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

Abstract

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