What were Galileo's principle contributions to the advance of science?
Galileo is best known for his work as an astronomer, and his contributions to that field are almost unparalleled in their revolutionary effect. While he was not the first to build a telescope, he was the first to utilize the device to its full potential, and with it, he discovered the mountainous, irregular surface of Earth's moon; the existence of moons orbiting Jupiter; the phases of Venus; the rings of Saturn (although he mistook these as indication of Saturn's existence as a triple star); and sunspots, a discovery for which he shared credit with several others. At the same time, he made great advances in the field of physics, paving the way for the great Sir Isaac Newton later in the 17th century. In a famous experiment, he proved that all objects fall at the same rate, regardless of their weight, thus disproving the theories advanced by Aristotle millennia before. He also established the basic principles of the lever and pulley, experimented with inclined planes, and formulated the law of inertia–namely, that a body in motion will continue moving indefinitely in one direction and at a constant speed unless interfered with by another force. This would later become famous as Newton's first law of motion, but it was Galileo's brainchild. Perhaps most important, though, was Galileo's philosophical assertion of the independence of scientific inquiry from outside influences–such as religion–this notion would become the guiding philosophy of the Scientific Revolution.
What proofs did Galileo's observations offer for the Copernican system?
The Polish astronomer Copernicus first proposed heliocentricity early in the 16th century as a better mathematical description of observed phenomena than the description provided by the geocentric theory. But it was left to Galileo to provide more concrete evidence. His discovery of the moon's mountainous, earth-like surface suggested that rather than being unique and central, the earth might be only one of many similar planets. The moons of Jupiter that his telescope revealed served a similar function, since they demonstrated that a planet could have satellites in orbit around itself, and yet still orbit around a larger body–in this case the sun. But the clinching point, at least from Galileo's perspective, came when he discovered the phases of Venus–the way that Venus, viewed from the earth, waxed and waned, which had long been considered a necessary consequence of the hypothesized earthly orbit of the sun. Still, it is important to note that none of these pieces of evidence proved the heliocentric system. They were very suggestive, but they only indicated the truth of Copernicus's theory, and it was this that the Catholic Church would seize upon in insisting that heliocentricity was "only" a theory. They were right: it was only a theory, but it turned out to be the only theory that fit the facts.
Why did the Catholic Church put Galileo on trial for heresy?
In a broad sense, the Protestant Reformation provided the main motivation for the Church's trial of Galileo. It was this threat that had created the Counter-Reformation, and placed the Church in a distrustful and defensive posture, constantly on guard against heresy and threats to the eternal truths embodied in the faith. The Copernican system, while not a direct threat to Catholic dogma, threatened to wreck the foundations of a philosophy and science upon which the Church had rested securely for centuries. Admitting that the earth went around the sun would have necessitated a large-scale reappraisal of the Catholic world-view, and with the struggle against Protestantism still flaring, the guardians of orthodoxy felt such a reappraisal would be extremely impolitic, undermining the Church's power even further. Instead of showing vision and foresight, they took the path of least resistance, and directed the fearsome apparatus of the Inquisition against the heliocentric ideas. However, the unfortunate trial might still have been avoided–the leaders of the Church did not really want to provoke a public confrontation with Galileo. But Galileo's ambition proved too great to resist publishing his Dialogue Concerning the Two Chief World Systems, and the resentment of his enemies in the Church was strong enough to overcome the support of his friends. Due to mutual misunderstanding and Galileo's lack of diplomacy, the middle ground fell away, and the result proved a disaster for all involved.