For the next two and a half centuries, Io remained an unresolved, 5th-magnitude point of light in astronomers' telescopes. During the 17th century, Io and the other Galilean satellites served a variety of purposes, including early methods to determine longitude, validating Kepler's third law of planetary motion, and determining the time required for light to travel between Jupiter and Earth. Based on ephemerides produced by astronomer Giovanni Cassini and others, Pierre-Simon Laplace created a mathematical theory to explain the resonant orbits of Io, Europa, and Ganymede. This resonance was later found to have a profound effect on the geologies of the three moons.