In Florence, Galileo's search for a house from which he could continue to make telescopic observations reveals how totally absorbed he now was in his astronomical studies. In 1610 he sang the praises of a house with 'an elevated terrace that reveals the whole sky all around.' And in fact a letter was addressed to him a little later 'in Porta Rossa, at the Tower of the del Meglio', but there is no other evidence of his having resided in this quarter. Instead, he was frequently to be found living in the hills around Florence, more suitable to his work and his fragile health, always afflicted by the damp, heavy, mentally oppressive air of Florence. Viviani was to note with hindsight: 'It seemed to him that the city was in a certain way the prison of speculative minds, and that the freedom of the countryside was the book of nature, always open to the man who, with the eyes of the mind, loved to read and study it.' Galileo was the guest of Antonio de' Medici in his villa at Marignolle, and also stayed at the Villa delle Selve near Lastra a Signa, put at his disposal by his friend Filippo Salviati.

Whether the villas of his friends were responsible or not, Galileo's progress in astronomy during this period was remarkable. Continuing his observations of Jupiter's satellites, he succeeded, with the aid of instruments such as the jovilabe, in establishing with remarkable exactitude their periods of revolution as viewed from the Earth, and he sensed that he had to correct his calculation of their positions, taking into account the terrestrial orbit around the Sun. For seafarers, new possibilities for measuring longitude were opened in this way, and Galileo was to try several times to sell his discovery to the maritime powers, first to Spain and subsequently to the States General of Holland. The 'longitude business' however did not succeed: the complicated and prolonged negotiations always came to nothing.

Not satisfied to rest on this new discovery, Galileo extended his observations to Saturn and Venus. His telescope was not powerful enough to allow him to distinguish the ring around Saturn, a planet that he first thought was composed of three distinct parts, then of three lobes joined together. But it did reveal to him that the planets do not shine with a light of their own, and did allow him to demonstrate 'by means of reason', observing their phases, that 'Venus necessarily moves around the Sun, and Mercury too', a further proof of the unsustainability of the geocentric hypothesis.

In the spring of 1611 Galileo requested and received the Grand Duke's permission to go to Rome, to expound his discoveries in detail to the Jesuit scientists of the Collegio Romano. Initially convinced that Galileo's discoveries were to be explained as optical illusions, astronomers such as Cristoforo Clavio and Odo van Maelcote now fully acknowledged the credibility of Galileo's telescopic observations and even expressed their compliments. But they always refrained from the least consideration of the implications in the philosophical field as regards the structure of the universe, thus putting into practice the advice given to Galileo by his Paduan friend, Paolo Gualdo, who warned him - a portent, as it were, of what was soon to happen - that 'many things can be said in dispute which it is unwise to declare to be true, especially when you have universal, long-established opinion against you.' Galileo was received by Pope Paul V, who showed his esteem by refusing to allow the scientist to kneel before him. He was welcomed with all honours by the Academy of the Lincei, whose founder, Federico Cesi, had been seduced by that 'mountainous, cavernous, sinuous, watery moon', that 'horned Venus', and that 'triple Saturn of his.' With such a warm welcome, Galileo convinced himself that he had won everybody over to his side, excepting the immovable Peripatetics, 'more partial to Aristotle than Aristotle himself would have been.' But under the ashes, fire was smouldering. The first protests arose within the Jesuit Order, and the Inquisition ordered information to be gathered on Galileo and his imprudent association in Padua with Cesare Cremonini, then under investigation on many charges.