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1 Galileo: Wow, I see moons around Jupiter!
2 Galileo: I shall name them after the discoverer, myself. They shall be known as... The Galilean Satellites!
3 Man in Black: There's no such things as moons around Jupiter.
4 Galileo: Er, of course... my mistake. They must be... stars, I guess. I shall name them... The Medicean Stars!
4 Man in Black: Much better.
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Galileo Galilei was the first person to see the four largest moons of Jupiter, through his early telescope in 1610. His discovery of what have since come to be known as the Galilean Satellites (or Galilean Moons) marked an important point in the history of astronomy, and of science overall.
To understand the importance of what Galileo saw through his telescope, you must understand the prevailing scientific thought of the time about the universe. Observations could reveal the relative positions of objects in the sky, and very little else about them. Nobody knew what stars or planets, or the sun or moon, actually were. The only thing people really knew was that these objects appeared to move across the sky.
Quite naturally, people came to believe that these things really were moving, and that the Earth on which we stood was fixed and motionless. After all, you can't feel the Earth moving. And, as philosophers argued with little chance of being shown wrong, if the Earth was moving, surely the clouds and the birds in the air and anything you threw up into the air would all be left behind.
So the Earth - which by this stage was well understood to be more or less spherical - obviously was in the centre of the universe, and all the things in the sky revolved around it.
The relative distances to the moon and planets could be estimated reasonably well by this time too. The moon was closest to Earth, followed by Mercury, Venus, the sun, Mars, Jupiter, and Saturn (all the planets known at the time; there was a bit of a mix-up between Mercury and Venus, but otherwise correct). And, according to the best observations of the time, their motions were consistent with all of these objects revolving around the Earth. (There was a little complication called epicycles, but we can ignore that for the time being.)
This system worked, and it was difficult to mount an argument against it, because everything that could be seen in the heavens manifestly revolved around the Earth. The moon, sun, all the planets, and the set of "fixed stars" (i.e. fixed in relation to one another) all swept across the sky in regular, more or less predictable patterns, exactly as if they were indeed revolving around the Earth, and - here is the important bit - not around some other object.
So this is where Galileo's observation comes in. He saw four objects near Jupiter. At first he thought they were stars, since his telescope had shown him multitudes of new stars that nobody had ever seen before. But as he tracked the positions of these new "stars" over several nights of observing, he saw that they followed Jupiter across the sky, leaving the fixed stars behind. What's more, they moved relative to Jupiter as well. Before long he had it figured out. They were moving in circular paths around Jupiter.
This was the important breakthrough. Up to now, it was thought impossible for objects in the sky to move around any object other than the Earth because, quite simply, there was no evidence for it. Here was the evidence. There were objects that manifestly did not revolve around the Earth.
Once the existence of such objects was proven, the stranglehold the Earth had on being the rightful centre of the universe was broken. It was now possible not only to imagine other objects being in the middle of the universe, as Copernicus had done some 70 years before by placing the sun in the middle, but to defend it as a valid position. In this way, Galileo laid the groundwork for the revolution in astronomy - and our understanding of our place in the universe - that would soon follow.
On his discovery, Galileo was inspired to name the moons after his patron, Cosimo de' Medici. He initially proposed calling them the Cosmica Sidera ("Cosimo's Stars"), but was persuaded by Cosimo himself to name them after his family name to honour himself and his three brothers. So Galileo named them the Medicea Sidera ("Medicean Stars").
The moons would later come to be known as the Galilean moons, and today bear the familiar individual names of Io, Europa, Ganymede, and Callisto. But if Galileo's disciple Giovanni Battista Hodierna had had his way, the moons would have been named after the four Medici brothers: Principharus, Victipharus, Cosmipharus, and Ferdinandipharus.
I think there's at least one thing we can be thankful for there.
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