forced to resign, and from 1592 to 1610 was Professor of Mathematics at Padua.
In 1609 he became interested in the newly invented telescope, working out the optical theory of its operation and effecting considerable improvements. With it he discovered the mountains and craters of the moon, the phases of Venus (thus giving visual proof of the correctness of the Copernican theory), the satellites of Jupiter and the resolution of the Milky Way into a multitude of small stars. The Church, however, attempted to suppress him, and for 16 years fear of punishment kept him silent. But the publication of his Dialogue on the Ptolemaic and Copernican Systems led to his arrest and imprisonment hy the Inquisition. He was compelled, under fear of torture, to sign a recantation of his assertion that the earth moves. It is said that, rising from his knees, he then exclaimed, "Eppur si muove" (For all that, it does move), but this historic remark is most probably not authentic. He made further important astronomical observations after his release.
He was a versatile experimenter, mathematician, and popularizer of science. His principal scientific contributions were to astronomy and mechanics, notably his observations with the newly invented telescope and his investigation of the laws of motion. Galileo is also remembered for his conflict with the Roman Catholic Church. He considered himself a loyal Roman Catholic, and wished to remain so. However, he was eventually to find severe restrictions placed on his work, and his writings condemned, by the Church.
In Galileo's time there was a growing division between conservative scholars, whose ideas were in the medieval tradition derived originally from Aristotle, and the scholars at newer and more liberal universities, notably the University of Padua in northern Italy. Galileo was the most outstanding and forceful member of the younger generation, and he advocated the new ideas in a series of highly readable and popular books. His disregard of conservative beliefs brought him into conflict with influential members of the Vatican, and he spent his old age in disgrace.
Contributions to Mechanics
Two problems about motion had preoccupied philosophers and mathematicians throughout the Middle Ages: the nature of acceleration in general, and the motion of freely falling bodies in particular. There are legends that Galileo dropped weights from the Leaning Tower of Pisa to demonstrate that objects of different weights fall in exactly the same way. However, it had been well recognized since 500 A.D. or earlier that Aristotle's general theory of motion did not fit the facts in this case, and the law of free fall had been a matter of much dispute.
Acceleration: Galileo developed a new way of approaching the problem of free fall and linking it to the general problem of acceleration. Mathematically, he worked out a system of mechanics in which acceleration was defined in terms of the changes in a body's speed over equal periods of time, rather than over equal distances traveled. He demonstrated that a body accelerating uniformly from rest will cover a distance from its starting point proportional to the square of the time that it has been moving. He then applied this general formula to the special case of a falling body and showed that if air resistance is disregarded, the acceleration of a freely falling body is uniform in a downward direction.
Galileo's experimental demonstration of this fact was ingenious. Previous observers had been handicapped by the great rate at which falling bodies move, since they had no instruments capable of recording with sufficient accuracy the time such bodies took to fall through specific distances. Galileo simplified the problem by studying balls rolling down sloping planes instead of objects falling freely. He argued that free fall was merely the extreme case, in which the angle of slope was increased to 90°. When the slope was gentle enough it was quite easy to measure the time taken through different vertical distances and to confirm that these distances increased, as the formula requires, in proportion to the square of the time from rest.
Inertia: Galileo also considered the continuing motion of a ball along a horizontal surface such as the top of a table. He argued that, in the absence of resistances, this motion will continue at unchanged speed, without any external force being needed to keep it going. This was the first clear statement of the modern concept of inertia, for most earlier mathematicians had believed that a force is needed to keep a body moving horizontally at a constant speed. Yet Galileo himself did not take the final step: He did not define uniform motion as motion in a straight line. In his opinion a horizontal plane is one that is at every point at a constant distance from the center of the earth. He concluded that, if left to itself with no other forces acting on it, a ball moving on a horizontal plane would keep moving in a circular path until it had traveled completely around the earth.
Combination of Motions: Finally, Galileo considered the motion of a body traveling both horizontally and vertically. For example, a ball that rolls off the edge of a table will continue to move sideways at a constant speed while at the same time accelerating downward. He showed that this combination of motions causes the ball to move in a curved path that is a parabola. From this analysis, Galileo demonstrated that a can-nonball should achieve its greatest range if fired at an angle of 45° to the horizontal.
