What was Galileo's work on Jupiter's moons proven to demonstrate, in contrast to his Milky Way discovery?

Answer

That not everything orbited the Earth

His work on Jupiter’s moons demonstrated that some celestial bodies did not orbit the Earth, while his work on the Milky Way demonstrated the immense and extensive nature of the heavens themselves.

What was Galileo's work on Jupiter's moons proven to demonstrate, in contrast to his Milky Way discovery?
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