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In wikipedia's article on the phases of Venus it says:

The Ptolemaic system 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 Venus's orbit in its entirety is between the Earth and the Sun,

But the moon's orbit "in its entirety is between the Earth and Sun", and is "fully lit from the perspective of the Earth" once a month, so how can we conclude that Venus revolves around the Sun?

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The Moon orbits the Earth in such a way that it sometimes can be on the opposite side of the Earth as seen from the Sun. In other words, it’s possible to have Sun-Earth-Moon along an imaginary straight line, in that order.

However, by Ptolemy’s time, it had already been noticed that Venus is always seen close to the Sun (maximum angular distance about 47°). So it can never get opposite to the Sun as seen from Earth.

Ptolemy didn’t know why (the reason is that Venus orbits the Sun, not the Earth, which was inconceivable to Ptolemy), but his system made it so that Venus (and Mercury, for that matter) were orbiting the Earth closer to it than the Sun, and in such a way as to always be near it.

So imagine moving your two hands at arm’s length, but one closer to your face than the other. Imagine the distant one is the Sun. Then your closest hand would never get completely lit. Unless you put it behind your back, where Venus (and Mercury) never go.

So that’s why in the Ptolemaic system, Venus (or Mercury) would never get fully lit.

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  • $\begingroup$ But Venus and Mercury do get fully lit, when they are in superior conjunction. It's true that then they tend to be obscured by the Sun, but they can readily be seen to approach fullness in a small telescope. $\endgroup$
    – TonyK
    Mar 1, 2021 at 20:32
  • $\begingroup$ Indeed! And this fact alone proves that the geocentric system is false—not everything turns around the Earth, but at least some objects turn around the Sun. We now know that the Moon is the only major celestial object to turn around the Earth. $\endgroup$
    – Pierre Paquette
    Mar 2, 2021 at 0:34
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The moon's orbit is most certainly not "in its entirety between the Earth and the Sun"! A little more than half the time, it is further away from the Sun than the Earth is. As you will realise if you give it a little thought.

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  • $\begingroup$ Oh, I see my mistake there now. But then, did the ptolemaic system actually say Venus' orbit is entirely between the sun and Earth? I mean, that system said Venus orbits the Earth, so similary to what you said about the moon, Venus would half the time be further away from the sun than the Earth is. I'm probably missing something again. $\endgroup$
    – Erik Vesterlund
    Feb 28, 2021 at 23:30
  • $\begingroup$ That's a different question. $\endgroup$
    – TonyK
    Feb 28, 2021 at 23:45

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