How did the ancient Greeks and Romans explain the waxing and waning of the moon?
The same way we do–the Sun shines on different parts of the Moon in the course of the month, as the Moon revolves around the Earth.
Yeah, I’m pretty sure the correct explanation goes back at least as far as Aristotle. And even there, he probably didn’t come up with it himself, either, but was just relaying an explanation he’d heard from other scholars.
Yes, I think I have seen the ‘discovery’ attributed to Parmenides (early 5th century B.C.) somewhere, but I am not sure that there is any very solid evidence for that. On the other hand, Anaximander (c. 610 BC–c. 546 BC) did not know this (he suggested that the light of heavenly bodies is fire shining through holes in the sky), so the ‘correct’ theory seems to have emerged in Greece some time between him and Aristotle, probably in the early to mid 5th century B.C. (i.e., around Parmenides’ time, whether or not it was actually his idea).
Was there a mythological explanation?
Yes: link.
(It would be strange if something so significant as the Moon was omitted from any mythology.)
Once you’ve worked out the basic cosmology of a spherical earth surrounded by sky, the fact that the sun is shining on the moon follows pretty easily. The lit side of the moon always faces the sun, and it waxes as the moon moves opposite the sun in the sky. And you can see the entire disk via earthshine in the crescent phase, so it’s obvious the moon itself isn’t changing shape.
The real obstacle isn’t in figuring out the answer once you’ve asked the question; it’s in realizing that the question is worth asking in the first place.
I’m going to assume that everyone already knows that the ancient Greeks knew that the Earth was round and that they had a good estimate of its diameter.
Aristarchus had a good estimate of the distance of the moon (and thus he had a good estimate of the diameter of the moon):
He was quite low in his estimate of the distance of the sun:
He knew theoretically how to calculate the distance of the sun, but the instruments that were used to do it weren’t accurate enough yet. So anyone from the time of Aristarchos on knew basically what the sun-moon-Earth system looked like. Within that system, it was obvious what caused the phases of the moon.
Well, Aristarchus’ method for measuring the distance to the Sun relied on first having an understanding of the phases of the Moon in the first place, so it doesn’t really help in that regard. As for the accuracy of his measurement, it was at least good enough to correctly deduce that the Sun is larger than the Earth.
True, it was good enough to know that the sun is larger than the Earth, but my point was that the available instruments couldn’t measure angles in the sky quite accurately enough to allow him to discover the real distance. He thought that the distance to the sun is only about 19 times the distance to the moon, whereas it’s actually about 389 times as far. It’s true that somebody at some point had to make the guess that the sun and moon were huge spheres with diameters somewhere around that of the Earth, perhaps by starting with the fact that the moon had phases. Once you make that guess, you can then start to do calculations based on your observations. In any case, once you reach the point that you know basically what the sun-moon-Earth system looks like, the fact that the moon has phases is obvious.
Aristarchus also lived quite some time later than the other people who have been mentioned upthread - Aristotle, Anaxagoras, Parmenides who had already figured out what causes the phases.
I disagree that Aristotle, Anaxagoras, or Paramenides “figured out” what caused the phases of the moon, but I’m just quibbling about what the term “figured out” means. That make it sound like they did observations and measurements that they looked at and somehow deduced from those numbers what the phases must be. I presume that what happened was that someone, on a dark night when someone else had a torch and a large sphere, noticed that the sphere also displayed phases. They said, “Hey, maybe the moon is a large sphere and maybe the sun is lighting it only on the side facing it.” I would call this a clever guess rather than figuring it out. This sort of outright guess would have to have preceded doing observations and measurements.
It should also be said that Aristarchus’ measurement error wasn’t actually all that bad, it’s just that the method he was using was very sensitive to even small errors. His angle measurements were off by less than 3 degrees; it’s just that 3 degrees makes a big difference when you’re taking the tangent of an angle near 90 degrees.
