Feynman's Lost Lecture: The Motion of Planets Around the Sun
Average customer rating: 4 out of 5 stars
  • If you are a Feynman fan
  • Feynman's proof of the law of ellipses
  • Lucid explanation of Feynman's proof of the law of ellipses
  • An Entertaining And Captivating Lecture
  • authors create a labour of love for Feynman
 Feynman's Lost Lecture: The Motion of Planets Around the Sun
David L. Goodstein , Judith R. Goodstein , and Richard Phillips Feynman
Manufacturer: W. W. Norton & Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 0393039188

Amazon.com

Richard Feynman, the rock star of theoretical physics, has left an image that belies his nerdy side. Not many bongo-playing surfer beatniks would have spent hours of their spare time proving Newton's law of elliptical planetary motion using only plane geometry. But Feynman's Lost Lecture: The Motion of Planets Around the Sun shows that the great man did just that. Originally delivered to an introductory physics class at Caltech in 1963, this 76-minute CD and book set contains everything the math-savvy listener needs to savor the pleasures of applied math. Caltech physicist David L. Goodstein and archivist Judith R. Goodstein found the notes and tape amid another professor's papers and set to work making sense of them; unfortunately, photographs of the blackboard drawings didn't survive. The book briefly covers their find and recovery work, then presents the proof as reconstructed--crucial reading if one is to follow the lecture. There's nothing easy about it, as Feynman acknowledges in the lecture:
I am going to give what I will call an elementary demonstration. "Elementary" means that very little is required to know ahead of time in order to understand it, except to have an infinite amount of intelligence.
He means, instead, that he is strictly using geometrical methods to reach his destination, which explains why it was so difficult to reconstruct without his diagrams. His charming Brooklyn accent and good humor show through in this lecture, even if the material is quite a bit drier than his fans might expect. Still, those interested in adding a new dimension to their understanding of this brilliant scientist--and those with a deep interest in Newtonian physics--will find The Motion of Planets Around the Sun a rare and unexpected treat. --Rob Lightner

Book Description

Rescued from obscurity, Feynman's Lost Lecture is a blessing for all Feynman followers. Most know Richard Feynman for the hilarious anecdotes and exploits in his best-selling books "Surely You're Joking, Mr. Feynman!" and "What Do You Care What Other People Think?" But not always obvious in those stories was his brilliance as a pure scientist--one of the century's greatest physicists. With this book and CD, we hear the voice of the great Feynman in all his ingenuity, insight, and acumen for argument. This breathtaking lecture--"The Motion of the Planets Around the Sun"--uses nothing more advanced than high-school geometry to explain why the planets orbit the sun elliptically rather than in perfect circles, and conclusively demonstrates the astonishing fact that has mystified and intrigued thinkers since Newton: Nature obeys mathematics.

David and Judith Goodstein give us a beautifully written short memoir of life with Feynman, provide meticulous commentary on the lecture itself, and relate the exciting story of their effort to chase down one of Feynman's most original and scintillating lectures. David and Judith Goodstein live in Pasadena, California.

Customer Reviews:

5 out of 5 stars If you are a Feynman fan.......2007-09-04

This is a lot of fun -- if. If you are pretty good at mathematical games and have a love for all things Feynman. What makes it work is the CD with Feynman giving the lecture. He goes at the speed of light, but he is always amazing, even when you have no idea what he just said! I can't imagine what it was like for the young folks trying to make sense out of what was going on. But, I bet he inspired them for the rest of their careers. He still does that to people today. If you want a sample of the Feynman magic this is a tough place to start. But do find a way to start.

