This is a drawing of the evolution of moons.
Image from: The New Solar System
The co-formation theory explains the origins of moons as objects which formed out of the initial cloud of gas and dust at the same time and roughly the same place as the parent planet. As shown in this picture, while they were forming in the solar nebula, the beginning of the moons-to-be (called proto-moons) drew material to themselves from the cloud of gas and dust around them. This theory seems to explain the many icy moons around the giant planets in the outer solar system.
The cooler temperatures which played a role in the formation of the planets seems also to have played a role in the formation of these moons. Just as the planets became more and more icy the further from the sun, moons seem to be more and more icy the further from the planet they orbit. For example, Jupiter's moon Io (close to Jupiter) is very rocky, but Europa (farther from Jupiter) has more ice, Ganymede and Callisto (further still from Jupiter) have lots more ice.
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