Originally, Kepler wanted to be a theologian. Lacking money, he made a living as a mathematics teacher in a small Austrian town where he supplemented his income with astrological calendars. There, at age 25 while teaching, he realized that the orbits of the then known 5 planets could be circumscribed within the 5 known regular solids. Eventually, Kepler became Tycho Brahe's assistant at the imperial court in Prague. Brahe died shortly after Kepler's arrival and Kepler took over as court mathematician and astronomer.
At Brahe’s request that he be able to prove that his model was correct and armed with Brahe's extensive data, Kepler discovered that he could indeed arrive at a mathematical fit for the observed paths of the planets and eventually described the three laws of planetary motion. They were to prove not only the Ptolemaic system wrong but also, despite his hopes, the Tychonic (Brahe's) system as well.
More on Kepler's life
The first telescope was most likely the invention of a Dutch spectacle maker, Lippershey around 1600. By 1609, it was known all over Europe. Galileo, then professor of mathematics at the University of Padua, also ran an instrument making shop to supplement his income. Having learned how telescopes were made, he produced a nine power telescope for Venice in 1609, which he quickly (within four months) improved to a 30 power instrument. Using this refracting telescope as an astronomical tool in January 1610, he noticed all sorts of new features in the sky which so impressed him that he published them in a 24 page pamphlet entitled Sidereus Nuncius (the Starry Messenger) in March of the same year.
In 1616, he went to Rome to defend himself against that charge (heresy), and had an audience which included no less than the same Pope Paul V. Unable to convince the church of the validity of the Copernican model (neither with his evidence nor his theological arguments) the notion of a moving earth was specifically condemned as the result of this meeting. However, he himself was neither condemned nor were his books forbidden.
In 1624, Galileo returned to Rome to ask for the right to publish a comparison between the Copernican and Ptolemaic systems. He is refused. Nevertheless, in 1632, he published the Dialogue on the Two Principal Systems of the World, in which he defended the Copernican point of view and showed the limitations of the geocentric model. Caught within the catholic church's counter-reformational need to reaffirm ancient christian dogma, the church forced the extremely ill 70 year old Galileo to come to Rome where he was tried in 1633. His books were forbidden, Galileo had to abjure that the earth was moving, and he was imprisoned and died under house arrest nine years later (1642), but not before publishing a book on mechanics upon which Newton built his laws of motion and another on the strength of materials.
In 1638 he published the Dialogue of Two New Sciences, which included uniform motion, acceleration of falling bodies which included the notion that objects fall at the same rate regardless of their size, density or weight and the parabolic trajectory of projectiles. He also discovered that the period of a pendulum is a function of its length.