Nicholas Copernicus is considered to be the founder of the heliocentric theory, which states that the sun is in the center of the solar system and that the planets revolve around it, in contrast to the geocentric world view common at that time, where the earth was considered to be the center of the solar system.
In print, his system was only published in Rheticus' Narratio prima (1540). Copernicus wrote a larger manuscript in 1530, De revolutionibus orbium coelestium (On the orbits of the celestial bodies). Because this theory contradicted the scientific views of the time that explained the worldview with the physics of Aristotle and Ptolemy, and because he was afraid of justified criticism - the Copernican model showed several weaknesses and hardly any advantages - Copernicus was long hesitant about publishing a theory which raised more problems than it solved.
Galileo concluded that the Sun is at the center of our solar system. The interpretation of his own observations contradicted Ptolemy's then-current geocentric model, while supporting Nicholas Copernicus's heliocentric theory. However, he could not really prove the motion of the earth around the sun, because it requires the observation of the parallax of the stars.
Kepler had also suggested the heliocentric model as correct in 1597. In the fall of 1610, he was able to see Jupiter's moons with a borrowed telescope, and was the first scientist to confirm Galileo's observations.