Galileo grew up in Pisa and Florence. He studied medicine at the University of Pisa, and eventually became a mathematics teacher at the University of Padua from 1589 to 1610. After publication of Siderius Nuncius, he returned to Florence as a mathematician and philosopher to the Grand Duke Cosimo De Medici. While in this position, he writes several letters attempting to reconcile the picture of a moving earth with Biblical passages having been interpreted as indicating a stationay earth.
After a meeting in 1616 with officials from the Catholic Church, Galileo stops promoting the "Copernican hypothesis" until 1623 when a new pope (Urban VIII) is elected. Galileo met and got permission from Urban to write a neutral discussion of the various planetary systems, which results in his book of 1632 called Dialogue on the Two Great World Systems. As a result of this book, Galileo ends up in a very famous trial in Rome, and subsequently is placed in house arrest for the rest of his life.
In 1638, he published his last book, Dialogue on Two New Sciences, which had to be smuggled out of Italy and published in the Netherlands because of his punishment from the Catholic Church. Using the same three people as his other Dialogue, he presents his findings on (1) the strength of materials and how they scale, and (2) laws of motion. This is where he gives his Law of Falling Bodies. This book is much more mathematical than his other writings, and finished up a lot of the ideas he first presented in Dialogue on the Two Great World Systems. While we used algebra and calculus in the first two units of this class, all the ideas and concepts really come from Galileo between these two books.
In 1609, Galileo hears of early telescopes and builds his own, and looks up at the night sky with his (at the time) high quality telescope. He is so astounded by what he sees, he rushes Sidereus Nuncius to press in 1610 announcing some amazing discoveries with far reaching consequences. Sadly, I will not tell you what they are here, so read the book like you are supposed to.
By the winter of 1610, Galileo had observed Venus over a few months, and watched how Venus was undergoing phases, like the moon. This was a major discovery, as it proved that Venus had to go around the sun, thus disproving the Ptolemeic theory. (Note that it does NOT prove that the earth goes around the sun, as there was the Tychonic model which had a stationary earth, and a Venus that went around the sun.) (See ../concepts/ptolemywrong.html for more details.
Through 1611-12, Galileo made observations of sun spots, along with a few other scientists at the time. He made very accurate drawings of what he saw, and was able to show that the sun was spherical and rotated from his observations. (Kepler later thought that this rotation of the sun somehow caused the revolution of the planets.)
The number of discoveries made with the telescope (along with the works of Kepler who had found that Mars went around the sun in an elliptical orbit) ignites a battle between the geocentrists and the heliocentrists. In addition to the incorrect Aristotlian physics that was commonly believed, the religious issues all hinged on interpretations of some lines from the Bible. The various Christian factions were arguing over deep religious issues, and everyone was using and interpreting the Bible to further their own causes.
Galileo also wrote a number of letters to important people regarding the Bible and scientific knowledge. (Some of these became quite widely circulated.) In these letters, Galileo argues that the point of the Bible was not to teach scientific principles, and that it often speaks figuratively in order to be more easily understood. In the "Letter to the Grand Duchess Christina" Galileo quotes someone "That the intention of the Holy Ghost is to teach us how one goes to heaven, not how heaven goes."
In 1616 Cardinal Bellarmine, the Catholic Churches lead theologian, called Galileo into Rome for a meeting. Galileo was told that Copernicus' book was going to be put on the list of Prohibited Books and that he should not teach that the earth goes around the sun. The Catholic Church was not interested in trying to reconcile the Bible with a moving earth because it felt that this opened the door for reinterpreting other parts of the Bible, which is what the Protestant Reformation was all about. Bellarmine said in a letter in 1615 to someone who had been writing in favour heliocentrism:
Third, I say that if there were a true demonstration that the sun is at the center of the world and the earth in the third heaven, and that the sun does not circle the earth but the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary; and say rather that we do not understand them than that what is demonstrated is false. But I will not believe that there is such a demonstration, until it is shown me. (Letter to the Paolo A. Foscarini, on Galileo's claim in favor of heliocentrism.)
Basically, without any real proof that the earth went around the sun and rotated on its axis, the Catholic Church was not going to budge on the matter of Biblical interpretations. Galileo understands this, and so seeks absolute proof that the earth must move. He thinks he found proof in his theory of the cause of the earth's tides.
In 1623, Urban VIII was elected the new pope. Galileo had known him before, and has a series of meetings with the new Pope. As a result, Galileo felt free to write a "neutral" discussion of the various cosmologys of the day. By 1632, Galileo published his book Dialogue on the Two Great World Systems. The book was written as a discussion spread out over four days between three men: the wise teacher who was clearly promoting the Copernican system, a reactionary idiot who was promoting an Aristotelian and geocentric point of view, and the open-minded student who basically agreed and extended the ideas of the teacher. It was anything but neutral and unfortunately ends up getting Galileo in trouble with the Pope and the Inquisition.
The first day of discussions in the book attacks the notions from Aristotle that the heavens are perfect and that the earth is not. Galileo uses his observations of the moon and of sunspots to argue that neither is perfect.
The second day really discusses motion - examining straight line, circular, and projectile motion. Galileo talks about some of his experiments (notably with ramps) He points out how completely wrong Aristotle was in all of his statements about motion and causes of motion. The concept of inertia is finally fully argued. Galileo hints at a more mathematical analysis of motion that he will write in the future. (Before Galileo got sucked into astronomy, he had already studied motion extensively, and had worked out many basic ideas, but had not published anything.)
The third day is spent discussing the motion of the earth around the sun. Notably, he points out the observations of Venus to prove that Ptolemy's model is wrong. He also uses his observations of sunspots and the moons of Jupiter to argue that the heliocentric model is simpler and more easily explains the observations. Galileo ran into trouble here because he does not mention the Tychonic hybrid model, which was in fact the madel "used" by the Church. This angered the Church because there is no observational difference between the Copernican and Tychonic model - only Ptolemy was proven wrong.
The fourth day was spent on what Galileo considered his proof of the rotation of the earth - his theory of the cause of the tides. Sadly, this entire section is wrong, and actually goes against what he was trying to say about the concept of inertia earlier in the book.
While Pope Urban VIII may have been friendly with Galileo before, the book upsets him, and Galileo ends up being called into Rome by the Inquisition, and his book being put on the Index of Prohibited Books. Galileo is ultimately found guilty of teaching the Copernican system and not heresy. Heresy involved a matter of fundamental faith; teaching the Copernican model was simply disobeying orders not to teach it. Depsite that, Galileo was put under house arrest for the rest of his life, and also prohibitted from writing any more books. (Galileo does write one more book anyways - the follow up to the ideas of motion that he talked about in the the Dialogue, but it has to be smuggled out of Italy in order to be published.)
Galileo never found his proof that the earth moved. But between his work straightening out the physics of motion, his (and others) numerous telescopic observations and Kepler's mathematical Laws of Planetary Motion, the Ptolemeic and Tychonic models were dead. Officially, the Church held onto the Tychonic model for another 100 years, but science moved on based on the heliocentric system. Galileo and Kepler succeeded in changing the questions asked by science: we knew what the planets did around the sun, and the question became what was the cause of the motion. This was answered by the end of the seventeenth century with Newton and his theory of Universal Gravitation. (But that is the next unit, so don't worry about it now.)
As an aside, actual proof of the earth's motion didn't come until the middle of the 1800s, and even the Catholic Church had moved on by then. (See ../concepts/earthmoves.html for some more details.