The other thing he does is he doesn't like Kepler's theories of the moon because they violate the area rule. Horrocks is the one person, he doesn't accept the physics, but he sure does accept the area rule. So he decides he's gotta construct a new theory of the moon obeying the area rule.

The theory has this inner epicycle complex. The next diagram, which I am including here cuz you're gonna see it later in the course, it's his theory of what's called the evection. Remember, the evection is a swinging back and forth of the apogee. The apogee moves forward on average 3 degrees per revolution of the moon, but it goes as much as 9 degrees reverse and 12 degrees forward, swinging back and forth.

And the eccentricity oscillates, and it does this every six months. The evection is a word Yo introduced in the 1650s, you'll meet him later in the course. Meaning it's like it's being thrown out of its orbit and into another orbit. This model shows the evection. M is the mean position.

A is the actual apogee and it shows it going around. You can see the positions one through eight, showing the different positions. This is actually taken from a letter of Crabtree to Gascoigne, describing what he had hear in conversation with Horrocks. We don't have this diagram in Horrocks itself.

This diagram however, appears in Newton's theory of the moon, because it is the starting point for Newton's work on the moon. This was by far the most accurate model of the moon anybody ever had, Horrocks but again lost until the 1670's, and even then it was Flamsteed, the royal astronomer who convinced Newton to start from Horrocks not start from a Keplerian orbit.

So for the moment all I'm trying to do. We're not going to study Horrocks in this course much. We'll look back at him in the 1670s, when the stuff surfaces. The point I'm making somebody was actually pushing Keplerian astronomy for all it was worth. And in doing so made enough progress that when his work finally surfaced.

The view of Kepler in astronomy was substantially different from what it was just before that work came forward. In particular, the three halves power rule started being taken very, very seriously as the best way of getting mean distances. I've got two more things. Then final slides. This is a mapping of the moon.

This happens to be one done by somebody named Melon as part of a Gassendi purist project. They set up a project that's called celanography of mapping the moon from telescopic observations. As you know, most of these dark areas are called Seas Mare. I think that Galileo was the one who originally proposed that they were seas, but I'm not sure of that.

It may be later. This is done with the Keplerian telescope. Not with Galilean telescope. The Keplerian telescope shown here ,the main difference, there a couple of main differences from it. But the key difference is it inverts. So whatever you're looking at is upside down. The eye does the same thing, what the image on the retina is the opposite of what we see, this is true of Keplerian telescopes.

So you wouldn't want to have this as your opera glasses since it would be funny to see the singers walking upside-down all over the stage, etc. But there are several wonderful things about it. One is it's not limited in magnification. You can push it very, very far if you moved the two lenses far enough apart.

That's one key thing. A second key thing is because the image is seen from here. You can put micrometers in here and measure what you're looking at. You can't do that in a Galilean telescope you can't put micrometers in. You can't even really put crosshairs in. The first person to put micrometers in was Gascoigne.

That name I just mentioned before. But when he was killed in the civil war, English civil war, that disappeared. And they had to be reinvented in the 1660s. This was a case where it didn't continue. But from henceforth we're talking about far better telescopes. With increasing power. When we come back to astronomy five weeks from now, after five weeks of mechanics, we'll see Huygens getting fantastic power in his telescopes for about a four year period.

He produced the world's best telescopes, then a guy in Rome surpassed him. But the point is once we get to this kind of a telescope a huge amount can be done that just couldn't be done by Galileo and the people working with that kind of telescope. So real advances started being made such as Fontana definitely seeing the phases of Mercury, Fontana seeing the lines across Jupiter.

Seeing different, they don't know what to call them at the time. He certainly didn't call them rings, but different protuberances from Saturn, and what else did he see? He saw the red spot, as I recall on Jupiter. There's not a whole lot else you can see. You can't see any detail on Venus, as most of you probably know, it's covered by cloud, so we can't see anything.

Mercury's pretty small. Mars is pretty small. It's very hard to get any detail from those telescopes other than the color. It's red. But Jupiter you could get a fair amount of, and then Saturn you could hope to get something if you could just figure out what those protuberances were.

That we'll see how it was done. Five weeks from now. So this is the assimilation of the telescope. We've not gone to a far better telescope, and people are doing big-time projects. They are not yet doing big-time projects on replacing Tycho's data, and I've already told you why.

If you don't know the parallax and atmospheric corrections, it's no good to have acuity down to seconds of arc if your corrections are in minutes of arc and you don't know that they're any good. So, telescopic observations don't replace Tycho's until the end of the century. It takes that long for positioning.

But for other things they can do wonders.