Feynman's Lost Lecture: The Motion of Planets Around the Sun
This book is about the lost lecture of Richard Feynman on the motion of the planets around the sun. It is not a book by Feynman but by David and Judith Goodstein.
The book contains Feynman’s elementary proof that planets move in elliptical orbits around the sun (being one of the focus points) by first showing that the so-called velocity orbit of each planet is a perfect circle. For this fact he “only” needs the famous laws of Newton and the law of gravity. Elementary, but not simple at all.
Feynman's reasoning is based on the work of Sir Isaac Newton, however he deviates at the point where he could not follow the arguments of Newton anymore. Feynman challenged himself in providing a geometric proof in the tradition of the ancient scholars instead of using the nowadays more custom analytical methods. As he states himself his proof is elementary but not simple. The whole idea behind this proof is truly elegant. Instead of focusing on the orbit swiped out by the "position" vector - that is the vector spanned by the position of the sun and the position of the planet - he changes the point of view to the derived picture, that is looking at the “velocity” vector, that is the vector given by the absolute velocity and direction of the planet (relative to the sun), and the orbit swept out by these vectors when the planet moves around the sun. My own first guess was that the orbit in this velocity diagram would be similar to the position orbit, but much to my surprise it was even simpler: it turns out to be a circle where the starting position of the velocity vectors is not at the center of the circle, but is off-center.
The elegance comes not only from this "simple" velocity orbit, but also from the way Feynman proves that it is indeed a circle. His ingredients are the laws of Newton and the fact that gravity depends on the inverse of the squared distance. This latter fact is derived from the third law of Kepler. The first and second law of Kepler are then reconstructed from Newton's laws and geometric arguments. Kepler's second law states that the area swept out by a planet (with respect to the sun) is equal for equal times. This follows directly from geometrical reasoning using Newton's laws. Kepler's first law states that planets move around the sun in elliptical orbits. Feynman uses Newton's laws and the law of gravity to geometrically prove that the velocity orbit is indeed a perfect circle. From this proven fact he then continues to show that the position orbit of the planet is indeed an ellipse, thereby proving the first law of Kepler.
The difference between the empirical laws of Kepler, describing the motions of the planet around the sun, and the logical reasoning of Newton (and Feynman) using Newtons famous laws to derive these empirical laws, is interesting in our current time frame, where the question is asked whether AI is capable of logical understanding. Kepler’s laws were based on observations and recognising patterns, but there was no understanding underlying these patterns. Newton managed to start with a few basic assumptions and then derive the laws of Kepler, but also a lot more than this. Feynman ends his lecture using his approach to gain understanding of the structure of atoms and derives the scattering law of Rutherford which was used to prove that matter inside an atom is concentrated at the center of this atom. The Goodsteins describe in great details the story about this lost lecure and how it was recovered and eventually led to this book. They describe how they have reconctructed the line of reasoning of Richard Feynman step by step, filling in the gaps or unclarities of Feynman's lecture notes. Finally they present the original transcript containing the storyline of Feynman himself. Since the proof of Feynman is based on the work of Sir Isaac Newton and the work of Johannes Kepler, the Goodsteins also provide as introduction a brief overview of our understanding of the celestial bodies in our heavens or universe as we would call it by now. It ranges from the work of Plato, Aristotle and Copernicus, to Tycho Brahe, Johannes Kepler, Isaac Newton and Galileo Galilei. Jeroen Bos-mulder's Reviews > Feynman's Lost Lecture: The Motion of Planets Around the Sun
Feynman's reasoning is based on the work of Sir Isaac Newton, however he deviates at the point where he could not follow the arguments of Newton anymore. Feynman challenged himself in providing a geometric proof in the tradition of the ancient scholars instead of using the nowadays more custom analytical methods. As he states himself his proof is elementary but not simple. The whole idea behind this proof is truly elegant. Instead of focusing on the orbit swiped out by the "position" vector - that is the vector spanned by the position of the sun and the position of the planet - he changes the point of view to the derived picture, that is looking at the “velocity” vector, that is the vector given by the absolute velocity and direction of the planet (relative to the sun), and the orbit swept out by these vectors when the planet moves around the sun. My own first guess was that the orbit in this velocity diagram would be similar to the position orbit, but much to my surprise it was even simpler: it turns out to be a circle where the starting position of the velocity vectors is not at the center of the circle, but is off-center.
The elegance comes not only from this "simple" velocity orbit, but also from the way Feynman proves that it is indeed a circle. His ingredients are the laws of Newton and the fact that gravity depends on the inverse of the squared distance. This latter fact is derived from the third law of Kepler. The first and second law of Kepler are then reconstructed from Newton's laws and geometric arguments. Kepler's second law states that the area swept out by a planet (with respect to the sun) is equal for equal times. This follows directly from geometrical reasoning using Newton's laws. Kepler's first law states that planets move around the sun in elliptical orbits. Feynman uses Newton's laws and the law of gravity to geometrically prove that the velocity orbit is indeed a perfect circle. From this proven fact he then continues to show that the position orbit of the planet is indeed an ellipse, thereby proving the first law of Kepler.
The difference between the empirical laws of Kepler, describing the motions of the planet around the sun, and the logical reasoning of Newton (and Feynman) using Newtons famous laws to derive these empirical laws, is interesting in our current time frame, where the question is asked whether AI is capable of logical understanding. Kepler’s laws were based on observations and recognising patterns, but there was no understanding underlying these patterns. Newton managed to start with a few basic assumptions and then derive the laws of Kepler, but also a lot more than this. Feynman ends his lecture using his approach to gain understanding of the structure of atoms and derives the scattering law of Rutherford which was used to prove that matter inside an atom is concentrated at the center of this atom. The Goodsteins describe in great details the story about this lost lecure and how it was recovered and eventually led to this book. They describe how they have reconctructed the line of reasoning of Richard Feynman step by step, filling in the gaps or unclarities of Feynman's lecture notes. Finally they present the original transcript containing the storyline of Feynman himself. Since the proof of Feynman is based on the work of Sir Isaac Newton and the work of Johannes Kepler, the Goodsteins also provide as introduction a brief overview of our understanding of the celestial bodies in our heavens or universe as we would call it by now. It ranges from the work of Plato, Aristotle and Copernicus, to Tycho Brahe, Johannes Kepler, Isaac Newton and Galileo Galilei. Jeroen Bos-mulder's Reviews > Feynman's Lost Lecture: The Motion of Planets Around the Sun
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