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Why Can’t Venus be Fully Lit by the Sun in the Ptolemaic System?

17 May 2015, 01:09 UTC
Why Can’t Venus be Fully Lit by the Sun in the Ptolemaic System?
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Question: The first known observations of the full planetary phases of Venus were by Galileo at the end of 1610 (though not published until 1613). Using a telescope, Galileo was able to observe Venus going through a full set of phases, something prohibited by the Ptolemaic system (which would never allow Venus to be fully lit from the perspective of the Earth, as this would require it to be on the far side of the sun, which is impossible if its orbit is, as the Ptolemaic system requires, between the Earth and the sun). This observation essentially ruled out the Ptolemaic system, and was compatible only with the Copernican system and the Tychonic system and other geoheliocentric models. [From the Wikipedia page on the Phases of the Venus].
Can you please explain this? In the Ptolemaic system if Venus orbits the earth why would it not be fully lit when it is on the far side of its orbit around the earth just like the moon when it is not between the earth and the Sun. – Joe
Answer: In the Ptolemaic system the order of the planets, the Sun, and the stars from the Earth was as follows:

Moon

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