Resumen de Minimizers for the Kepler Problem

Richard Montgomery

• We characterize the minimizing geodesics for the Kepler problem endowed with the Jacobi-Maupertuis metric. We focus on the positive energy case, but do all energies. The more complicated negative energy case was solved in Jacobi (Crelles J 17:68–82, 1837. 10.1515/crll.1837.17.68), with his work translated and completed by Todhunter (Researches in the Calculus of Variations, Principally on the Theory of Discontinuous Solutions. Macmillan and Co., Cambridge, 1871), and later summarized in Wintner’s book. Our discussion of these old results includes a new proof for the positive energy case and perspectives coming from metric and differential geometry. For the negative energy result we need Lambert’s theorem which we discuss.