Motion of a Pair of Gravitating Bodies in Dark Energy Presence: Small Deviations from Keplerian Motion

The problem of the motion of two gravitating bodies in the presence of dark energy (DE), considered as a perturbing factor, is investigated. In addition to the orbit precession frequency obtained in previous studies, the correction to the orbital motion frequency was calculated, and the oscillations of the semi-major axis and the eccentricity of the orbit caused by the influence of DE were studied.