The remarkable developments in Galileo's theory of motion revealed by his letter to Guidobaldo del Monte in 1602 have never been easy to account for in view of the almost complete lack of direct evidence. By examining the nature of the empirical evidence for the new ideas he advanced in 1602 and his earliest writings on motion in De motu, it is argued that the source of this transformation was his Copernican beliefs. There exists evidence that those beliefs led him to start work on his theory of the tides by 1595, and by 1597 to state to Kepler that Copernicanism had allowed him to account for many otherwise inexplicable phenomena. These comments very probably related to his new study of rotary and linear motion, linked to his theory of circular fall, which it is argued was devised at this point, and to an investigation of the pendulum. Such an investigation would account for his new interest in isochronism and his discovery of the link between linear and circular motion and to the two laws of isochronism announced to Guidobaldo in 1602: that of the pendulum and the law of chords.