5 out of 5 stars Feynman's proof of the law of ellipses.......2007-02-04

First we see that planets sweep out equal areas in equal times, following Newton's easy proof. Now to prove that planets move in ellipses. Cut the orbit into infinitesimal, equiangular pieces (as seen from the sun). Each little piece of the orbit corresponds to the velocity vector at that point. Draw a velocity diagram by moving all of these velocity vectors so that they have a common origin point. Obviously, as we move around the orbit, the velocity vector will make one revolution around the origin. In fact, it will trace out a circle, as we shall now prove. The orbit is cut into infinitesimal triangles with equal angles at the sun, so clearly these triangles are similar with a scaling factor r, i.e. an area scaling factor r^2. But time is the same as area, so time also varies as r^2. The change in velocity in one of these pieces is force*time=(1/r^2)*(r^2)=independent of r, so the dv steps in the velocity diagram are all of equal size, and because of the equiangular division they all make equal angles with each other (dv parallel to PS), so the velocity vector does indeed trace out a circle, and the equiangular division of the orbit as seen from the sun translates to an equiangular division of this circle as seen from its center. Of course, the center of the circle is not the origin of the velocity vectors; in particular, the velocity vector going through the center of the circle is the longest velocity vector, so it corresponds to the position on the orbit closest to the sun (as is obvious by the law of equal areas). If we turn the orbit diagram so that this position is straight to the right of the sun, then the longest arrow in the velocity diagram points straight up, since the velocity vector drawn in the orbit diagram will of course be parallel to the tangent to the orbit. When we have advanced a given angle beyond this starting point on the orbit (as seen from the sun), the corresponding velocity vector (i.e. the tangent to the orbit at this point) is found by advancing the same angle in the velocity diagram (as seen from the center of the circle) and connecting this boundary point with the origin of the velocity vectors, and conversely. So the velocity diagram contains complete information about the tangents of the orbit, so it contains complete information about the orbit up to scaling. So the problem becomes: for any velocity diagram, to recreate the orbit. To do this we turn the velocity diagram 90 degrees to the right. To recreate the orbit we must now find a curve that is always perpendicular to the velocity vectors. This can be done as follows. For any point p on the circumference of the velocity diagram circle, draw the line connecting it to the origin O of the velocity vectors and the line connecting it to the center C of the circle. Mark the point P where the perpendicular bisector of Op cuts Cp as a point on the orbit. Now we prove that the orbit generated in this way, as p moves around the circle, is an ellipse (we assume O to be inside the circle; if it was on the boundary the orbit would be a parabola, etc.). The perpendicular bisector cuts the triangle OPp into congruent halves (SAS), making OP=Pp, so CP+OP=CP+Pp=radius of the circle=independent of p, so P traces out an ellipse with foci C and O, and the perpendicular bisector is tangent to this ellipse (because all its other points are outside of the ellipse because they have greater sum of distances to the foci), as required. QED.

5 out of 5 stars Lucid explanation of Feynman's proof of the law of ellipses.......2003-09-11

The book first walks you through the works of Copernicus, Galileo, Brahe and Kepler. Then it gives a brief account of Feynman's life and his work. Then, through numerous diagrams, the authors clearly explain Feynman's ingenious proof of the law of ellipses. Finally, the book presents Feynman's lecture "The Motion of Planets Around the Sun".

It is amazing how Feynman, starting on the lines of Newton, and then not being able to follow Newton's reasoning, devised a different but elegant proof of the law of ellipses.

4 out of 5 stars An Entertaining And Captivating Lecture.......2003-04-04

This Review refers to the paperback edition of Feynman's Lost Lecture: The Motion of Planets Around the Sun with audio CD.

The title of Goodstein's book, Feynman's Lost Lecture, may be a bit misleading in terms of the overall content. The book is, in truth, mainly an explanation of the elliptic patterns performed by the planets, among other things, that an unpublished Feynman lecture originally referred to (although the lecture is included in text and on CD, the lecture is only a fraction of the overall book). Goodstein provides a geometrical means of explaining elliptical patterns that even a non-physicist will find easily comprehensible, especially considering the frequency of companion diagrams. The book also includes a rather unique introduction providing a brief biography of Feynman along with the author's personal experiences related to the well-known physicist. An unexpected, but greatly appreciated, addition is Feynman's original notes regarding his lecture contained in the back of the book.

Feynman's Lost Lecture details how to use geometric proofs to find answers to problems such as the speed of a planet when in motion around the sun and how to prove geometrically that an object is an ellipse. The author properly explains and demonstrates these concepts throughout the book via written and visual examples.

Goodstein presents the topics in such a fashion that the reader can easily try for himself\herself the idea portrayed. This is generally due to a generous selection of diagrams and exemplary situations, which properly convey the ideas that Goodstein presents (although it would probably be much more beneficial if more of the diagrams accompanied Feynman's actual lecture). The main text is also of a form easily understood and more than adequately conveys the topic that the author presents. However, the literary style is slightly lacking - in that it often becomes a bit informal in description and detail.

