He now asks what's the physics of this? And he gets a very clever idea. Well, he knows the earth is magnetic. Why isn't Mars magnetic and has magnetic fibers? And those magnetic fibers interact with the magnetism of the sun. So that at the line of apsides, notice the orientation of the magnetic fibers?
One north, one south? But they're perpendicular to the line of apsides so they're having no effect. As you go around, the arrow point starts moving closer to the sun and you're drawn in because the two poles attract one another until you reach perihelion. Then you go to the other side and it's the other pole now pointing to the sun and so you're pushed away.
And therefore the orbit is physically being driving by two factors. The first is the push of the Sun, which is perfectly circular at each radius but is different at every radius by one over r. He comes back and ends up doing that in a slightly different way. And let me give it to you, he never says it's a astronomia nova but subsequently he says, oh I see what's going on.
It's the velocity perpendicular to the radius vector. That's what's being pushed and that velocity is indeed always proportional to one over the distance. And that's what the area rule entails. That component of velocity. We call it something else. We call it conservation of angular momentum. Okay, but that notion gets introduced a century and a half later.
All we have, for the moment, is the area rule and the area rule being equivalent to this. Okay, so he gets that picture of the driving around, and then superposed on that is magnetic fibers which differ from one planet to another. They explain why some of the eccentricities are larger and smaller, because it's the strength of the magnetic interaction.
Now of course he can't derive that, but he has an explanation for things. So now he thinks he's got physics too. And there just is no reason to back off of any of this. It looks like exactly the right account. This figure is a vocal Gingrich figure I showed you before.
The top figure of these two shows you Kepler's inaccuracies versus Ptolemy’s the best possible Ptolemaic theory. The Kepler inaccuracies at that scale look like a straight line. They're not quite. Okay, that's in degrees the one in the bottom is in minutes of arc and it's shown in three different ways.
The Rudolphian tables which we haven't got into yet but there was the improve Mars elements. And a calculation done by Majini, a friend of Kepler's who did not like the area of rule but kept all the other Keplerian reforms except the area of rule and didn't do nearly as well as Kepler did.
You see that his errors go as high as six and seven minutes of arc with a best fit. Whereas the Rudolphian tables with a best fit, with best parameters run about three minutes of arc. So it really is an extraordinary jump. It's in some ways a mind blowing jump from the one to the other.
I'm gonna pause there and entertain any questions. Let me summarize this before I get to the philosophic question. The point I'm trying to drive home above anything else is how much Kepler recognized the risks of drawing conclusions from inaccurate observations using tentative theories with inaccurate observations with less than exact corrections to them, using tentative theories and approximate methods of math in place of rigorous methods.
He appreciated that at all moments. Every where he makes a move, he finds ways to cross check it. And ultimately what convinces him he has the exact orbit is this principle of three different ideas, two of each of the three entailing each other. One of, since I have a moment, I'm gonna go with the last slide is all philosophy, and I'm gonna devote that to that.
There's a comment and it'll prepare you for the reading next week. Kepler always liked to turn to design arguments. It isn't just the design argument of the regular solids. He really did sit there trying to read the the mind of God. At the same time he knew and gave enormous amount of faith into careful reasoning from observations.
What's interesting about him is he keeps the two segregated from one another, okay? Design arguments don't get into arguments from observation. Arguments from observation don't, you'll use them, but the design arguments are trying to read the mind of God. I once remarked, and I'm leading to a story, I was remarked to Bernard Cohen that the only major scientist in history that Kepler seems at all like is Einstein.
Cuz Einstein was very comfortable, metaphorically speaking, reading the mind of God. And Bernard laughed on the spot and said you realize I did the last living interview with Einstein. It appeared as a Scientific American article, and when he led me into his study in Princeton, he had exactly one picture on the wall.
Kepler. Kepler was his great hero. And I've always thought I was lucky, just due to the comparison, but I think the personality of always wanting to go to some kind of a design argument, a big picture is a feature of Kepler as much as of Einstein, though I don't know that Einstein did anything like the detailed reasoning from observations that Kepler did here because that was not what Einstein was terribly comfortable doing.
But be that as it may I thought that would at least intrigue you because the Kepler person, the reason he has this reputation of being somewhat of a mystic, is the tendency to go back and forth between design arguments and this kind of argument.