On the Lie symmetries of the classical Kepler problem

Abstract

The standard version of Noether's theorem, when applied to the classical Kepler problem, leads to the constants of energy and angular momentum but does not give the 'hidden symmetry' known as the Runge-Lenz vector. Lie's theory of differential equations is used to obtain all three constants of motion. The transformations of solutions under the point transformations to which these constants correspond are studied. The results are generalised to n dimensions.