Overall, the literary shortcomings do not interfere with the author's ability to convey the topic and makes for a rather interesting read. Yet another above-par lecture accompanied by a surprisingly above-par explanation, Feynman's Lost Lecture: The Motion of Planets Around the Sun is more than worth it's price and should be a welcome addition to any reader's (both physicists and non-physicists alike) personal library.

4 out of 5 stars authors create a labour of love for Feynman.......2002-07-22

This book is a labour of love by Judith and David Goodstein for their friend Richard Feynman. I really enjoyed the revelations of the human side of the great physicist, especially the 20 page reminiscene by David Goodstein (a fellow physicist at cal tech) and Feynman's sometimes gruff answers to questions after the lecture. A different view of the human side of Feynman than what you read in "Surely, you're joking". I found the technical side of the book even more rewarding (see next paragraph) but be warned: this is pretty intense geometry and logic - I have a hard time imagining anyone without at least a couple years of post secondary math or physics or engineering following all the arguments.

But if you have the background and patience, it's some pretty cool stuff. Like many folks, I learned planetary dynamics using calculus, not geometry, and so this was my first exposure to the elegant relationship between velocity diagrams and orbits. While Feynman's lecture is somewhat unorganized and not entirely clear, the book does a great job filling in the blanks. There are certainly some rough spots (way too much time on the initial simple properties of ellipses, the argument connecting Kepler's third law to the law of gravitation is not clear, and more) but anyone with sufficient background willing to invest a few hours will be able to get past these minor problems. I kind of like how the pace accelerates to a ridiculous level by the end, leaving you to pretty much work out all the hard details of Rutherford's law of scattering for yourself.

Listen to the lecture, scratch your head wondering "what the heck was that", then read the book and study the arguments, then listen again and feel enlightened.
Classical and Celestial Mechanics: The Recife Lectures
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    		Classical and Celestial Mechanics: The Recife Lectures

    Manufacturer: Princeton University Press
    ProductGroup: Book
    Binding: Hardcover

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    ASIN: 0691050228

    Book Description

    This book brings together a number of lectures given between 1993 and 1999 as part of a special series hosted by the Federal University of Pernambuco, in which internationally established researchers came to Recife, Brazil, to lecture on classical or celestial mechanics. Because of the high quality of the results and the general interest in the lecturers' topics, the editors have assembled nine of the lectures here in order to make them available to mathematicians and students around the world. The material presented includes a good balance of pure and applied research and of complete and incomplete results. Bringing together material that is otherwise quite scattered in the literature and including some important new results, it will serve graduate students and researchers interested in Hamiltonian dynamics and celestial mechanics.

    The contributors are Dieter Schmidt, Ernesto Pérez-Chavela, Mark Levi, Plácido Táboas and Jack Hale, Jair Koiller et al., Hildeberto Cabral, Florin Diacu, and Alain Albouy. The topics covered include central configurations and relative equilibria for the N-body problem, singularities of the N-body problem, the two-body problem, normal forms of Hamiltonian systems and stability of equilibria, applications to celestial mechanics of Poincaré's compactification, the motion of the moon, geometrical methods in mechanics, momentum maps and geometric phases, holonomy for gyrostats, microswimming, and bifurcation from families of periodic solutions.

    Lectures on Celestial Mechanics (Classics in Mathematics)
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      		Lectures on Celestial Mechanics (Classics in Mathematics)
      Carl L. Siegel , and Jürgen K. Moser
      Manufacturer: Springer
      ProductGroup: Book
      Binding: Paperback

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      ASIN: 3540586563
      Classical Many-Body Problems Amenable to Exact Treatments: (Solvable and/or Integrable and/or Linearizable...) in One-, Two- and Three-Dimensional Space (Lecture Notes in Physics)
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        		Classical Many-Body Problems Amenable to Exact Treatments: (Solvable and/or Integrable and/or Linearizable...) in One-, Two- and Three-Dimensional Space (Lecture Notes in Physics)
        Francesco Calogero
        Manufacturer: Springer
        ProductGroup: Book
        Binding: Hardcover