Contributions to Astronomy
In Galileo's time the greatest unresolved problem in astronomy had to do with the geometrical arrangement of the bodies forming the planetary system. The two most sharply opposed sets of ideas were those of the geocentric, or earth-centered, system and the heliocentric, or sun-centered system. Supporters of the geocentric system held that the planets and the sun moved in concentric circles around the earth. The system was a development of theories dating back to the astronomer Ptolemy, who lived in Alexandria in the 2d century A.D. Supporters of the heliocentric system held that the planets, including the earth, moved in concentric circles around the sun. This system had been worked out by the Polish astronomer Nicholas Copernicus early in the 16th century. In about 1600, many people also advocated a compromise system, developed by the Danish astronomer Tycho Brahe. He held that the planets moved around the sun and the sun itself traveled around the earth, carrying the planetary orbits with it. Galileo himself strongly supported the Copernican view and advocated it in a series of vigorous writings.
The Telescope: In 1609, Galileo learned of the invention of the telescope in Holland and constructed one for himself. With an improved telescope that magnified 6 times in diameter, or more than 30 times in area, he studied the heavens and quickly made a series of startling discoveries. He observed mountains and valleys on the moon, spots moving across the face of the sun, and four small moons revolving around the planet Jupiter. All these observations cast doubt on traditional doctrines about the heavenly bodies. For example, it had been believed that they were perfectly spherical, that they were composed of an unchanging material substance, and that they all revolved around a single center of rotation. Galileo cited his discovery of the moons of Jupiter, in particular, to support the Copernican theory, which held that the planets and their moons had different centers of rotation. He also discovered that there were many more stars than had been observed earlier with the naked eye, and so compelled astronomers to reconsider earlier ideas about the scale and arrangement of the universe.
Galileo made many other contributions to science. He explained why a small machine may work well for a long time, while a large machine of exactly the same design and material may collapse in a very short time. The reason is that as the dimensions of the machine are increased, the weight of the parts increases at a faster rate than their strength.
Galileo wrote notable papers on centers of gravity and on the hydrostatic balance, an instrument for finding the specific gravities of substances. He pointed out that an object will float in water if its density is less than that of water. He discovered that a pendulum always takes the same time to complete one swing, regardless of whether the swing is large or small. He was thus able to use the pendulum as a timing device and to design a pendulum clock. He also helped to develop the microscope and the thermometer. By refining measuring instruments to achieve greater accuracy, Galileo greatly assisted the progress of science.
Dispute With the Church.
In 1610, Galileo published a first account of his astronomical observations. The book made him famous throughout Europe and was widely circulated. A copy actually reached Peking in China within five years. Galileo went to Florence and became official mathematician to the ruling Medici family. At first he was on good terms with the Roman Catholic Church, whose more liberal-minded members, such as his friend Cardinal Bellarmine, had no wish to see an open dispute between theology and the new scientific ideas. Before long, however, the more conservative authorities of the Church became alarmed at the growing support for the Copernican theory, which was associated in their minds with the much more extreme teachings of Giordano Bruno, who had been executed for heresy in 1600. Bruno had stated that the universe was infinite and that the earth was only a small body. Churchmen were also concerned by the uncompromising way in which Galileo was advocating the Copernican theory. In 1615, Galileo made a trip to Rome to present his views personally to the authorities. In the following year, however, under pressure from the extreme conservatives, the religious court of investigation known as the Inquisition declared the Copernican theory to be heretical and admonished Galileo not to defend it.
Despite this instruction, Galileo published in 1632 an important book, Dialogue Concerning the Two Chief World Systems. In it he claimed to state the case for the geocentric and the heliocentric systems impartially, but he did so in such a way that his own belief in the great superiority of the heliocentric system was made quite obvious. Galileo was summoned to Rome to be tried for this act of disobedience to the spiritual authority of the Church. Although the Inquisition treated him with unusual consideration and respect, it ended by convicting him in 1633 of teaching false doctrines and compelled him to renounce the Copernican theory in public. He was also sentenced to be imprisoned, but the sentence was changed to house arrest.
Last Years: Galileo spent his remaining years in his country house at Arcetri, where he was watched closely but was allowed to continue his scientific work. He became blind in 1638, shortly after completing his second major book, Dialogues Concerning Two New Sciences. The book was smuggled to Holland, a Protestant country, and was published there in 1639. Galileo died three years later.
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