In the early 1600's Galileo Galilei (1564-1642) made extensive observations with one of the first astronomical telescopes. He discovered several significant things: (1) the phases of Venus; (2) blemishes in the heavens { sunspots, lunar craters, lunar maria ("seas"); (3) Saturn had "ears"; (4) the four large satellites of Jupiter (the Galilean satellites); (5) ... .
All of these discoveries were interesting in their own right, but here we consider the Galilean moons (Io, Europa, Ganymede, and Callisto) because of what they show about Kepler's Laws of Planetary Motion.
We could calculate P**2 and a**3 using the above numbers, however things would not be obvious. Let's scale the results just as we did for the Solar System. For the Solar System, we chose to use the Earth as our preferred object. That is, we chose to measure the P's and a's in terms of the Earth's period and orbital size. Let's do something similar for the Galilean moons. We will measure everything in terms of Io. To do so, we simply divide all periods by the period for Io, P = 1.769 days and we divide all orbital sizes by the orbital size for Io, a = 421,600 km. This leads to
As advertised, the Galilean moons obey Kepler's Laws of Planetary Motion. The moons, in this sense, form a mini-Solar System. As we will argue later, the Galilean moons also mimic the Solar System in terms of the compositions of the moons.
This suggests that Solar System formation is a natural process