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        ASIN: 3540417648

        Book Description

        This book focuses on exactly treatable classical (i.e. non-quantal non-relativistic) many-body problems, as described by Newton's equation of motion for mutually interacting point particles. Most of the material is based on the author's research and is published here for the first time in book form. One of the main novelties is the treatment of problems in two- and three-dimensional space. Many related techniques are presented, e.g. the theory of generalized Lagrangian-type interpolation in higher-dimensional spaces.This book is written for students as well as for researchers; it works out detailed examples before going on to treat more general cases. Many results are presented via exercises, with clear hints pointing to their solutions.
        Celestial mechanics (Mathematics lecture note series)
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          		Celestial mechanics (Mathematics lecture note series)
          Shlomo Sternberg
          Manufacturer: W. A. Benjamin
          ProductGroup: Book
          Binding: Unknown Binding

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          ASIN: 0805391029
          Chaos and Stability in Planetary Systems (Lecture Notes in Physics)
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            		Chaos and Stability in Planetary Systems (Lecture Notes in Physics)

            Manufacturer: Springer
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            1. Dynamics of Extended Celestial Bodies And Rings (Lecture Notes in Physics) Dynamics of Extended Celestial Bodies And Rings (Lecture Notes in Physics)

            ASIN: 3540282084

            Book Description

            This book is intended as an introduction to the field of planetary systems at the postgraduate level. It consists of four extensive lectures on Hamiltonian dynamics, celestial mechanics, the structure of extrasolar planetary systems and the formation of planets. As such, this volume is particularly suitable for those who need to understand the substantial connections between these different topics.

            Dynamics of Extended Celestial Bodies And Rings (Lecture Notes in Physics)
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              		Dynamics of Extended Celestial Bodies And Rings (Lecture Notes in Physics)

              Manufacturer: Springer
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              Taking both a theoretical and observational perspective, this book is an introduction to recent developments in the field of celestial mechanics. It emphasizes the application to extended celestial bodies and devotes much attention to rotational aspects. In particular, it explains the state of art for accurate modelling of the rotation of celestial bodies such as the Earth, the Moon, and Mercury, which involves principles related to hydrodynamics and geodesy. Comparisons between the light curves of the asteroids and their rotational state are made and spatial techniques leading to the determination of the Earth's gravitational field are explained. Also, the book provides a general overview of the collisional processes in the solar system and of the dynamics of the rings. It is addressed to graduate students and researchers in space sciences and celestial dynamics.
              Galaxies and Chaos (Lecture Notes in Physics)
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                		Galaxies and Chaos (Lecture Notes in Physics)

                Manufacturer: Springer
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                Galaxies and Chaos examines the application of tools developed for Nonlinear Dynamical Systems to Galactic Dynamics and Galaxy Formation, as well as to related issues in Celestial Mechanics. The contributions collected in this volume have emerged from selected presentations at a workshop on this topic and key chapters have been suitably expanded in order to be accessible to nonspecialist researchers and postgraduate students wishing to enter this exciting field of research.
                Generating Families in the Restricted Three-Body Problem: II. Quantitative Study of Bifurcations (Lecture Notes in Physics)
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                  		Generating Families in the Restricted Three-Body Problem: II. Quantitative Study of Bifurcations (Lecture Notes in Physics)
                  Michel Henon
                  Manufacturer: Springer
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                  Book Description

                  The classical restricted three-body problem is of fundamental importance because of its applications in astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. A central role is played by periodic orbits, of which many have been computed numerically. This is the second volume of an attempt to explain and organize the material through a systematic study of generating families, the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. We use quantitative analysis in the vicinity of bifurcations of types 1 and 2. In most cases the junctions between branches can now be determined. A first-order approximation of families of periodic orbits in the vicinity of a bifurcation is also obtained. This book is intended for scientists and students interested in the restricted problem, in its applications to astronomy and space research, and in the theory of dynamical systems.
                  Singularities in Gravitational Systems: Applications to Chaotic Transport in the Solar System (Lecture Notes in Physics)
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                    		Singularities in Gravitational Systems: Applications to Chaotic Transport in the Solar System (Lecture Notes in Physics)

                    Manufacturer: Springer
                    ProductGroup: Book
                    Binding: Hardcover

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                    ASIN: 3540437657

                    Book Description

                    Chaos theory plays an important role in modern physics and related sciences, but -, the most important results so far have been obtained in the study of gravitational systems applied to celestial mechanics. The present set of lectures introduces the mathematical methods used in the theory of singularities in gravitational systems, reviews modeling techniques for the simulation of close encounters and presents the state of the art about the study of diffusion of comets, wandering asteroids, meteors and planetary ring particles. The book will be of use to researchers and graduate students alike.

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