It is well known that the Kepler problem admits two vector constants of the motion, the angular momentum and the Runge-Lenz vector. In this paper a generalization of the Runge-Lenz vector is found when a uniform constant electric field is present. The component of this vector in the direction of the external field is a constant of the motion.

• Received 24 October 1963

DOI:https://doi.org/10.1103/PhysRev.133.B1352