Two-Body Problem with Dark Energy
We formulate the problem of particle motion in the central field of a point mass and the uniform dark energy (DE) background. We introduce potential energy and describe the equilibrium (no-gravity) sphere. Equations of energy and angular momentum conservation are given showing two classes of motion, radial ones, with the zero angular momentum, and planar motions occurring when the angular momentum is non-zero. The classical Hubble law for all infinite motions holds due to DE presence.