Why did Galileo name Jupiter’s four satellites the Medicean Stars?

Galileo Galilei named the four moons of Jupiter the "Medicean Stars" (Sidera Medicea) in 1610 to honor his patron, Cosimo II de’ Medici, the Grand Duke of Tuscany.12

Galileo had previously served as a mathematics tutor to Cosimo II for several summers. By dedicating his book, The Sidereal Messenger—which detailed his discovery of the moons—to the Grand Duke and naming the satellites after the Medici family, Galileo sought to secure royal favor. The gesture was successful; shortly thereafter, Cosimo II appointed Galileo as the mathematician and philosopher of the Grand Duke of Tuscany, a prestigious position that allowed Galileo to return to his native land.23