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Chaos over order : mapping 3D rotation of triaxial asteroids and minor planets
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Makarov, Valeri V. , Goldin, Alexey, Tkachenko, Alexei V., Veras, Dimitri and Noyelles, Benoît (2022) Chaos over order : mapping 3D rotation of triaxial asteroids and minor planets. Monthly Notices of the Royal Astronomical Society, 513 (2). pp. 2076-2087. doi:10.1093/mnras/stac962 ISSN 1745-3933.
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WRAP-Chaos-over-order-mapping-3D-rotation-triaxial-asteroids-2022.pdf - Accepted Version - Requires a PDF viewer. Download (2015Kb) | Preview |
Official URL: https://doi.org/10.1093/mnras/stac962
Abstract
Celestial bodies approximated with rigid triaxial ellipsoids in a two-body system can rotate chaotically due to the time-varying gravitational torque from the central mass. At small orbital eccentricity values, rotation is short-term orderly and predictable within the commensurate spin–orbit resonances, while at eccentricity approaching unity, chaos completely takes over. Here, we present the full three-dimensional rotational equations of motion around all three principal axes for triaxial minor planets and two independent methods of numerical solution based on Euler rotations and quaternion algebra. The domains of chaotic rotation are numerically investigated over the entire range of eccentricity with a combination of trial integrations of Euler’s equations of motion and the GALI(k) (Generalized Alignment Index) method. We quantify the dependence of the order–chaos boundaries on shape by changing a prolateness parameter, and find that the main 1:1 spin–orbit resonance disappears for specific moderately prolate shapes already at eccentricities as low as 0.3. The island of short-term stability around the main 1:1 resonance shrinks with increasing eccentricity at a fixed low degree of prolateness and completely vanishes at approximately 0.8. This island is also encroached by chaos on longer time-scales, indicating longer Lyapunov exponents. Trajectories in the close vicinity of the 3:2 spin–orbit resonance become chaotic at smaller eccentricities, but separated enclaves of orderly rotation emerge at eccentricities as high as 0.8. Initial perturbations of rotational velocity in latitude away from the exact equilibrium result in a spectrum of free libration, nutation, and polar wander, which is not well matched by the linearized analysis omitting the inertial terms.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QB Astronomy | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | ||||||||
| Library of Congress Subject Headings (LCSH): | Asteroids , Asteroids -- Orbits, Celestial mechanics , Ellipsoid | ||||||||
| Journal or Publication Title: | Monthly Notices of the Royal Astronomical Society | ||||||||
| Publisher: | Oxford University Press | ||||||||
| ISSN: | 1745-3933 | ||||||||
| Official Date: | June 2022 | ||||||||
| Dates: |
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| Volume: | 513 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 2076-2087 | ||||||||
| DOI: | 10.1093/mnras/stac962 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2022 [owner as specified on the article] Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved. | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Description: | Free access |
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| Date of first compliant deposit: | 4 May 2022 | ||||||||
| Date of first compliant Open Access: | 4 May 2022 | ||||||||
| RIOXX Funder/Project Grant: |
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