The present work shows the equivalence between the simple harmonic motion and the uniform circular motion using the orbital parameters of the Galilean Moons of Jupiter. We use the data obtained by Galileo Galilei in 1610 with the very first telescope in history, which were published in the monumental book Sidereus Nuncius. We compare the Galilean diagrams featuring in Sidereus Nuncius with the images of Io, Europa, Ganymede and Callisto, obtained with the Cartes du Ciel, an open-source computer program that works as an interactive ephemerides. We obtain the Medicean Planets orbital radii by assuming Kepler's third law and using the orbital data calculated from the plots of the angular separation of the four moons from Jupiter as a function of time.
Galilean moons; simple harmonic motion; uniform circular motion
