Laplace surface dynamics, revisited: satellites, exo-planets and debris with distant, eccentric companions

TL;DR

This paper extends classical Laplace surface theory to include higher multipoles, revealing complex stationary orbits and dynamical structures relevant for satellites, exo-planets, and debris influenced by eccentric, inclined companions.

Contribution

It introduces a higher multipole framework for Laplace surface dynamics, capturing complex equilibria and secular behaviors in eccentric, inclined systems beyond the quadrupolar approximation.

Findings

Identified eccentric and inclined Laplace equilibria across a broad parameter space.

Mapped stable and chaotic regions for Trans-Neptunian Objects influenced by a hypothetical ninth planet.

Demonstrated relevance of extended Laplace dynamics for multi-planet systems in binaries.

Abstract

To date, studies of $\textit{Laplace Surface}$ 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 such astronomical settings in mind, we extend the classical Laplace framework to higher multipoles, and map out the backbone of stationary orbits, now complexified 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 which we capture via Poincar$\'{e}$ sections, while highlighting a beautiful interplay between Laplace and Kozai-Lidov secular dynamical structures. An eminently classical tale revived for the exo-planetary 21st century!