OK, so there are tons of Feynman books out there. What's so great about just one more on top of the heap of them? In "Feynman's Lost Lecture: The Motion of Planets Around the Sun" ("FLLTMOPATS" for slightly shorter) the reader gets to see Feynman test his intellect against that of Newton as Feynman recreates Newton's geometric interpretation of gravitation.
The book (as discussed in the preface and introduction) is a re-creation of one of Feynman's guest lectures, the content of which was very difficult to obtain and reproduce for various reasons. Essentially the lecture was given for fun because the class to which it was given had an exam soon, and the professors did not want to throw anything new at the students.
After the preface and introduction, the book first traces humanity's progressively improving understanding of the heavens as the torch passes from Copernicus to Brahe to Kepler to Galileo to Descartes and finally rests on the three pillars of Newton's Laws. Having made a solid foundation, the second of the two chapters is then a brief biographical chapter on Dr. Feynman. This section of the book is certainly not as in depth as many of the other books out there (neither was it written to be), however Goodstein presents several anecdotes that place Feynman in an academic setting, which is a slightly different canvas than most of the ones on which Feynman's life stories are normally painted. This results in some entertaining reading.
Finally, 63 pages into the book, we come to it: Feynman's Proof of The Law of Ellipses. This portion of the book is not Feynman's transcribed lecture (that's yet to come). These pages are a reproduction, in full, of Feynman's process of thinking. There is nothing more advanced to any of it than high school geometry and algebra, and there are plenty of illustrations to help make clear the points and proofs. This is really the meat and potatoes of the reading, and it is likely not material you'll understand if you're not paying full attention to what you're reading (that comes from personal experience). As stated in the book, it's a simple process (requiring about 2 lines) to work through all the details and gravity laws with calculus. It is not that the calculus method lacks elegance and beauty; it is that there is something far more gratifying about following this long, geometric ‘proof' the whole way through that yields a satisfaction you just can't get out of PHY2049 or equivalent. And while the words used in this part of the book aren't those of Feynman, they are careful and well explained glimpses of what's to come.
Admittedly, it's difficult to read and follow the written words of Feynman's lecture (about 25 pages near the end of the book), but that's why they give you a CD. Reading and listening to Feynman's words as he discusses his own, inventive validation of Newton increases the sensation that the analytical manner in which our physics today are taught to us may not be so fulfilling. So, FLLTMOPATS is not the book you want if you're looking for crazy, wacky stories of one of the most famous physicists of recent times (although there are some elements of that in it). What FLLTMOPATS has to offer over any other collection is a unique, new way to view relatively 'early' physics through the eyes of a great teacher.
