All right, let's go back to part one. I said what point in part one is to establish that we should be referring all motions to the actual Sun, not to the mean Sun. And I've already given you Kepler's reason for that. He thinks the actual sun is crucial to the physics.
And he thought that all the way back before he got near Tiko. When he told Massaline that the statement, not just about the actual sun, but physical causes will show which system, Massaline, of course it shouldn't surprise you, said physics has no place in Mathematical Astronomy. And, when he told Tiko, he got exactly the same reaction.
Mathematical Astronomy is an autonomous discipline unto itself, physics should not be put into it. So when he calls it the new astronomy, he's calling that not just because of the reforms, by the way, all are still with us. Every reform introduced in this book is still part of astronomy.
First thing we've had in this course where we've got stuff that's still part of astronomy and exactly as he did it. But he's as much also referring to doing astronomy with physics being part of the consideration. That it was radically new. All right, so when he told Tiko that they should be referencing the actual sun rather than the mean sun, Tiko's reply was, what difference does it make when you're near opposition?
The difference in longitude between the actual sun and the mean sun is too small to be fighting over. So what Kepler does is to back off and to figure out when is the difference between the actual sun and the mean sun great enough that you can see it.
So the first question, and this diagram shows it, is distances are quite different from A to X and Y, and B to X and Y. X being the reference to the actual sun, and Y being the reference to the mean sun, and I guess it could be the other way.
No, that's the right way. B is the true sun, and A is the actual sun. So that indeed, what you need to be doing is looking off at an angle. But that means looking at Mars when it is very far from opposition. Which means you're gonna be looking at it low in the horizon and you're gonna be complicated by atmospheric refraction, etc.
But of course, there weren't much data because people hadn't done observations and recorded them for Mars. In that case, because they knew about atmospheric refraction. And didn't want to trust the data. So, what does Kepler do? He first takes the Copernican system and goes through the whole thing of Mars complete orbit in Copernican manner referencing the actual sun, then referencing the mean sun.
And he identifies a greater than one degree difference in longitude at locations away from opposition. Identifies in fact where you wanna look and when you wanna look to see the difference. Then he does the same thing in the Ptolemy. Does the whole thing through two ways, actual sun and mean sun, and identifies a set of observations that would choose between the two.
And then he starts the tectonic and finally says, that the reader can do the rest after he does the first half. So he does five of six calculations of complete orbits in three systems to determine where you would most be able to tell the difference between the actual sun and the mean sun.
In every case it's greater than one degree, greater than two moon diameters, and he leaves it there because there are no observations. He just goes right on and says when the observations are made, you'll see it's the actual Sun. I'm gonna proceed with the actual Sun. Okay. Now this acquired a name from Francis Bacon.
A name that Robert Hooke made famous, then Newton adopted it from either Bacon or Hook, I'm never sure which one, experiment in cruxes. What the words mean is experiment of the cross, cruxes is not a classic Latin word, it's a medieval Latin word referring to the Christian cross.
And Bacon's point is there are experiments, this is the other phrase he used, finger points at a crossroads, experiments that will choose between two alternatives. That's essentially what Kepler has done here on all three systems. He has identified an observation that will choose between the two, and then simply takes it for granted, when they get around to doing that observation, what it's gonna show.
Okay so, the rest of the book, he sometimes uses the mean sum for purposes of argument to show he gets the same conclusion from using the mean Sun as the actual Sun. But from here on, the Sun is the actual reference. And he then, in the same part, this is an explanation from Bruce Stephenson, and I'm putting a lot of this book on Astronomia Nova.
I'll pass this around. This is by far the best book, it's a doctoral dissertation, Bruce Stephenson's, now at the Adler Observatory in Chicago. This is the best book on Kepler's evidential reasoning that's ever been done. It was done, the dissertation was done under Curtis Wilson, but it's just a beautiful job of working on all the arguments through all of Kepler's books.
Looking at how the physics enters in. Having got this, he now says the following. Okay, we're gonna reference the actual sun. I'm gonna put Mars in a plane in which the intersection with the ecliptic goes through the actual sun. And when he does that, he then identifies some observations that would give the inclination of that plane.
Okay, and it's a series of observations. There's some described in the Curtis Wilson reading for the day. The best observations, the ones that'll show the most, is with the Earth on the lines on the nodes. The nodes are the points where the two planes intersect. So the Earth is gonna be right where the Mars orbit intersects, at a 90 degree angle relative to Mars, and at a 90 degree angle relative to the sun.
Then you could observe the latitude, celestially, from the Earth, and it simply is the latitude relative to the sun. And let me just finish, what he discovers is latitudes fall right into place if we simply assume it's a plane passing through the actual sun and stays constant. So 2000 years of screwing around with latitudes unsuccessfully disappears almost over night, when you put the plane of the Mars orbit through the actual sun.
Of course, the Earth-Sun orbit is through the actual Sun, and now reference the inclination of the plane as a constant. And you can measure it and determine it stays constant. We'll come back to that at the end. It's doubly striking, at the end of the book, he wearies that maybe the inclination has changed since Ptolemy.
So he goes back and extracts the data Ptolemy had to use in order to get his own theory of latitude and shows it's entirely consistent with the one degree 50 minute inclination of the Mars orbit. Now this is from the end of the book, chapter 62, after he's done everything.
He shows you the inclination. He shows you the visible latitude. And, he shows you, from our table, the largest errors are around five minutes. There's one larger than that, but it's actually a typo. Typo in the original, not just in the translation. But they're all within five or six minutes of arc versus degrees.
And his attitude is, this has gotta be left for for the future because, in particular, since latitudes are being seen as a declination, and therefore subject to atmospheric refraction, there's no reason to think you can do much better than this until you have an adequate account of atmospheric refraction.
But I'll come right back, there are two, okay, I'll come right back. So here are two reforms in astronomy that are still with us that just did a fantastic amount to eliminate prior problems. Reference everything to the actual sun, the mean sun is just an empty point in space, and therefore it can't have any physical meaning.
By the way, the reason for using the mean sun is just a basis for time. We still use the mean sun as a basis for time, okay. So it's not crazy to have used the mean sun, but if you're gonna get physics in there, it's a very bad idea.