Ptolemaic Model of the Solar System

[ZapperZ]

TL;DR Summary

The phases of Venus in the Ptolemaic model of the Solar System

OK, this is more on history of astronomy than anything else. I hope someone has an insight on how they were thinking of things back then.

The Ptolemaic model of the Solar system, i.e. the Geocentric model, placed Venus inside the sun's orbit around the earth. And to account for the retrograde motion of Venus, it is also orbiting around another center, very much like the model shown in this simulation (Flash required):

https://astro.unl.edu/classaction/animations/renaissance/ptolemaic.html

Now, here's my question. Why did the Ptolemaic model coupled the motion of Venus to the sun? You notice that the center of the smaller orbit of Venus is always in line with the sun. Anyone knows why those folks back then forced it to move this way? There must be a reason why they thought Venus was always very close to the sun and can't move too far away from it.

Zz.

 

[Janus]

They were basing the model on what they saw, and Venus doesn't gets that far from the Sun in the sky; Never getting more than 47 degrees away. Ptolemy hypothesized that Venus was between the Earth and Sun, so this model seemed to be the best fit to match observation and maintain a geocentric view.
Several centuries later a transit was finally observed which seemed to bolster this view.
It wasn't until the 17th century that Galileo noted that Venus went through the full set of phases, meaning that it had to orbit the sun.

 

[ZapperZ]

They were basing the model on what they saw, and Venus doesn't gets that far from the Sun in the sky; Never getting more than 47 degrees away.

Do you know why they only saw such a small separation of Venus from the sun? Considering that Venus is rather bright in the sky, I would think that they would have noticed Venus through its entire orbit.

I'm having a minor issue here in trying to justify why they would constraint the motion of Venus. Without such constraint, then the Ptolemaic model can still explain the full phase of Venus that we see, because there's nothing then to say that Venus and the sun can't be on opposite sides, with the Earth in the middle.

The only rational reason that I can think of is that the gibbous/full phase of Venus occurs when it is on the other side of the sun from the earth, and thus, it is very small and very far in the sky. Maybe they could not see it till Galileo and his telescope?

Zz.

 

[brainpushups]

For what it is worth this is the mention that Ptolemy gives to the planetary positions in book IX of the Almagest (Toomer translation):

"First, then, [to discuss] the order of their spheres, which are all situated [with their poles] nearly coinciding with the poles of the inclined, ecliptic circle: we see that almost all the foremost astronomers agree that all the spheres are closer to the Earth than that of the fixed stars, and farther from the Earth than that of the moon, and that those of the three [outer planets] are farther from the Earth than those of the other [two] and the sun, Saturn’s being greatest, Jupiter's the next in order towards the earth, and Mars' below that. But concerning the spheres of Venus and Mercury, we see that they are placed below the sun’s by the more ancient astronomers, but by some of their successors these too are placed above [the sun’s], for the reason that the sun has never been obscured by them [Venus and Mercury] either. To us, however, such a criterion seems to have an element of uncertainty, since it is possible that some planets might indeed be below the sun, but nevertheless not always be in one of the planes through the sun and our viewpoint, but in another [plane], and hence might not be seen passing in front of it, just as in the case of the moon, when it passes below [the sun] at conjunction, no obscuration results in most cases. And since there is no other way, either, to make progress in our knowledge of this matter, since none of the stars has a noticeable parallax (which is the only phenomenon from which the distances can be derived), the order assumed by the older [astronomers] appears the more plausible. For, by putting the sun in the middle, it is more in accordance with the nature [of the bodies] in thus separating those which reach all possible distances from the sun and those which do not do so, but always move in its vicinity; provided only that it does not remove the latter close enough to the Earth that there can result a parallax of any size."

Do you know why they only saw such a small separation of Venus from the sun? Considering that Venus is rather bright in the sky, I would think that they would have noticed Venus through its entire orbit.

The 47 degrees is the (roughly) the maximum elongation of Venus that can be observed because of the size of its orbit. When it is close to the sun (angularly speaking) they couldn't see it. When you see Venus you probably will note that it has always been relatively soon after sunset when it is relatively far from the sun and high in the sky.

 

[Janus]

Do you know why they only saw such a small separation of Venus from the sun? Considering that Venus is rather bright in the sky, I would think that they would have noticed Venus through its entire orbit.

