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At this late stage one has to wonder if there can be any worthwhile material by or about Feynman that hasn't already been published - the answer is, in this case, yes - but this doesn't offer a tremendous amount that would be new to dedicated Feynman fans. It's really for completests and neither a great nor terrible place to start for newcomers.

For just such newbies to Feynman I will briefly disclose that he was a Nobel Prize winning theoretical physicist who worked on the Manhattan Project in his youth and became famous not only for his professional skill but his quirky and irreverent public persona and his capabilities as an educator, both of the general public and of student physicists.

This lecture was omitted from the famous three volumes of lectures based on a two year undergrad introductory course that Feynman taught at Caltech. It is a demonstration of the fact that planets orbit the sun in elipses if Newton's Law of Gravitation is correct and perturbations from all the other planets are ignored - using only plane geometry. Since only a few diagrams and notes from the lecture remained, along with a voice recording of it, it was quite a task to reconstruct the proof, which as is pointed out by Feynman himself is, whilst elementary, not simple. That said, the explanation of the demonstration could not be clearer and anybody who can follow school level geometry will be fine. Because there are a large number of diagrams, what appears to be a lengthy (and therefore possibly intimidating) wodge of physics is in fact something you could read and understand in a couple of hours easily.

Additionally to the reconstruction and explanation of the proof, there is a mini-biography of Feynman which is best (as always) when telling anecdotes, not history, a transcript of Feynman delivering the lecture and a brief history of the relevant discoveries about the nature of the solar system, gravity and the way things move.
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This book has four chapters and an epilogue. The first chapter is historical, about the emergence of a solid heliocentric theory. It's vague, I'm pretty sure it is inaccurate, as if written straight from the authors' memory, and it really doesn't add much. The second is about Feynman himself, and it's not that interesting either. Somebody wrote that Feynman lived his life so that he could write anecdotes about himself, and it seems to have worked for others, too. So much for Feynman. The third chapter is the real contribution; the explanation of Feynman's lecture. This is the longest chapter and I feel very sure I wouldn't understand Feynman's lecture without it. As I've read more and more about the history of science, I've become more and more uncertain about the actual meaning of Kepler's and Newton's work, and about what can really be said about the motion of the planets, and this lecture should answer some real questions I have. The fourth chapter is Feynman's lecture, which is _much_ shorter than the explanation and also available on audio. Then there is an epilogue, which I have yet to get to.

Now for a discussion of the actual proofs.

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The first part is just about the properties of ellipses. There are two allied facts:
* the old string and push-pins construction, which you can make a formula of
* a light at one focus will have all its rays reflected back to the other focus
Geometrical constructions relating these two facts are developed.

There is also one interesting corollary. Take a circle. Choose a point in the circle that is not the center. The circle and the choice of the second point define an ellipse constructed according to a particular formula. The illustration of this fact in the book, on page 79 is not quite right:

Draw a line through F and F' which intersects the ellipse and the circle. Call the intersection on the ellipse closest to F', E', and the intersection on the circle closest to F' C'. Then F'E' must equal E'C', but in the diagram they are noticeably different.

Nonetheless, the geometric relationships are worth pondering.

One statement of the theorem:

Let F, F' be the two foci of the ellipse. Let D be the distance from F to any point p on the ellipse to F'. By the definition of ellipses, D is a constant. Let t be the line tangent to the ellipse at some arbitrary point P on the ellipse. Then it must be the case that the angle between the tangent and FP is equal to the angle between the tangent and F'P.

It turns out that it is Feynman's explanation that really clicked for me, finally. He draws the geometric diagram with the ellipse. Once he's done, the question still remains: is G'F a straight line? He uses a simple proof by contradiction and the fact that in a plane, the shortest distance between two points must be a straight line to demonstrate that it must be.

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The next step is to talk about the motion of a body under a single applied force that is always directed toward one spot. If we assume Newton's law of inertia, and that the entire change in motion must be toward the force, then we can show that regardless of the strength of the force, the line from the body to the spot where the force is directed must always sweep out equal areas in equal time. Start by showing that the line between the body traveling at constant velocity and a fixed point will always sweep out equal areas in equal times. Then, based on that, show that if the force is always applied solely in the direction of the fixed point, this property will still hold true. What is not demonstrated is that it is impossible for some other arrangement to result in the same behavior, in fact, there is a bit of a logic error in the text: asserting the inverse. But it is true, that even if the velocity toward the one point varies, the equal areas in equal times rule will still hold.

Note that the fact that a body traveling at constant velocity will always sweep out equal areas in equal times with respect to any fixed point is not actually covered in the text. It seems counterintuitive, but as the body recedes from the point, the angles change and the triangle becomes ever narrower and narrower. The angle between the moving body and its velocity vector will always increase, regardless of their relative position and velocity. To me this seems a surprising result, but I can not see anyway to avoid it. More precisely, if the angle is exactly 0, it will remain 0 until, as it passes the point, it instantaneously jumps to 180. If it is 180, it will remain 180 for ever. If it is greater than 0 it will increase smoothly, approaching, but never quite reaching 180.

The title is irresistable. But, like most of my "reading Feynman" projects, it's more work than I thought it would be. He is, after all, a physicist.

But, it's not a bad lecture and it comes with a story about how it was reconstructed. So, it's another labor of love for a man who makes us proud to be human.

It's approximately the same level of material that's in Six Easy Pieces. I think I would've liked it better if I'd heard it before SEP. As it is, it was a lot of money for "just one more lecture".

I'd say, "Get it if you're considering getting SEP". It's a taste of what you're getting yourself into. ( )

Richard Feynman will always be my favorite geek. I’ve read at least three of his books, but have never heard him speak anywhere, although he was the principle investigator of the Challenger disaster and there was much televised about that. The edition of this lecture was a CD that was available from my local library, no book. Other than the poor quality of the original recording transferred from the tape, I found his talk to be excellent.

I never studied Physics in school, but read a few books on the subject over the years, especially when my interest in Astronomy hit a fevered pitch around twenty-five years (or more) ago. Fortunately, I have a gift for all-things-mathematical, and was able to follow his lecture while driving at 70 mph up the highway. Planetary Motion explained in Plane Geometry – and done so eloquently! Then he follows that up with (if I recall correctly) an explanation of Rutherford’s Law (the scattering of subatomic particles) using PG again! When the lecture was over, the tape recorder was left running for another fifteen minutes as students came up to him and asked questions about various aspects of his lecture. He was generous to a fault with his time and his enthusiasm, and worked out the misunderstanding/answers with them.

Feynman speaks in the same style as he writes. Engaging would be a good word to start with. It was thrilling to hear him make comments to himself, give brief asides about a point he had just made, off-the-cuff remarks… The man was as brilliant as they come, and endlessly curious.

I can’t comment about the book because it is not available to me. So, suffice to say that if you have a half-way decent background in Math, you could probably learn from listening to the CD. If you have a nerdy side to you, you’ll probably like this more than you’d prefer to admit. I wish I had more professors with his level of enthusiasm when I went to college! ( )