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Galileo reasoned that the phases of Venus could not be explained, if the Earth is in the center of the system of the planets. So Ptolemy's geocentric system could not be correct.

Edit: That's correct, but it doesn't answer the question, which is about Jupiter.

The idea is that Jupiter having moons proved that there are other places

that can be centres of motion, apart from Earth.

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Q: How did Galileo's observations of jupiters moons help to show that the geocentric explanation is incorrect?
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