And he radically altered the perception of the planets with his telescopic observations on Jupiter. He noted and mapped the positions of Jupiter's associated stars, which changed position each night: 

Each large circle in the figure to the left represents Jupiter; the asterisks are the points of light near Jupiter. Each line is one of the figures from Sidereus nuncius, in which he presented his drawings of Jupiter and its associated "planets" one at a time. In the text Galileo described his observations and reasoning about the movement of the small points of light. I've taken all the drawings of Jupiter from the successive nights in the original text, and combined them into this figure. The diagrammatic presentation gives you the clue to what's going on -- the points can be connected to form cycles about Jupiter, or in other words, "satellite" moons in orbit. 

The only way to see this was with a telescope, and his contemporaries realized that Galileo had provided a new kind of evidence and new questions for astronomy. The new argument was a definitive disproof of Ptolemy (and thus Aristotle) -- obviously more than one center of motion is not an impossibility after all.