Orateur
Description
We present an analytical solution for the dynamics of spinning binary black holes on eccentric orbits at second post-Newtonian (2PN) order, extending the 1.5PN results of Cho and Lee. For the orbital angular momentum L and the individual spins S1 and S2, we exploit the separation of timescales between orbital motion and precession to construct a hybrid solution that combines the 1.5PN oscillatory structure with complete 2PN secular corrections. For the orbital variables (r, φ), we derive their equations of motion and, using an ansatz method analog to Klein, construct a quasi-Keplerian parametric solution. This parametrization introduces generalized Keplerian elements that remain approximately constant over orbital timescales while incorporating 2PN spin-spin corrections.