Are you unfamiliar with the use of metaphor in general, or just with this common metaphor?:rolleyes: “Figured out” does not have to imply (and probably most usually does not imply) that there was math involved. It merely implies reasoning (and not guessing).
There is no reason to think that Anaxagoras or Parmenides were merely guessing, unless you are going to say that every scientist who puts forward a theory is merely guessing. Of course the theory was based on observation. They had observed the waxing and waning of the moon. They had observed the pace at which the sun and moon each move across the sky. They would be able to deduce from this whereabouts the sun would be in the heavens relative to the moon (even when they are not both visible), and, lo and behold, they would have found the geometry of the sun-Earth-moon triad to be fully consistent with the hypothesis that the moon is a sphere that shines by the reflected light of the sun. This is not guesswork, it is science (although, back then, they called it philosophy).
Aristarchus did precisely nothing to confirm or strengthen the case for this theory. He took the already well-established theory and, by combining it with a correct but trivial bit of geometrical reasoning (based upon Pythagorus’ Theorem, also well established and well known by this time) and with some inaccurate measurements, he arrived at a wildly wrong estimate of the relative distances of the moon and the sun from the Earth (about one sixth of the true value, IIRC). It is true that he should not be faulted for the fact that his measurements were inaccurate - he did not have the resources to do better - but he really should be faulted for not realizing what should have been obvious, that, given the measuring techniques and instruments available to him, he could not possibly make a measurement accurate enough to provide a meaningful result.
Aristarchus tends to be given far too much credit as an astronomer because of the alleged fact (the evidence for it is actually fairly weak) that he advocated a heliocentric model of the universe at a time when everybody else was an unquestioning geocentrist. However, none of the evidence that convinces us, or that convinced 17th century astronomers such as Galileo and Kepler*, of the truth of heliocentrism could possibly have been available to Aristarchus. There is no record of his actual reasons for embracing heliocentrism (if he actually did), but it is an effective certainly that they could not have been anything like what we would regard as good, scientific reasons. (Most likely, they had much more to do with religion than with mathematics or empirical evidence.)
*Not Copernicus, whose own reasons for accepting heliocentrism were essentially nonsense, albeit highly mathematized nonsense of a sophistication unavailable to Aristarchus. Actually, most of the reasons that originally inclined Galileo and Kepler toward heliocentrism were nonsense too, but by the ends of their careers they had each discovered some better ones.njtt, do you realize that putting snide little smilies in your posts doesn’t actually help convince me of anything? In fact, it only shows me that you don’t really want to argue with me. That “eyes rolling” smilie isn’t used to communicate with me at all. It’s used to communicate with everyone else reading this thread. It’s saying to everyone else in the thread, “Hey, this idiot doesn’t understand something that’s been shown with great detail to him. I’m going to explain it again, but that’s not for his purposes, since he’s too slow to understand me. It’s just to show all of you that I’m a guy who tries to explain things carefully, but certain idiots don’t even make an effort to understand me.”
I’ll post this evening about the content of your explanation, but I have to leave for work immediately.
First of all, Aristarchus’ measurement was, in fact, good enough to produce a meaningful result, namely that the Sun is far enough away that it must be larger than the Earth. And the fact that the Sun is larger than the Earth is, in fact, a reasonable argument for heliocentrism. And Copernicus’ reason for embracing heliocentrism was even better, being that even the simplest heliocentric model could qualitatively explain all known observations of the motions and brightnesses of the planets, where even a complicated geocentric model couldn’t explain them all.
Well, my use of the rolleyes was certainly not intended to say all that. As I think ought to have been apparent from its placing in my post, it was intended to say that your picking on my use of the common metaphor “figured out” was pedantic and silly. Frankly, I think that by making the point with a smiley I was being a little less blunt than I would have been if I had spelled it out as you have just compelled me to do. And yes, the rolleyes was addressed to everyone in the thread, and was not particularly intended to convince you, specifically, of anything. Yes, it was intended to be (very mildly) offensive, because I was (mildly) offended by your nitpicking at my innocuous metaphor. Do you really want to escalate this any more?
