The Runge–Lenz vector is determined in a rotating coordinate system, for nonrelativistic Kepler motion modified by an inverse cube force. In the rotating coordinate system the problem reduces to that of nonrelativistic Kepler motion. Using the Runge–Lenz vector it is shown how to obtain the classical orbit equation and the quantum mechanical energy eigenvalues. Attention is confined to classical motion between two turning point method can be extended to other kinds of motion that are possible in this force field.