Laplace surface dynamics, revisited: satellites, exoplanets, and debris with distant, eccentric companions

To date, studies of $\textit{Laplace Surface}$ dynamics have concerned themselves with test particle orbits fixed shape and orientation in the combined field an oblate central body (to which is bound) a distant, inclined, companion captured to quadrupolar order. While amply sufficient for satellites around planets on near-circular orbits, approximation fails capture essential dynamical features induced by wide binary (be it star, planet or black hole) fairly eccentric orbit. With similar such astronomical settings mind, we extend classical Laplace framework higher multipoles, map out backbone stationary now complexified broken axial symmetry. Eccentric inclined equilibria, had been presaged systems large enough mutual inclination, are here delineated over broad range mutually perturbations. We recover them particles hot Jupiter stellar binary, highlighting their relevance architecture multi-planet binaries. then deploy our machinery closer home, as consider secular Trans-Neptunian Objects (TNOs) presence putative ninth planet. show how generalized equilibria seed islands objects be sheltered around, within chaotic seas via Poincar$\'{e}$ sections, while beautiful interplay between Kozai-Lidov structures. An eminently tale revived exo-planetary 21st century!