From 1578 to 1597, he did observations of the sun crossing the meridian altitudes. They were really the altitude as it crossed the meridian. And produced out of that, best theory of the sun's motion that anybody had ever had. Extremely accurate, and he concluded the precession of the equinoxes uniform.
It's 26,000 years to complete, the precession of the equinoxes off of his observations. Those were the highest quality observations of the sun we had until Cassini in the 1660s. We'll get there later in the course. In the case of the moon, he has two theories of the moon.
In the process, discovering a new inequality that Ptolemy had missed, everybody had missed, called the variation. It amounts to about 40 minutes in longitude. It turns out to be in some respects, we'll have to get to Newton to see how important it is. It turns out to be the most informative inequality in the motion of the moon.
Okay? I'm not gonna bother you with that now, but it was discovered by him. On the planets from 1581, when he got the mural arc, et cetera, until 1597 when he had to leave Avin and go elsewhere. He averaged, according to Thorne, 85 nights per year. Now, picture this is near Copenhagen.
That means there is no darkness or maybe one hour of darkness from June through. Is that right? May through August. But then you get the reverse, right? From October through March, it's dark almost all the time. It's cold, but it's dark. And it's ideal conditions for observation. So I'm showing you a contemporary list for those, and you'll see the early ones.
And suddenly, you'll see when you get to 1585, night after night after night. This particular set of observations of Mars alone is 280 observations over 20 years. Surely the best record we have, and that's the record I'm showing you this, cuz that's where Kepler started, was from these data.
Not these data tabulated this way, but this data as Tycho originally tabulated then. One of the things Tycho fully recognized about these observations is there are two forms of error automatically going into them. Those two forms are summarized here. It's important to hear this, I'll go fast with it, but drive the point home.
Parallax correction is needed. What you want is the angle, the heliocentric position, excuse me, geocentric position of the planet, relative to the center of the earth. But to get that, you have to be online with the center of the earth. You're not online and up in Copenhagen with the center of the earth.
You're looking at it at an angle. Therefore, you need to correct it from one place to another so that you infer what it looks like from the center of the earth. That inference has to presuppose how far the planet is away. The further it is away, the smaller that correction is.
He had no idea how far the Sun was away, but he concluded that the horizontal parallax of the sun is three minutes of arc. That would make it 1000 earth radii away. It is in fact 22,000 earth radii away. Something that took a long while. In this course, we'll watch it unfold, to discover.
That means all his parallax corrections were wrong. They were based on the Sun being too near, Mars being too near, etc. In addition to that, there's atmospheric refraction correction. That's not very much needed if it's directly overhead. But to the extent, it's not directly overhead. And no planet goes directly overhead as far north as Copenhagen.
You've gotta do a correction for atmospheric refraction. But how do you do that, how do you get what the atmosphere does to refract? They knew things. They knew the sun was still visible to us, naked eye, when it was below the horizon. So very near the horizon, they could figure it out from watching the sun technically be below the horizon, but the whole of it still being visible.
But as you start going up in altitude, you have no real basis for doing it except by looking at your data, and saying there are irregularities in these data. We need to correct them. It's doubtlessly for refraction. But now, you see a problem. First you do the parallax, then you look for irregularities for refraction.
The parallax is wrong. So is the refraction wrong. It's about one and a quarter minutes of arc that Ptolemy was off. And that limited the accuracy of the observations to somewhere around, he claimed two minutes of arc. When Bill Harper and I did a survey of his data, we concluded it was pretty, almost always within four minutes of arc.
There were occasional ones outside of four minutes of arc that are probably just bad observations. Four minutes of arc, though, is very good compared to Ptolemy's claim of ten minutes of arc, which he probably didn't realize. So there is a real improvement in observation. And this forms the basis now, for Kepler, as you will see next week.
I wanna make sure I get you out of here on time. The other thing to say about these two, this is anticipation for the rest of the course. When you get the telescope, the natural thought is, oh I can mount the telescope and get much better accuracy then I can from naked eye observations with an instrument.
No. You can't until you figure out what the praralaxic atmospheric corrections are because the telescope is going to be totally at the mercy of those two corrections. It, in principle, gives your greater precision of observation, in the naked eye instrument. But, the trouble is you've got to have the corrections.
So it took until about a century after the telescope came in before it could be used to do better longitude and longitude observations. Tycho's data remained the principal data supplemented by some telescopic observations, but the principal data all the way up to 1700 for just this reason. That's why I put that slide in there.
And this again is the tichonic system with the comet shown going through the orbit, and that being the basis for claiming that no spheres, etc. Down here of course, is Cassidy in a later diagram, showing both the Copernican system and the Platonic system side by side. Two quick remarks about this, and then I will take three quick remarks.
One oddity of this tichonic system is that Venus and Mercury are going in the opposite direction from the three outer planets. Three outer planets go counter clockwise looking from the North, Venus and Mercury have to go easter way. That's a slight oddity, and it will be important when we get to Descartes.
Descartes says that planets are carried by vortices. They don't get carried by vortices in opposite directions. Second comment, Tycho, so typical of him said we ought to resolve the question of Copernicanism versus Tychanism by observation. Namely if the earth is going around the sun, then over the course of the year, the angel at which we look at stars near the north pole should show a motion.
The motion is called annual stellar parallax. And Tycho did everything he could to measure it, and concluded it's not there. The Copernican's had already said, that's because the stars are too far away, of course. The reaction that Tiko had was, why isn't it if the Earth is not moving?
And he added to that, you can calculate this, how far do the stars have to be away to not observe any stellar parallax? Answer, a thousand times further than Saturn is away. And Tycho just flat says, why should God have put this planetary system here, and the stars incredibly much further away?
This is an example of the same data being evidence for two totally opposite conclusions. That is if you conclude that the stars are reasonably near the absence of stellar parallax as the Earth is not in motion. If you conclude to the contrary the stars are indefinitely far away.