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Higher-order effects in the dynamics of hierarchical triple systems. II. Second-order and dotriacontapole-order effects
We analyze the long-term evolution of hierarchical triple systems in Newtonian gravity to second order in the fundamental quadrupolar perturbation parameter, and to sixth order in $\ensuremath{\epsilon}=a/A$, the ratio of the semimajor axes of the inner and outer orbits. We apply the ``two-timescale'' method from applied mathematics to the Lagrange …