In his Letter to Christine of Lorraine Galileo had been over-confident in supposing that the heliocentric theory could not be suppressed. 'Closing the mouth of one man' would not be sufficient: it would be necessary to 'ban … the work of Copernicus and the writings of other authors who held the same doctrine', 'to prohibit the whole science of astronomy', to the point of stopping men from 'looking at the sky.' Today we know that he was ultimately right, but unfortunately certain historical processes last much longer than the lifetime of a man. However, some faint signals that the drops were carving a groove in the stone were soon to emerge. No longer able to deny the evidence of what was demonstrated by telescopic observation, but still refusing to countenance, as a concept 'damned', the mobility of the Earth, many Jesuit astronomers had begun to embrace a mixed system hypothesized by the Danish scientist Tycho Brahe (d. 1601), who had attempted to mediate between the Ptolemaic and the Copernican systems. This had given rise to a sort of geo-heliocentrism, whereby the Sun was held to complete one revolution around the Earth, together with all the other planets rotating around it in their turn. The Tychonic system failed to explain all the phenomena, but it did leave the Earth firmly immobile at the centre of the universe. This was enough for the Jesuits, so terrified by the idea of a mobile Earth as to overlook even the fact that, from the orthodox Catholic viewpoint, Tycho Brahe was an abominable heretic of Protestant faith. Galileo, for his part, had never taken Tycho's efforts seriously, finding in his cosmic system 'the major difficulties' that had made him 'part ways with Ptolemy.' He had even refused - decided, difficult character that he was - to have any contact with Tycho in person, never agreeing to the latter's requests for an exchange of ideas.

Galileo continued to pursue his studies with discretion. In 1617 he withdrew to the country, renting a villa on the hill of Bellosguardo, where he moved with his son Vincenzo. His two daughters, both nuns, had already been living nearby for some years in the convent of San Matteo in Arcetri, also outside the city walls. The retired residence on the Florentine hills, over which Galileo travelled on mule-back to visit his daughters, was not paralleled by a similar intellectual isolation, despite the precautions taken after the events of 1616. On the contrary, Galileo was still considered the protagonist of scientific debate, a protagonist in his own individual way, bitingly critical of the dusty scholastic philosophies and ardently defending his own working methods.

In 1618-19 an occasion for new controversy was provided by the appearance of three comets, which Galileo could not even observe directly, since he was, as often, ill and confined to his bed. This time Jesuit thought was embodied by Father Orazio Grassi, who published an anonymous treatise (De tribus cometis anni mdcxviii disputatio astronomica [An Astronomical Disputation on the Three Comets of the year 161 8]), to which Galileo replied in 1619 with the Discourse on Comets, prudently signed by his pupil Mario Guiducci, but in fact essentially his own. The discussion on the nature of comets was concerned with their collocation in the heavenly regions, their appearance when enlarged by the telescope and, above all, the curvature of their tails and their motion, which Galileo, in opposition to Grassi, believed to be rectilinear, though the observations clearly revealed an apparent deviation that called for an explanation. Underlying the discussion, though not made explicit, was the clash between two different world systems: that of Tycho against that of the unnameable, but essential, Copernicus. 'We,' states the Discourse, 'should content ourselves with the little that can be conjectured amid the shadows, until the true constitution of the parts of the world has been determined, because that promised us by Tycho remains imperfect.' What then could be the silent reason for that apparent curve in the movement of comets? 'I hear someone, I know not who, who whispers in my ear, fearful and subdued: the motion of the Earth. Away with this false locution, grating to the ears of a devout man!' said Father Grassi maliciously, repaying Galileo with a coin supposed to ring truer, since it was fused with other metals than those of science alone.