In a letter to Giuliano de' Medici (1574-1636), Tuscan ambassador to Prague, dated December 11, 1610, Galileo (1564-1642) made the announcement of a sensational astronomical discovery by means of a complex anagram that Kepler (1571-1630) tried in vain to decipher. The enigma was then revealed in another letter to Giuliano de' Medici dated January 1, 1611: the mother of Love, that is, Venus, imitates the configurations of Cynthia, that is, the Moon. In other words, the planet Venus, exactly like the Moon, presented phases.
This discovery held great cosmological implications. In the Ptolemaic system, in fact, each planet moved in a circle, the epicycle, whose centre rotated in a larger circle, called deferent, around the Earth, immobile at the centre of the universe. To explain the fact that Venus and Mercury never moved beyond a certain angular distance from the Sun, the Ptolemaic model held that the centre of the epicycle had a period of one year and was always centred on the Sun. The two planets were thus perennially found below the solar orb and consequently would have been obliged to show the phenomenon of the phases without every exceeding a narrow sickle.
In the Copernican system instead, the Sun is immobile at the centre of the universe, while all of the planets, Earth included, rotate around it. The orbits of Venus and Mercury are thus found within the Earth's orbit. For this reason, they should show the entire range of phases, which is what Galileo managed to observe for the first time.
The discovery of the phases of Venus reinforced Galileo's conviction of the truth of the Copernican system.