Okay, I wanna do a little more review of Astronomia Nova trying to now drive home more of what was done and we'll come back and look at the problems. In Kepler's own mind he had three goals. And one goal was the goal that Tycho had given him. Mainly to introduce reforms to orbital theories that remove all excessive discrepancies versus observation.
And that means all. Anything significantly, any systematic discrepancy outside of the level of observational accuracy is not to be allowed. It's telling you something, you're supposed to do something about. And that's Tycho. Second, determine the true motions of Mars, at least with respect to the sun if not the fixed stars.
And the issue here, what I was trying to do is separate the issue of the Tychonic system and the Copernican system. From just Mars going around the sun and both but of course he had to also allow for the Ptolemaic. So he ends up giving the correct epicycle for the outer planets and the correct efferent for the inner planets.
And then the third thing he wanted to do was establish the Copernican theory, though we knew from the beginning he can't do that, from orbital reforms because they can be incorporated in everybody's, it has to be done with physics. And as he says, conjectural physics, he makes that word in reading from tonight.
I hope you all looked and said, physics has to be conjectural. Well when did it change? That's it I mean that's what this course is in a way all about because it's with the Principia that one can make a case that physics ceased being conjectural. That's slightly unfair to Huygens and even Galileo but moreso Huygens.
All right that's, oh I didn't do justice to this, and the problems he had to work with are fairly straightforward. First of all, he's working with a limited set of observations, at most 24 years. Most of them are in a ten year period. That's not a lot. Fortunately for Mars, it's a fair number.
For Saturn, I'm trying to think, you wouldn't have gone around twice. Those outer planets are slow. But the way I usually impress this upon people is Neptune was discovered in 1845. How many times has it gone around since then?
Now it's right around finishing now. It may have finished in the last couple of years the first time around or maybe about to.
I have to always sit down and calculate it, I don't keep it in mind. That's a long time to wait for data second time around isn't it? Okay, but it tells you something right away, and Saturn is very slow and of course Uranus is between the two.
But I think it's somewhere around 150 years is the period for Neptune.
But don't hold me to the exact I just now that it's been in the lifetime of this course if it's happened. Second, you've gotta use theory to reach conclusions about orbital motion, and you don't wanna beg questions. And in his case, he's constantly using theories that he takes to be false.
So how could he be consciously using false theories, and not creating problems? Third, he knew the observations were of limited precision, but it's gonna turn out he was very right in worrying about how much the corrections for parallax and atmospheric refraction were making the recorded observations less good than the naked eye assessment of their accuracy suggested.
You know it's one thing to take a person and try then to do it better. Try ten different people on a given night with the same observation using different equipment and see what the spread is. And you can then say okay this is an estimate of the error, but it's another thing if they're systematic error because that doesn't show up as a random deviation that shows up as systematic.
And if they're all being thrown off, you don't see that right away and he was very worried about those corrections. And then finally, he was quite wary that a theory of the Earth-sun orbit could be introducing significant discrepancies even though it was a fantastically accurate orbit theory that Tycho had, and I finally just list the theories Tycho's Earth-sun theory proved to be false.
So did his first modification of it when he's had a circle with an equine and bisected eccentricity. The final theory is an ellipse. So he used two false theories in reasoning, but he was confident, gave good longitudes. Second was his vicarious hypothesis almost from the outset he knew was false, but he used it very heavily because it gave him heliocentric longitudes or in the case of Ptolemy gave him longitudes on the epicycle.
Then in some places he uses Tycho's theory of heliocentric longitudes of Mars. Because he doesn't want to beg a question against Tycho's system. So rather than using his vicarious theory he uses Tycho's and shows they give him the same kind of conclusion. That's particularly when he's doing the bi-section of the eccentricity.
And of course, all the time, he's just, through the calculations, he's constantly assuming that Mars orbits the sun. Though, he fully recognizing that the Talamate does not and therefore, he has to handle the Talamate specially. Which he does, of course. Now, the notes last time go through this in some detail.
I'm just gonna do it cursorily now and the main reason is that the evidence it ended up ended up not mattering historically to virtually anybody but Kepler himself. That is people didn't go back and see the evidence in Astronomia Nova for his conclusions. Physicists like to say when you start confronting them about theory, well it worked.
You know, what more do you want? And that's the attitude they had toward Kepler somewhat. His reforms worked. Who cares what the was but you'll start seeing that later tonight. So, line of apsides passes through the true sun. What's the primary evidence? There are two piece of evidence.
One is he gives you this crossroads experiment of observations away from opposition which are more than one degree different on all three systems whether you refer everything to the actual sun. Or to the mean sun. So, the world can pick out between those two at least for the three systems.
We have other possible systems sitting around, but for the three systems, there's a choice. And then, secondly, he ends up with triangulation showing that if the line of apsides is put through the mean sun, there's no symmetry on either side of it whatsoever, whereas if you put it through the true sun you get symmetry.
