The first sensible set of predictions on this is by the Babylonians. They discovered that if you looked for a long enough period you would see the patterns I just showed you start repeating. There are two periods up here. The period in tropical years, tropical time, is the time it takes to go from the vernal equinox on the ecliptic back again.
And the synotic period is the time between one retrograde loop and the next. And when those two have integers in common, then you get a repeat of the pattern. So the Babylonians discovered every 71 years corresponds to six tropical years of Jupiter, and 65 of the retrograde loops, and at that juncture, it repeats.
So all they've done here is to keep records and notice that it stay around long enough of course longer than any one person's life. Stay around long enough you see a repeating pattern. And they did it. They get a better one for Jupiter at 83 years. The Venus one in eight.
Mercury 46. I won't read them all off. The moon in 18 years. But they were in a position to predict. And it was that, that the Greeks inherited, though how many of the people in the Greek tradition that we're about to turn to ever saw that much Babylonian data, it is not clear.
We know Thales had some tie with Babylonian data, because he became prominent by predicting a solar eclipse, which the Babylonians were doing, like child's play by 450 BC. Aristotle refers to some Babylonian data. But it looks like it's fairly late in the game after Alexandria conquers all of the Mediterranean world that the people in the Hellenistic period in Greek speaking world.
Got hold of a really good collection of Babylonia data, and I'll get to that in a moment. The only thing I want to stress right now, is the prediction problem by itself is solvable by just looking for patterns in finding them and having them repeat. Okay, so if prediction were the only thing of interest, the Babylonians solved their problem.
Now the Babylonians actually did construct some planetary theories, but they don't look like ours, they're sawtooth. They have the planet moving in a sawtooth fashion. They didn't have the math to do smooth curves, etc. That's much more of a Greek development than a Babylonian development. Fair enough? All right, so what the Greeks wanted to do with this, the word they used was logos.
They translated, we usually translate it in Plato as an account. Now what it means to give an account of this is a perfectly interesting question. The word logos for those who know the magic of the word. In the Bible when God is reported to have said I am the Word, the word is Logos.
Logos is somewhat a magic word in Greek open to many translations. But the standard account in Plato shows up all over the place is account and that's fundamental what the Greeks wanted, an account of this. Now I'll offer another Anglicized Greek phrase. An account that saves the phenomena.
Phenomena in Greek is appearance, so what you want is some sort of an account of the emotion of all these objects from which you recover the way they appear to us. Okay? That's what it is to save the appearances. The first such account is by Eudoxus, and it consists of homocentric spheres.
I'm gonna read much of this to you. If you look in, I didn't bother to look in Google, because I knew what I was going to find if I looked. You'll probably see drawings of Eudoxus' system. We have no drawings of Eudoxus. We have no extant works of Eudoxus except for handful of fragments.
Our total basis of understanding of the Eudoxus system comes from three paragraphs in Aristotle's metaphysics. Namely book Lambda. For those who don't know what book Lambda is that's the book of the unmoved mover. That's the book that made Aristotle respectable to the Christians in the Middle Ages. And it's a funny book because it doesn't belong with the rest of The Metaphysics.
It's an earlier work. The Metaphysics is a compilation at Aristotle's death by his two children putting together his various lectures. And Lambda is thrown in there. In the Middle Ages, Lambda was thought to be the culmination of the whole work. Now we know that it almost doesn't belong there at all.
But here's the description. I'm gonna read parts of this because it's striking. Eudoxus supposed that the motion of the sun or of the moon involves, in either case, three spheres, of which the first is the sphere of the fixed stars. The second moves in, sorry, in the circle which runs along the middle of the Zodiac.
And the third in the circle which in inclined across the middle of the Zodiac. But the circle in which the moon moves is inclined at a greater angle than that in which the sun moves. So we got three spheres moving around different axes, located separately from one another, at three different speeds.
Now the planets. And the motion of the planets involves, in each case, four spheres. And of these also the first and second are the same as the first two mentioned above. For the sphere of the fixed stars is that which moves all the other spheres. And that which is placed beneath this and has its movement in the circle, which bisects the Zodiac and common to all.
But the poles of the third sphere are in the circle which bisects the Zodiac. And the motion of the fourth sphere is in the circle which is inclined at angle to the equator of the third sphere. And the poles of third sphere are different for the other planets, but those of Venus and Mercury the same.
The next paragraph proposes extra spheres that Callippus suggests need to be there. I've left it out to save space. Then Aristotle proposes we need more, too. But it's necessary if all the spheres combined are to explain the phenomenon, that for each of the planets there should be other spheres, one fewer than those hitherto assigned.
Which counteract those already mentioned, and bring back to the same position the first sphere of the star which in each case is situated below the star in question. For only then can all the forces at work produce the motions of the planets. Since then the spheres by which the planets themselves are moved are 8 and 25.
And of these, only those by which the lowest situated planet is moved Need not be counteracted. The spheres which counteract those of the first two planets, will be six in number. And the spheres which counteract those of the next 4 will be 16. And the number of all the spheres, those which move the planets and those which counteract these will be 55.
So this is a system of 55 spheres nested inside of one another, producing the motion, okay? And Aristotle tells us it does pretty well. During the late 19th century, people picked up on this description, and started trying to figure out how to make the model work to see how well it has.
I know one chap I know, an Israeli, actually worked out a computer model that showed for one planet you get retrograde motion. How well it agrees with what's observed, how well they even try to make it agree, I don't know.