Tilting Styx and Nix but not Uranus with a Spin-Precession-Mean-motion resonance

TL;DR

This paper develops a Hamiltonian model to study spin resonances caused by planetary interactions and migration, explaining high obliquities of moons and planets, but concluding Uranus's tilt likely has a different origin.

Contribution

It introduces a first-order perturbation Hamiltonian model for spin resonances involving planetary mean motions and precession, with applications to moons and planetary obliquities.

Findings

Spin resonance can tilt moons Styx and Nix to high obliquity via migration.

Uranus's high obliquity cannot be explained by long-term spin resonance capture.

The model provides insights into spin dynamics in satellite and planetary systems.

Abstract

A Hamiltonian model is constructed for the spin axis of a planet perturbed by a nearby planet with both planets in orbit about star. We expand the planet-planet gravitational potential perturbation to first order in orbital inclinations and eccentricities, finding terms describing spin resonances involving the spin precession rate and the two planetary mean motions. Convergent planetary migration allows the spinning planet to be captured into spin resonance. With initial obliquity near zero, the spin resonance can lift the planet's obliquity to near 90 or 180 degrees depending upon whether the spin resonance is first or zero-th order in inclination. Past capture of Uranus into such a spin resonance could give an alternative non-collisional scenario accounting for Uranus's high obliquity. However we find that the time spent in spin resonance must be so long that this scenario cannot be responsible for Uranus's high obliquity. Our model can be used to study spin resonance in satellite systems. Our Hamiltonian model explains how Styx and Nix can be tilted to high obliquity via outward migration of Charon, a phenomenon previously seen in numerical simulations.