That's all in last weeks note. The second the orbits pad lies through a plane etc., passing through constant angle with respect to the angle of inclination with respect to the ecliptic. The main evidence for that of course is you can keep measuring that angle at the appropriate times.
Number one and number two, the latitudes fall into place. Now that's tricky. The latitudes fall into place provided you've got a good enough theory of longitude that you're saying what the latitude is, corresponding to a longitude. That's why, the other reason, the latitudes occur at the end. You've gotta have the longitudes worked out before you can do final latitudes.
But, the point is after centuries of the latitudes being wildly off, with really Rube Goldberg type schemes trying to represent them, you get the latitudes remarkably cheaply, okay? A bisection to the eccentricity of Earth-sun orbit, I think that's almost the most interesting, that may be the most interesting evidence problem here.
Because of course, there's no way to do it just looking from the Earth. The cleverness is to do triangulation as if you're looking from Mars, and then come back for the Ptolemaic and do the same exercise, essentially recasting it onto the epicycle. Now what he gets is not bisection.
All he gets is the eccentricity is much nearer half, that is the center of the motion is much nearer half the total eccentricity, than it is near the total eccentricity. It's much nearer 0.18 than it is 0.36. And then from that, he then idealizes, saying my observations are not good enough to pick out the specific number.
But given the long tradition of bisection of eccentricity on all the other orbits, of course, based on shape and timing of retrograde loops, of which the Earth-sun has none. Based on the success with all other orbits and their retrograde loops, we'll go for the same bisection of eccentricity that Ptolemy went for.
And as you already note, Ptolemy couldn't get an exact 0.5 either. He tells you that, tells you it's near enough to take 0.5. So the evidence is a little bit ambiguous, but there's definite evidence for it, and fairly isolated. From anything else other than that you know where Mars is every 680.
You know that Mar is in the same place every 687 days. That's the key feature. Or the center of its epicycle is in the same place. The diameter of distance rule, the evidence for it, is just fundamentally triangulations that agreed into the fourth significant figure for distances, that the rule, and I gave you that table last time, you know?
And it ranges from 166 down into the 140s, so it means it's going all the way around the orbit, he gives double calculations from different years and things like that and it really looks like the diameter distance rule. Has direct empirical evidence for it. Now direct empirical evidence subject to a Earth-sun orbit that he had refined from Tycho, and the vicarious hypothesis.
Cuz those triangulations are assuming those two. Okay, so, but there's evidence for it. So the case, and here I'm agreeing with Curtis Wilson. The area rule in the ellipse, it's not clear that there's any evidence for them. Excuse me, that's too strong. The evidence for them has to be done in tandem.
That is, given the diametral distance rule, either one of them gives you the other one. That's very nice. But as far as getting any evidence for the are area rule independently of diametral distance in ellipse, it's problematic. And you'll see how problematic when we look at other planets.
It's somewhat of a hunch on his part that looks like it bears out. And, of course, the ellipse he held back from because, it's very, you know, why should nature be so nice? That, if it's gonna be an oval, it picks out a geometrically legendary curve? Legendary, because of Apollonius.
You know? How can it be so nice, to do that? So I think there's evidence there, but when we come back in the second half tonight and start looking at that evidence what it really shows, it's very, very far from a total knock down case and so one shouldn't be that surprised that astronomers didn't just jump on board if they had worked through the numbers the way he wanted them to.
That's why he wrote the book the way he did. He was very clever. He knew if he just threw this out, it wasn't gonna do anything. If he can get them to go through all the steps, and do the calculations, and do what he did, he thought he would persuade them because they would go through the same machinations, have the same doubts, make the same discoveries all over again.
But nobody that I know did that. And as a consequence, he convinced himself very well, but the rest of the world remained outside. And if you now asked to what extent did the evidence presented in it support the Copernican system over the Tychonic system is very hard to say anything other than its supposed physics, okay?
That's about the only thing he has. Now you read for the tonight, the 18 reasons for preferring, 18 reasons for dropping the Tychonic. You'll notice none of them, they're all described as probabilistic reasons. Probabilistic reasons is a translation for a word that amounts to these are not solid scientific these are conjectural.
They have a significant speculative element. And over the Ptolemaic system I think he has a little more in the following sense. If you make the change in the Ptolemaic system and have the outer planets on an elliptical epicycle attached to a deferent at one focus, and describing equiangular motion about the other focus or area rule in place of the of the equant, either one.
That so undercuts the spirit of Ptolemaic astronomy that you might naturally say luck, just what he said. These three outer orbit epicycles, they're exactly the same with the same eccentricity and the same features. Isn't it natural to think there's just one orbit here, okay? Which is his probabilistic argument that he offers in Astronomia Nova.