I'm having a minor issue here in trying to justify why they would constraint the motion of Venus. Without such constraint, then the Ptolemaic model can still explain the full phase of Venus that we see, because there's nothing then to say that Venus and the sun can't be on opposite sides, with the Earth in the middle.

The only rational reason that I can think of is that the gibbous/full phase of Venus occurs when it is on the other side of the sun from the earth, and thus, it is very small and very far in the sky. Maybe they could not see it till Galileo and his telescope?

Zz.

Here's Earth's orbit and Venus in relation. The yellow lines represent maximum angular separation from the Sun (viewed along red line.)

During the whole of the orbit as seen from the Earth, the maximum separation is ~47 degrees.

 

[ZapperZ]

Here's Earth's orbit and Venus in relation. The yellow lines represent maximum angular separation from the Sun (viewed along red line.)
View attachment 257286
During the whole of the orbit as seen from the Earth, the maximum separation is ~47 degrees.

Thank you. I think this might do it for me.

Zz.

 

[mathman]

From the theory of relativity, there is no absolute center of the solar system. Putting the sun at the center (center of mass) makes all analyses much simpler. However one could just as well put the Earth at the center - getting very weird looking orbits.

 

[Janus]

From the theory of relativity, there is no absolute center of the solar system. Putting the sun at the center (center of mass) makes all analyses much simpler. However one could just as well put the Earth at the center - getting very weird looking orbits.

Like this for the the inner solar system:
Red: Mars
Cyan: Venus
White: Mercury
Yellow: Sun

And this, if you expand out to include Jupiter and Saturn:

 

[sophiecentaur]

Summary:: The phases of Venus in the Ptolemaic model of the Solar System

I hope someone has an insight on how they were thinking of things back then.

I think the main thing they were thinking was that Earth is clearly the largest, most important location in their world. Any model (no serious Physics yet), however complicated and arbitrary, would need that basic tenet. @Janus shows (above) just how involved things would need to be but why would that have affected their opinions? The Creator made many things very complicated so why not the Universe?

It's hard to place oneself in a time like that. Even Keppler just formulated the 'rules' without including our basic laws of Gravity.

 

[brainpushups]

@Janus shows (above) just how involved things would need to be but why would that have affected their opinions?

There is no evidence that astronomers considered the actual paths of the planets in this way before Kepler's Astronomia Nova (to the best of my knowledge). See https://www.keplersdiscovery.com/Hypotheses.html source (2/3 of the way down the page - requires flash for the animations).

Summary:: The phases of Venus in the Ptolemaic model of the Solar System

Now, here's my question. Why did the Ptolemaic model coupled the motion of Venus to the sun?

As alluded to in the quote I provided in post 4, there was disagreement about the order of the Sun, Mercury, and Venus. Aside from the relative positions of Venus and Mercury never exceeding the elongations explained above, the periods of the rotations of their deferents are equal.

There's a cool way to think about this that I had not considered before I just found in this paper. Briefly: For the inferior planets the period of the deferent is equal to the sidereal period of the Earth and the period of their epicycles is equal to the planets' sidereal period.

For the superior planets the roles are reversed: the epicycle period is equal to the period of Earth and the deferent period is equal to their sidereal period. In the footnotes the author mentions that Copernicus realized these 'coincidences' can be explained with a heliocentric model.

 

[Janus]

The Creator made many things very complicated so why not the Universe?

Basically, this was the argument put forward by the Church when Galileo was arguing for the heliocentric model; That while the heliocentric model was indeed simpler, God could have made the universe any way he wanted.

 

[Klystron]

By the time of Galileo's trials, Roman Catholic theologians and church hierarchy had been convulsed for centuries with the paramount issue of the poverty of Christ. The much discussed principle of Simplicity had generally been accepted and even codified by teaching, mendicant and cloistered orders. What is cloistered life if not simple?

Accepting the least or simplest explanation for astrological/astronomical observations meant accepting poverty as the fundamental path to God; a position literally anathema to wealthy church officials and vested interests even as Enlightenment and Reformation rose.

 

[mathman]

Basically, this was the argument put forward by the Church when Galileo was arguing for the heliocentric model; That while the heliocentric model was indeed simpler, God could have made the universe any way he wanted.

General relativity says both were right and both were wrong.