Years later, Galileo would describe his time at Padua as the happiest years of his life. His first lecture, of which no copy survives, achieved him great success, and he quickly became friendly with a number of Venice's leading citizens. After surviving a bout of financial trouble in early 1593, when the demands of his family and particularly his sister's dowry almost overwhelmed him, Galileo prospered, and eventually moved from a small cottage into a larger three-story house. The house's grounds included a walled garden where he often entertained students and other guests. In 1599, at the end of his first seven- year term, the university offered to renew his appointment, and Galileo gladly accepted. By this point in time he was keeping a mistress, a Venetian woman named Marina Gambi, who would bear him three children–two daughters, in 1600 and 1601, and a son in 1606. Galileo recognized these children as his heirs, despite their illegitimate status, but he seems never to have considered marrying Marina. Scholars often remained single during this time, and the aristocratic rank of his family, especially on his mother's side, forbade him from marrying anyone as common as Marina.

Meanwhile, although Galileo's lectures never won him a great following, his scientific research was thriving. It was during this period that he accomplished most of his work in the field of physics, although he would not synthesize it until late in life, when he published his Dialogues Concerning Two New Sciences. He established the basic principles of the lever and pulley, experimented with inclined planes, and eventually formulated the law of inertia, which states that a body in motion will continue moving indefinitely in one direction and at a constant speed unless interfered with by another force. This law would later become Sir Isaac Newton's famous first law of motion. At the same time, perhaps inspired by his father's music, he posited that musical notes were in fact wave lengths of air, and researched the relationship between vibrations in a stringed instrument and the pitch of the note produced.

But even as he did this work, a new interest was intruding on his studies. This was astronomy, the study of the heavens, and a field in much ferment during the 16th century. Throughout the Middle Ages, astronomy had been dominated by the theory of geocentricity, which held that the earth lay at the center of the universe, and the sun–and the other planets–revolved around it.

This theory, which had been rigorously upheld by Aristotle and the ancient astronomer Ptolemy, fit in neatly with the Catholic Church's view of the universe, as well as with every day common sense: to the casual observer, it seemed common sense that the sun "rose" in the morning and "set" at night, in its circling pattern around the earth. As a scientific system, however, geocentricity required a complex scheme of interlocking orbits, one that became more complex and convoluted with each passing century, as Ptolemy's successors attempted to "save the phenomena," as they put it–that is, to make their system accommodate the evidence of their observations.

The Ptolemaic system was a brilliant feat of geometric precision, despite being mistaken about the actual nature of the "phenomena" it attempted to describe. But in the 16th century, geocentricity fell under attack. The first to question it was Nicholas Copernicus, a Polish astronomer, whose work On the Revolution of Heavenly Orbs (published after his death, in 1543) proposed a heliocentric system, in which the planets, including the earth, orbited the sun.

This system, Copernicus argued, arranged the known universe in a more mathematically satisfying way; but he was careful to make no claims to scientific truth. Indeed, such a claim would have had no real basis at the time: the available facts, most scientists agreed, did not support a wholesale abandonment of Ptolemy's system. Later, the great Danish astronomer Tycho Brahe (1546- 1601), who made countless stellar observations from his island observatory, rejected Copernicus's scheme entirely. But the younger generation of astronomers began to embrace it, among them Brahe's pupil Johannes Kepler (1571-1630), who discovered the laws of planetary motion and whose Mysterium Cosmographicum (1596) fiercely advocated the Copernican system, albeit with some modifications.

Kepler sent his work to Galileo, who replied in a 1596 letter, "I have for many years been a partisan of the Copernican view, because it reveals to me the causes of many natural phenomena that are otherwise incomprehensible in the light of the generally accepted hypotheses." But not until the end of his stay in Padua would Galileo devote himself fully to astronomical work, and in the 1590s he seems to have been merely lukewarm in his support of the Copernican views; his lectures continued to advance the standard arguments for an earth- centered cosmos. Meanwhile, in a portent of things to come, Kepler's writings incurred the wrath of the Catholic Church, who had begun to take a hard line on the Copernicus-Ptolemy debate, hinting that heliocentricity could not mesh with Bible's teachings on the issue. The Church had long been a center for astronomical study, and the Jesuit order in particular included many notable scientists. But by the late 16th century, the Church focused its energies everywhere on stamping out heresy; the tolerant spirit of earlier decades was on the wane. And while Protestants under Luther condemned Copernicus's ideas with equal vigor, the Catholics had the machinery in place to enforce such zeal–as Galileo would soon learn first-hand.

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