  The angular and the radial parts of the dynamics of the perturbed Kepler
motion are separable in many important cases. In this paper we study the radial
motion and its parametrizations. We develop in detail a generalized eccentric
anomaly parametrization and a procedure of computing a generic class of
integrals based on the residue theorem. We apply the formalism to determine
various contributions to the luminosity of a compact binary.
