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We derive octupole-level secular perturbation equations for hierarchical triple systems, using classical Hamiltonian perturbation techniques. Our equations describe the secular evolution of the orbital eccentricities and inclinations over timescales long compared to the orbital periods. By extending previous work done to leading (quadrupole) order to octupole level (i. e. , including terms of order \³, where \\ a₁/a₂<1 is the ratio of semimajor axes) we obtain expressions that are applicable to a much wider range of parameters. For triple systems containing a close inner binary, we also discuss the possible interaction between the classical Newtonian perturbations and the general relativistic precession of the inner orbit. In some cases we show that this interaction can lead to resonances and a significant increase in the maximum amplitude of eccentricity perturbations. We establish the validity of our analytic expressions by providing detailed comparisons with the results of direct numerical integrations of the three-body problem obtained for a large number of representative cases. We also discuss applications of the theory in the context of several observed triple systems of current interest. short version
Ford et al. (Sat,) studied this question.