As for the substance of your claim - that before Aristarchus they were just making an “outright guess” about the illumination of the moon - for the reasons I have already explained, it is unfounded and almost certainly wrong. They could have had, and almost certainly did have, a lot more to go on than guesswork and the sort of modeling that you conjecture about. In any case, Aristarchus did nothing to strengthen the case for this theory of the moon’s illumination, because the theory is not a conclusion but a premise of his argument (and his actual conclusion, his actual estimate of relative distances, was false).
Well, yes, but, again, it was already accepted by Aristotle (and probably before his time) both that the sun is further away than the moon (and, indeed, further than Mercury and Venus), and that it is larger than the Earth (De Anima III.III 428b). In this case, Aristarchus may have strengthened the case for these conclusions a little bit, but they were not news.
Is it? Would you care to spell out the logic of that (without making anachronistic appeal to concepts such as gravity)? Anyway, it does not seem to have provided a strong enough argument to have swayed either Aristotle or anyone else between the time of Aristotle and the time of Copernicus. We do not even know if it was actually among Aristarchus’ reasons.
He had better reasons than Aristarchus, maybe, but still pretty poor ones.
A simple heliocentric model explains retrograde motion (at a qualitative level), but aside from that it most certainly does not explain “all … observations of the motions … of the planets” as they were known at Copernicus’ time. The very complex heliocentric model (full of epicycles, eccentric points and other fudges) that Copernicus actually proposed did this, but so did the comparably complex geocentric model of Ptolemy.
As for the brightness of planets, obviously that depends on a lot more than your geometrical model of the solar system, which is not going to tell you, for instance, why Jupiter is brighter than Mars or why Venus is brighter than either. I suppose it might tell you something about long term variations in the brightnesses of individual planets. I do not know if this was something that actually influenced Copernicus.
So far as I know, Copernicus’ model, at the time it was published, had three real advantages as compared to Ptolemy’s: it gave a slightly more accurate account of actual planetary motions across the sky, as then known (but still far from fully accurate, and there was no real reason to think that the Ptolemaic model could not potentially be made at least as good by tweaking a few parameters); it gave more principled explanations than Ptolemy did of retrograde motion and of the fact that Mercury and Venus always appear close to the sun;* it eliminated the inelegant mathematical fudge, which Ptolemy relied upon, of uniform motion about the equant point. As I understand it, it was this last point that mainly motivated Copernicus himself, but it would not mean much to anyone but a mathematician with fairly strong Platonist sensibilities (which Copernicus was).
*Retrograde motion and the Mercury/Venus issue *are* explained even by a "simple" heliocentric model, and I suppose they could have been considerations even for Aristarchus, but there is no evidence that they actually were.The Sun being more distant than the Moon is obvious from the fact of solar eclipses, but on what basis did Aristotle believe the Sun to be larger than the Earth? There’s no way, without Aristarchus’ measurement, that that could have been anything other than a wild guess (which was admittedly the basis for a lot of Aristotle’s natural philosophy).
Observation 1: Some planets (specifically Mercury and Venus) are never far from the Sun in the sky. Observation 2: The planets which can get far from the Sun sometimes exhibit retrograde motion. Both of these observations follow immediately from the heliocentric model, but require epicycles in a geocentric model. Observation 3: A planet which can exhibit retrograde motion is brightest at the time when it’s doing so. Again, follows immediately from heliocentrism, and requires epicycles in geocentrism. Observation 4: A planet which exhibits retrograde motion does so exactly when it’s directly opposite the Sun in the sky. This follows directly from heliocentrism, but there was no explanation whatsoever for it in the geocentric system: It was just an unexplained coincidence of the parameters. The Copernican heliocentric system accomplished all of this without any need for epicycles, equants, or any of the other sorts of “circles upon circles” of the Ptolemaic model.