Resonant Chains and Three-body Resonances in the Closely-Packed Inner Uranian Satellite System
Numerical integrations of the closely-packed inner Uranian satellite system show that variations in semi-major axes can take place simultaneously between three or four consecutive satellites. We find that the three-body Laplace angle values are distributed unevenly and have histograms showing struct...
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Main Authors | , |
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Abstract | Numerical integrations of the closely-packed inner Uranian satellite system show that variations in semi-major axes can take place simultaneously between three or four consecutive satellites. We find that the three-body Laplace angle values are distributed unevenly and have histograms showing structure, if the angle is associated with a resonant chain, with both pairs of bodies near first-order two-body resonances. Estimated three-body resonance libration frequencies can be only an order of magnitude lower than those of first-order resonances. Their strength arises from a small divisor from the distance to the first-order resonances and insensitivity to eccentricity, which make up for their dependence on moon mass. Three-body resonances associated with low-integer Laplace angles can also be comparatively strong due to the many multiples of the angle contributed from Fourier components of the interaction terms. We attribute small coupled variations in semi-major axis, seen throughout the simulation, to ubiquitous and weak three-body resonant couplings. We show that a system with two pairs of bodies in first-order mean-motion resonance can be transformed to resemble the well-studied periodically-forced pendulum with the frequency of a Laplace angle serving as a perturbation frequency. We identify trios of bodies and overlapping pairs of two-body resonances in each trio that have particularly short estimated Lyapunov timescales. |
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AbstractList | Numerical integrations of the closely-packed inner Uranian satellite system show that variations in semi-major axes can take place simultaneously between three or four consecutive satellites. We find that the three-body Laplace angle values are distributed unevenly and have histograms showing structure, if the angle is associated with a resonant chain, with both pairs of bodies near first-order two-body resonances. Estimated three-body resonance libration frequencies can be only an order of magnitude lower than those of first-order resonances. Their strength arises from a small divisor from the distance to the first-order resonances and insensitivity to eccentricity, which make up for their dependence on moon mass. Three-body resonances associated with low-integer Laplace angles can also be comparatively strong due to the many multiples of the angle contributed from Fourier components of the interaction terms. We attribute small coupled variations in semi-major axis, seen throughout the simulation, to ubiquitous and weak three-body resonant couplings. We show that a system with two pairs of bodies in first-order mean-motion resonance can be transformed to resemble the well-studied periodically-forced pendulum with the frequency of a Laplace angle serving as a perturbation frequency. We identify trios of bodies and overlapping pairs of two-body resonances in each trio that have particularly short estimated Lyapunov timescales. 2014, MNRAS, 445, 3959 Numerical integrations of the closely-packed inner Uranian satellite system show that variations in semi-major axes can take place simultaneously between three or four consecutive satellites. We find that the three-body Laplace angle values are distributed unevenly and have histograms showing structure, if the angle is associated with a resonant chain, with both pairs of bodies near first-order two-body resonances. Estimated three-body resonance libration frequencies can be only an order of magnitude lower than those of first-order resonances. Their strength arises from a small divisor from the distance to the first-order resonances and insensitivity to eccentricity, which make up for their dependence on moon mass. Three-body resonances associated with low-integer Laplace angles can also be comparatively strong due to the many multiples of the angle contributed from Fourier components of the interaction terms. We attribute small coupled variations in semi-major axis, seen throughout the simulation, to ubiquitous and weak three-body resonant couplings. We show that a system with two pairs of bodies in first-order mean-motion resonance can be transformed to resemble the well-studied periodically-forced pendulum with the frequency of a Laplace angle serving as a perturbation frequency. We identify trios of bodies and overlapping pairs of two-body resonances in each trio that have particularly short estimated Lyapunov timescales. |
Author | French, Robert S Quillen, Alice C |
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BackLink | https://doi.org/10.1093/mnras/stu2023$$DView published paper (Access to full text may be restricted) https://doi.org/10.48550/arXiv.1408.1141$$DView paper in arXiv |
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Snippet | Numerical integrations of the closely-packed inner Uranian satellite system show that variations in semi-major axes can take place simultaneously between three... 2014, MNRAS, 445, 3959 Numerical integrations of the closely-packed inner Uranian satellite system show that variations in semi-major axes can take place... |
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SubjectTerms | Chains Computer simulation Couplings Dependence Histograms Libration Orbital resonances (celestial mechanics) Pendulums Physics - Earth and Planetary Astrophysics Uranus satellites |
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Title | Resonant Chains and Three-body Resonances in the Closely-Packed Inner Uranian Satellite System |
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