In March 1964 Richard Feynman gave a lecture entitled 'The motion of the planets around the Sun' as part of a series of physics lectures to Freshmen at Caltech. Details of the other lectures were saved in Caltech’s archives but the ‘planets’ lecture was thought to be lost. That remained the case for more than three decades until David and Judith Goodstein published a book of the same title in which they describe the story of finding Feynman’s preliminary notes and some pictures in scraps of the transcripts. They reconstruct his lecture and tell the story of how Feynman followed Newton’s geometric method, based on Kepler’s laws, to prove that the planets move in ellipses. It is a story of Feynman’s genius in his ability to show phyisical concepts in pictorial form.