# How do the phases of Venus prove heliocentrism?

I have been doing research about the Copernican Revolution, and one of the main arguments that caused many astronomers to change their minds was Galileo's observation of all phases of Venus.

The proof goes somewhat like this:

If Venus revolved around the earth, closer to the earth than the sun, then we should never be abe to see Venus when it is full, because the light side should always be facing the sun, which is away from Earth. Therefore Venus must be orbitging the sun.

Reality:

Expected observations if Venus orbited the Earth:

My problem is this: Why can't we, in a geocentric model, see Venus when it is full if Earth is between Venus and the Sun? If the Sun and Venus orbit in rings around the Earth, then surely there must be a point when the Sun is on one side of the Earth and Venus is on the other, and the Sun illuminates the side of Venus facing Earth, making the Venus full?

• Venus is never on the opposite side of the Earth from the Sun. Venus is always within 47° of the direction of the Sun when viewed from Earth. May 23, 2023 at 13:08
• In the Ptolemaic model, Venus doesn't simply "orbit in a ring around the Earth" -- its motion on its epicycle ensures you never end up with "Sun on one side and Venus on the other" (which observers had long ago seen was never the case). May 23, 2023 at 20:36
• Don't focus on the phases, more on the apparent size of Venus in correlation with the phases. May 23, 2023 at 21:07
• @Novotny why not? What if Earth is on one side of the sun and Venus is on the other? May 23, 2023 at 23:23

Venus is never in opposition to the Sun. Venus goes through all its phases within about 47 degrees of the Sun.

The crucial point is to observe that there is a correlation between the angular size of the planet as viewed from Earth and the illumination phase. This shows that Venus is further away when it is "full" and much closer to use when it is a narrow "crescent". This quite naturally suggests it is orbiting the Sun and we see it as "full" when it is on the other side of the Sun from us and as a narrow crescent when it is on our side of the Sun.

• What does “in opposition to” the Sun mean? May 23, 2023 at 23:22
• @fartgeek opposite to the Sun in Earth's sky. May 24, 2023 at 5:13

As ProfRob pointed out, Venus is never in opposition to the Sun. This means it’s never 180° from the Sun. Moreover, it’s never more than about 47° from the Sun. That, by itself, is a first hint, but let’s say, for the sake of argument, that we still think it somehow turns around the Earth (on an epicycle [small circle] that turns on a deferent [larger circle], in Ptolemy’s model).

So, we have established that Venus is never far from the Sun in Earth’s sky. Don’t do the following experiment with the Sun, but a lamp whose light is bearable to your eyes will suffice. Place your finger between your face and the lamp. Do you see your finger as fully lit? No. You always see at least part of it that’s shaded, just like Venus in your second image.

But now, if you allow your finger to go past the lamp, then you can see it fully lit.

Technically, it doesn’t prove that Venus revolves around the Sun per se, as its epicycle could simply be large enough to encompass the Sun. However, Mercury shows the same phases (sometimes fully lit when it’s on the other side of the Sun, but sometimes a thin crescent when it’s closer to the Earth). Now, it would be quite a coincidence that both planets would have epicycles that encompass the Sun, wouldn’t it?

Another very important clue, as ProfRob mentioned, is the angular size of the planet’s disk and how it changes with time. Simple geometry can be used to demonstrate that the epicycle would not only encompass the Sun, but actually be centered on it.

The final nail in the coffin of geocentrism, though, was the discovery of the galilean satellites around Jupiter. It proved that celestial objects could revolve around other things than the Earth—in occurrence, around the planet Jupiter. Then we discovered satellites to Saturn, etc.

Before I conclude, I’d like to point out that the “Copernican Revolution” would better be named the “Keplerian Revolution,” as Copernicus’s model was very slowly accepted by scientists, as it did not offer anything better than Ptolemy’s model—actually, it’s almost the exact same as Ptolemy’s model, but “shifted” to a solar point of view. There were even two epicycles for the Moon, where Ptolemy had only one. And while instruments were not precise enough to reveal the difference at the time Copernicus’s De Revolutionibus was published, Tycho Brahe soon discovered instrumental and personal errors and took steps to compensate for them, allowing much better measurements. Kepler eventually complained that Copernicus’s model was five degrees off compared to actual observations—that’s a huge difference, the size of about three fingers held at arm’s length!

When in 1609 Kepler discovered that planetary orbits are (to first approximation) ellipses, then theory was found to perfectly fit with observations. The same year, Galileo discovered Jupiter’s four largest moons, and geocentrism was buried once and for all.

• Ibwould argue that if a plaanet's epicycle hoes around the Sun, then the planet might as well be considered to go around the Sun (by traveesing the "epicycle"). Jul 9, 2023 at 0:03

The key point is that Venus always goes in a tiny little circle in front of the Sun, in the geocentric model.

This was a necessity as they always saw that Venus was close to the Sun, in the morning or after sunset.

So when Galileo saw a "full Venus" (implying it was behind the sun) - that broke the model.

Here is an illustration: