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

-- | May 16, 2015

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
Mercury
Venus
Sun
Mars
Jupiter
Saturn
Fixed Stars

A key fact in this discussion is the fact that in the Ptolemaic system Venus is always between us and the Sun. Therefore, we would always see some of the night-side of Venus (the side which faces away from the Sun). This arrangement would never allow Venus to be fully-lit. Therefore, the fat that Galileo observed the full-phase of Venus required that Venus orbited the Sun between the Earth and the Sun.

Jeff Mangum

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