LAUSR

A unified tensor-product representation of Laplace-Runge-Lenz (LRL) vector about inversely-quadric and centric-force systems is derived. For a two-body Kepler system under gravitation or Coulomb force, the modified and unified tensor- product representation of LRL vector is also deduced by using an effective single-body description. Some properties of the vector are numerated and proved. Conservation of this vector is demonstrated in the tensor-product form. The energy formula for a bound-state elliptic orbit is simply derived via a novel approach. For a two-body system, the R-test rules for every kinds of Kepler’s motion are discussed in detail.