This is about the diameter of distance rule. And he lays it out in terms of the magnetic threads, emphasizing among other things that it's the angle that the orbit makes with respect to the radius vector that you have to take that angle into account to get the effect of the push.
So that's the point, he never makes it the way it's made now, the product of the component of velocity, perpendicular to the radius, times the length of the radius as a constant. But he's very close to it, he just doesn't say it the way we came to say it when we generalize to create the principle of conservation of angular momentum.
So because of the time, I'm not gonna go through the details on that. I've singled out the part you might not wanna read, but the whole trick here is to look carefully at the angles, and how the angle is not an exact right angle. This one includes the apology for the area rule.
That's the part I sort of singled out. In the same way, it will be demonstrated, the part that precedes it, labors to show you how he's summing all of these distances in each of 360 triangles. In the same way, it will be demonstrated that the delay of the planet in CF, which is equal in power to CP, is to the delay and same in GH, etc.
I'm gonna come back to that. I singled it out, because I wanna make a point. Then the final paragraph, a demonstration of this full equivalence is given on Mars, chapter 59, which is very late in the book, just before this section. It's the next to last chapter before this part five on latitudes.
On that page at the line such and such, one word error has brought in great obscurity, and if you change it to compute from will be to compute, everything will be clear. Although I confess that the thing is given rather obscurely there, most of the trouble comes from the fact that there, the distances are not considered as triangles, but as numbers and lines.
So that's his apology. Delay is important. Talking about velocity makes no sense to, well I have to rephrase that. Putting numbers on velocity makes no sense to Kepler or to anybody coming out of a Eudoxian tradition, because units of distance divided by time makes no sense. You can't have those.
You can only compare like units. So what he does in place of velocitiy, everywhere, is talk about delays. Delay in the time for the planet to be where it would be if it were moving in uniform motion, and it's finally getting there. Now that's just an indirect measure of velocity from our point of view.
And I chose not to be historically accurate in my presentation to talk about velocity all the time. He talks about velocity, but when it comes to numbers, he shifts to delays. I thought that was encumbering you with too much history that doesn't really matter to the subsequent development.
It's not very far down the road that velocity becomes okay to talk about. Though Galileo doesn't like talking about it for the same reason. He's following Eudoxian ratios, and there is this flat requirement only light can be compared to light. You can just think what acceleration was like to them.
Distance per time per time nobody, nobody, gives numbers not even Newton on accelerations. Okay, so you don't see those units, those are very much more modern. And then the last of these that I singled out, because this is actually interesting. The extrapolation of the three-halves power rule. I'm not gonna read it.
You can read it on your own. I set it out, but it comes down to this. The power is proportional, and I'm reading off my notes, the length of the path times the quantity of matter in the body divided by the magnetic strength of the sun times the volume of the body, and that yields a prediction.
The density of the planet should vary in proportion to one over the square root of their distance from the sun. Now, there are a couple of things about that. One is he's picturing this push, and the more matter in the body, the faster it slows down. We all know that, okay?
But it's not quite Newton's inertia, but it's along those lines. The more striking thing is he's saying this is a design feature. God had to choose the densities to produce the three-halves power rule. So for him, the fact it's a built-in design feature, you can't make the following claim.
If we were to put a further planet up there, have enough ability to shoot something up and put it into orbit, would it obey the three-halves power rule? The answer would be no reason at all to think so, because there's nothing about the three-halves power rule that results from fundamental physics.
It results from the accidental physics of Gott's design. That's gonna be important later, because that means the three-halves power rule from his physics point of view is of a different kind from his orbital rules. That physics, if we throw somebody up there, the sun is gonna have to push it, and if it has magnetic fibers, it should do what the planets do, in his mind.
Fair enough on that? I'm more or less gonna get where I wanna get. These are diagrams of the moon, trying to show, and I'm not gonna go through them. I'm showing them to try to drive home how complicated this is. How you get all these inequalities through an interaction of the sun and the moon.
And it's not in the portion you read from the epitome, and that's why its not in translation. I am pulling this out of the Latin just to show you the diagram to try and make you, try to impress upon how hard the moon really was. We'll come back to it again next week.
This theory of the moon, his first theory of the moon retained the area rule. This one he abandons the area rule. In an effort to try to get something that worked, he decided that, since two bodies were affecting the Moon, why should it satisfy the area rule with respect to either one of them.