  General relativistic Gauss equations for osculating elements for bound orbits
under the influence of a perturbing force in an underlying Schwarzschild
space-time have been derived in terms of Weierstrass elliptic functions.
Thereby, the perturbation forces are restricted to act within the orbital plane
only. These equations are analytically solved in linear approximation for
several different perturbations such as cosmological constant perturbation,
quantum correction to the Schwarzschild metric, and hybrid
Schwarzschild/post-Newtonian $2.5$ order self-force for binary systems in an
effective one-body framework.
