Abstract: A unified tensor- product representation of Runge- Lenz vector about inversely- quadric and centric- force systems,including both the two- body Kepler system under gravitation and the two point- charge system under Coulomb force,is given by introducing the energy- momentum tensor of a centric- force system. Based on the unified tensor- product representation,its conservation is demonstrated in a unified form; some properties of the vector are shown and verified. Meanwhile the criteria for every kinds of Kepler movement are derived,too. Specially a simple method of deriving the energy formula for the case of elliptic- trajectory movement is displayed in the end.

Key words: Runge-Lenz vector, centric force, Kepler movement, gravitation, Coulomb force, trajectory criterion