Galileo Galilei used his telescope in 1610 to make a decisive break with ancient ideas about the sky. Part of this break originated in his observation of Jupiter and it's four largest moons. When he found the four large satellites of Jupiter, he proved that planets have satellites, so the crystalline sphere could not be perfect. He was able to follow the paths of these four satellites as they orbited Jupiter. These satellites were crucial in reinforcing the Copernican revolution. Three and a half centuries later, they became the subject of modern physical studies as we gained the technology to send interplanetary probes.
The Galilean satellites are — in order of increasing distance from Jupiter — Io, Europa, Ganymede, and Callisto. In order of decreasing size, they are Ganymede, Callisto, Io, and Europa. The inner three of these moons have specially locked orbits that cause them to periodically align it what is called at 1:2:4 orbital resonance. This means that for every one time the more distant Ganymede goes around Jupiter, Europa orbits twice, and the inner most Io orbits 4 times. Tidal effects from this requiring alignments has dramatic effects. Io is fritionally heated into a molten and volcanic world. Europa displays strange patterns from constant upwelling of liquid from it's interior, and Ganymede also shows signs of resurfacing.
All four of these moons can be easily seen through binoculars, and it is possible to test Kepler's laws through easy observations of their positions over time. These moons not only demonstrated our Solar System is something other than what Aristotle imagined, but they went on to provided checks on orbitally theory, and to trigger imaginations to to ask "What if Jupiter were a bit bigger?" As we look at this gas giant and it's host of orbiting moons we can get a since of what life might be like in a system around a brown dwarf. Intriguingly, while Jupiter doesn't heat it's moons with internally generated light, it does heat some of them through tidal forces. Because of this alternative source of heating, it just may be possible to find life lurking on one of these Moons. NASA currently is looking for ways to explore beneath the ices of Europa, and many planetary scientists hope to see the probable sub-surface ocean of Ganymede explored as well.