Philosophy 167: Class 4 - Part 7 - The Epitome of Copernican Astronomy: Structure of the Book.
Smith, George E. (George Edwin), 1938-
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All right, The Epitome's worth, I'm not gonna spend a lot of time on details, but I wanna move through the structure of the book because it's so striking. It started this is book four, book five. So you noticed he makes this comment that you're gonna find this a really weird book cuz of all the physics in it.
Until you recognize quote speculative astronomy is one whole part of physics. The tradition of mathematical astronomy has always distinguished it from physics. It was a different area, it was a mathematical discipline about the empirical world. It was not physics. Kepler is very much arguing to change that. And the way he does it in the Epitome is instead of starting out with orbits or with data he starts out with physics and qualitatively argues his way into orbits.
Okay which of course nobody's gonna buy because they're not gonna buy the physics. But they read it, and they bought the result, but they didn't buy the argument. So, notice the way it starts. There are no solid spheres. Right? At the beginning, we get rid of the old cosmology.
Next, gotta have everything refer to the true sun. Then, you look at the order of the movable spheres and why there may be exactly six planets, et cetera. And what you get is this story of the perfect solids followed by the harmony. So all that stuff is right at the beginning of the Epitome's physics argument for his orbits.
Next, the ratios are the principal bodies to one another. And here he excuses the imperceptibility of annual stellar parallax. In other words, he's moving right through the key issues one by one. On the movement of the bodies, how many and what sorts of movements? Well he's gonna have rotation, he's gonna have the fixed stars not moving.
It's the Earth that rotates, not the fixed stars, and then he looks at the causes of the movements. He introduces his notion of inertia. A word that is in Latin inertia. That Newton adopted with a totally different meaning. So inertia as I said last week is the tendency to slow down.
The sun has to overcome that and the phrase here, the need for a motive force. Vis motris, a technical term in the Principia that people have been arguing about recently and I don't think any of them realized how often it occurs in Kepler. But vis motris. And what that means is a force that is producing motion, pure and simple.
In contrast to a static. I'm just gonna continue through this, so you get the full appreciation. So now we get the revolution of the sun about its axis and it affects. By this time, that's a confirmed result from your question last time. He knows the sun's rotating. So he says, see the sun's rotating and it's throwing off this wonderful vortex, magnetic vortex, or at least magnetic-like.
And it drives things. Its strength varies inversely with distance, and then he has a whole passage in there of why it's not inverse square, because remember he was the one who first published the intensity of light diminishes in an inverse square ratio of the distances. So it's a natural question, why is it inverse rather than inverse squared.
I'll let you read that. Not gonna dwell on it. Then the causes of the three halves power ratio. I'll come back to that in a slide a little later. Finally on the annual movement of the earth. That's of course against Tycho and against Ptolemy. So he starts with the phases of Venus, that's sufficient to get rid of Ptolemy as you'll see.
Then he asked a term for why you have to be doing everything with the true sun, 8 reasons, in his 18 reasons to reject Tycho. And then his argument for the rotation of the earth predicated in no small part on the fact that Jupiter rotates. And of course, Jupiter has moons.
There's the obvious question, why does Jupiter have moons or why does the Earth have moons, why does the sun have planets around it? Answer, they rotate. Okay? That's a feature they have in common, okay? And of course he did not know at the time that anything else had.
By the way the word is satellite, that's a Kepler word. That's another one fo the words Kepler first introduced into technical jargon referring to Jupiter in that title back there that you saw before. Okay so that's, that gets them into the Copernican system and now he starts looking at the real and true irregularity of the planets and its causes.
And the causes of the truer regularities in longitude. Well that's because of the area rule which he know very cleverly analogies to a lever. A lever so mispronunciation. Which is of course the right thing. Because what a lever does is the same fundamental principle of conservation of angular momentum that the area rule is doing.
So he doesn't have that concept, but he sees the tie between the two and it's a legitimate tie. Causes of the irregularity in altitude, that's of course the diameter or distance rule. That's what, those are my words, RRSP. And he goes through what the pattern is and what's causing it.
The threads in the planet. Magnetic threads are interacting with the threads of the sun. Why do we have different amounts of ingress from circle into an ellipse? Because of the strength of the magnetic fibers. Some of the planets have stronger magnetic fibers, some have weaker. There's no further explanation than that.
And continuing, just moving through this. On the movement and latitude, why there's no inclination at all. Why are the inclinations different from one another? Magnetic fibers again. They do the tilting. They're not aligned. Two-fold irregularities of the Moon and their causes. I'm gonna show you a diagram from that a little later.
This is a very, very key point for future of this course. Here's his problem. He's proposed all this physics, right? And clearly, it's totally conjectural. What he knows is that the moon is not an elliptical orbit and it does not satisfy the area rule, he knows that perfectly well.
Okay. So he comes, and you know something else, he knows that all of the principal known lunar inequalities are one way or another correlated with our sun positions. So he draws the natural conclusion what's happening to the moon is it's under the influence of two bodies, the Sun and the Earth.
And then he gets the clever idea if I can take my physics for the Sun and my physics for the Earth with his magnetic fibers et cetera, and work out a theory of the moon? I've got evidence from my physics. Unfortunately he has two theories of the Moon, neither work.
The failure of the first one held up the Epitome for a couple years while he worked out a second one. It still doesn't work. It's clearly far in excess of observational accuracy, the discrepancies. And it remained that way for a long, long time, okay? The reason this is so important is, guess what Newton does when he starts trying to sell his universal gravity?
He starts showing it can do the moon. The Sun and Earth together can do. So, it's the same move. It's the natural move. I mean the other way to think of it. The moon's a counter example to this. Isn't that a bad problem? No, it's an opportunity. Okay?
Get evidence. Okay? And that's the way Kepler thought. That's the way Newton thought. He wasn't alone but the two of them were dramatic in that regard. All right. Continuing down. Book five is now getting into the geometry that's coming out of that physics. So he starts with the eccentric circles, or schemata as he calls them.
Then just goes through, I'm not gonna go through these one by one. But you'll see some of the later ones again the area rule, the fluctuation of the distance rule, some of the vibration gone through, with that you will see accumulative of regressive changes in R. How you get to the Ellipse, I'll show you that later.
On the measure of time with an apology for the statement of the area rule in astronomia nova I'll show you that later. And then he tells you about the problem of figuring out where a planet is given time. Where it is on its orbit and that turns out you'll see later tonight.
That turns out to be an unsolvable problem geometrically or algebraically is not a finitely solvable problem. It becomes a Kepler's problem because he put it out there begging somebody to find a solution for it. We'll come back to that and then discussion of the latitude. And finally the part two he gives you in effect.
Giving you the technical terms and telling you how to work with them. Book six as I say is on the individual orbits. going orbit by orbit through the whole system in anticipation of the Ruldophian tables. And book seven is, goes back to, as I say, see page 164, goes back to Ptolemy and other such things.
And at the end of book six you simply have a summary of the main elements of all the order. So it's a very comprehensive work. I wanted you to read it partly to get the flavor of Kepler's writings and the flavor of his physics and how conjectural it was.
I don't want to go through it in detail primarily for the simple reason it didn't have much influence on anybody. Looks like the person that influenced the most was Leibniz. But in lots of ways Leibniz was just trying to find an alternative to Newton and Kepler gave him one.
You'll see that next semester.