The second post-Newtonian motion of compact binary-star systems with spin

In this paper a full analytic solution for the second post-Newtonian motion of compact binaries with spin is presented. Advantage is taken of the following facts: (i) the second post-Newtonian motion of compact binaries without spin is already solved by a generalized quasi-Keplerian parametrization, (ii) first-order spin--orbit terms cross with Newtonian terms only since spin--orbit terms in compact binary-star systems are numerically of second post-Newtonian order, (iii) in the case of compact binary-star systems spin--spin interaction and quadrupole-deformation contributions are negligible at the second post-Newtonian approximation level. The analytic solution for the quasi-elliptic motion is given in a generalized quasi-Keplerian parametrization. Coordinate time and proper time of one of the bodies are used to parametrize the motion. As a by-product the first post-Newtonian motion of a satellite in the field of a rotating spherical mass is obtained.