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Main Author: Pucacco, Giuseppe
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2410.12768
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author Pucacco, Giuseppe
author_facet Pucacco, Giuseppe
contents We analyse the stability of the de Sitter equilibria in multi-resonant planetary systems. The de Sitter equilibrium is the dynamical state of the Laplace resonance in which all resonant arguments are librating. The sequence of equilibria exists all along the possible states balancing resonance offsets and forced eccentricities. Possible additional new-de Sitter equilibria may exist when at least one of the forced eccentricities is large (the paradigmatic case is Gliese-876). In the present work, these families of equilibria are traced up to crossing exact commensurability, where approximate first-order solutions diverge. Explicit exact location of the equilibria are determined allowing us to verify the Lyapunov stability of the standard de Sitter equilibrium and of the stable branches of the additional ones.
format Preprint
id arxiv_https___arxiv_org_abs_2410_12768
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Dynamical Stability of the Laplace Resonance
Pucacco, Giuseppe
Earth and Planetary Astrophysics
General Relativity and Quantum Cosmology
Mathematical Physics
We analyse the stability of the de Sitter equilibria in multi-resonant planetary systems. The de Sitter equilibrium is the dynamical state of the Laplace resonance in which all resonant arguments are librating. The sequence of equilibria exists all along the possible states balancing resonance offsets and forced eccentricities. Possible additional new-de Sitter equilibria may exist when at least one of the forced eccentricities is large (the paradigmatic case is Gliese-876). In the present work, these families of equilibria are traced up to crossing exact commensurability, where approximate first-order solutions diverge. Explicit exact location of the equilibria are determined allowing us to verify the Lyapunov stability of the standard de Sitter equilibrium and of the stable branches of the additional ones.
title Dynamical Stability of the Laplace Resonance
topic Earth and Planetary Astrophysics
General Relativity and Quantum Cosmology
Mathematical Physics
url https://arxiv.org/abs/2410.12768