This manuscript contains observations and calculations made by the Italian scientist and mathematician Galileo Galilei (1564–1642) on the so-called Medicean Planets—the satellites rotating around the planet Jupiter that Galileo discovered using the powerful telescope he invented and built in late 1609. Galileo made these notes in the course of his intense astronomical studies of early 1610, when he was in the last months of his tenure of the chair of mathematics at the University of Padua. These observations were then synthesized in his Sidereus Nuncius (Starry messenger), published ...