Nicolas Copernicus published a work in 1543 that showed a model of the solar system in which the centre was the Sun, with Earth and other planets moving around it. This system was opposed to the Ptolomeic one which put Earth on the center, as this model was adopted by the catholic church, it became hegemonic.
Galileo supported the Copernicus model, based on his observations with telecopes, he was the frist one to use them for astronomical observation. He observed the phases of Venus, that are simmilar to the Moon ones, and determined that they were only possibled if Venus was between the Earth and the Sun. This could only work if the Sun was the centre of the solar system.