So we call them Kepler's laws, in particular the ellipse and the area rule. I'm listing the ones that are normally called laws. I'll come back to the shutter quotes in a second. The planets described elliptical trajectories about the sun or central body out of focus. Why is the in parentheses?
Because I want you also to consider the sentence without it. Planets. Not just the six we have. Planets period. Okay. We normally take the law to be without the the. There's nothing in Kepler to suggest that as such. Kepler's referring to the planets. The radius vectors sweep out equal areas and equal times about the sun.
Periods of the planets are sesquialtera altered in proportion to their mean distances from the sun. I chose to use the word used at the time. Rather than three halves power. So you would get accustomed to the phrase sesquialtera. That's three halves power. Okay? Sesquialtera proportion. Double proportion is square.
Sesquialtera is three halves. Okay, the diametral distance rule, the distance is again, D planets. Vary as shown and then finally, the fifth so-called law, the four and five are never called laws by anybody even though they're quite important. But they have at least as much status as the first three.
Trajectories defined by the planets are confined to single planes, ect. Center quotes on the word laws because the best, and now I'm depending on Curtis Wilson for this, although I assisted him in the effort, but it's he that ended up doing the most complete survey. The best we can tell, the first person to call either of the first two laws is Leibniz after the Principia.
Kepler never calls them laws nor does anybody else call them laws in the meantime. Even the word law takes on a new character after Descartes, okay. The word law was used all the time during the Renaissance and Renaissance naturalism, but after Descartes it takes on more or less the modern meaning.
And Newton of course uses it. And then Leibniz responding to the Principia though he insisted his response was written he wrote the Principia. I mean before he saw the Principia but we now know better thanks to Nico Baterlome going through the notebooks of Leibniz. So at any rate, they weren't called laws then.
Okay? And you'll see me, and I'll just all the time talk about the area rule and the three Fs power rule, because they're basically rules for modeling planetary motion. And after we get to Newton, I'll start calling them laws, but untill we get to Newton it's not clear whether they should be called laws.
And that leads me then to raise the point, after Newton, we have a thing called Keplerian motion, I describe it here. At least a high approximation the five planets move along ellipses sweeping out equal areas and equal times with respect to the true sun located at a focus common to all.
On planes passing through the sun at fixed angles of inclination. In periods proportional to the three-halves power of their three mean distances of the sun. That's called Keplerian motion, and it takes all the features of it to be Keplerian motion. That's the term that came to be used after Newton.
Because what Newton did was to show all those features are tied to exactly the same physics. Know it's one thing making them all tied to one another. Note, you'll see that the last two readings of this course, this semester, the last two weeks, you'll see Newton discovering that systemic ties between those, okay?
Now, that's a generalization. We can ask a bunch of questions about that generalization, and that's what I'm gonna be doing for the moment. I can do the same thing with the prior slide, and take the generalizations one for one. So starting with first question. What grounds were there for extending, projecting each of the generalizations beyond the five planets?
To support claims about any possible body orbiting the sun, anybody engaged in celestial orbital motion whatsoever, or any celestial body moving within our planetary system comets? Does everybody get that? Suppose we have very good evidence for the thing at the top. What are the grounds for saying it's got a hold of objects other than those five going around the sun?
What about our moon? We of course know it doesn't as I've already told you. What about the satellites of Jupiter? They're going around Jupiter. What about comets? And the question here is, what sort of evidence would justify projecting what we know about those planets, the six of them with the Earth, onto other possibilities?
The word projection is Nelson Goodman's. I think it's the right word in the following sense. Is Kepler worried about this? Every sensible scientist worried about this. They didn't think law versus accidental generalization. They asked, what's my grounds for extrapolating? Okay, and that's a very, very good question. Second thing, what grounds were there for concluding that the specific statement of each generalization was properly suited for any such projection.
This is very much a Goodman point. You can describe a regularity, but the way in which you describe it may not be the ideal way to project it to further cases. I'll give you a famous example. It's an example that's due to Kepler but you can't quite see it yet.
What is uniform circular motion? Well it's equal arcs at equal times. Or it's equal angles and equal times. Or it's equal areas in equal times. Which one generalizes? The one that nobody thought about. Okay, so if you want to describe uniform circular motion celestially, you best describe it as equal areas and equal times if you're going to generalize, okay.
And that's the notion here. Just because he's used the words he has to describe these generalizations, they may be merely approximating an alternative description that's much more suitable to generalize. Everybody see that? And again, what's the evidence you've got the right words? Third, what if any further qualifications, tacit, ceteris paribus conditions need to be noted with each generalization before projecting it?
The Nelson Goodman type of example. A tiger with a leg amputated is still a four legged animal, in the generic sense. It's not a counter example to tigers being four legged. Here would be if that comet that hit Jupiter a few years ago somehow or another knocked it out of orbit and into the sun.
It would not be a counterexample to Keplerian motion. Always, with these generalizations, there are unclear, unstated conditions over which they hold. They're in effect restrictions over what domain they hold or what the conditions are. And you generally don't know what they are, you discover them at a later point in life.
Okay, but that's the reason they're so often tacit. They don't always have to be tacit, but you're looking at it and saying, what are the restrictions to this? I'll give you a slightly different example. Does it still hold further out when we go past Saturn? Okay, when they first discovered Uranus, it didn't quite have the right orbit.
You'll see that later. It didn't quite have the right orbit, and the natural proviso, oh, the law of gravity breaks down after you get past Saturn. It's not a dumb proposal. It's a fortunately wrong proposal. But it's the same problem. Namely, what are the caeteris paribus in which under the conditions for Keppler to hold?
If you get far enough away from the sun, does it start breaking down? May it even be breaking down with Saturn? Okay, notice what the question at the top though. These are questions about generalizations and they're all asking the same thing. What grounds do we have for concluding the ceteris paribus conditions can remain tacit for the projection and for concluding that the generalization is well stated?
Okay. Now, what I'm doing to you I'm going to continue doing this much more dramatically with the next slide. You think the problem of evidence is the question of truth. And it is if you don't have a generalization. If we have a generalization there's a whole host of other questions about evidence.
It's one thing to have evidence that the generalization holds to very high approximation over a finite period of time, it's a totally different thing to project it beyond those cases all over the place. So far, so good? Questions about evidence? I'm not gonna try to answer them, so I think if you start thinking about it, how can you answer these without physics?