The dynamical stability of a Kuiper Belt-like region

Celletti, Alessandra; Kotoulas, Thomas; Voyatzis, George; Hadjidemetriou, John D.

doi:10.1111/j.1365-2966.2007.11868.x

Cited by 8 publications

(4 citation statements)

References 25 publications

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“…Poincaré sections have been used previously by several authors to study Neptune's exterior resonances (e.g. Malhotra 1996;Hadjifotinou & Hadjidemetriou 2002;Kotoulas & Voyatzis 2004;Celletti et al 2007). In particular, Malhotra (1996) used Poincaré sections to map the boundaries in the (a, e) plane of the stable libration zones of a few of Neptune's exterior resonances, and Wang & Malhotra (2017) used a similar approach to map the stable zones of the 2:1 and 3:2 interior resonances of the hypothetical planet 9.…”

Section: Resonance Width In the Planar Circular Restricted Three Body...mentioning

confidence: 99%

Neptune's 5:2 Resonance in the Kuiper Belt

Malhotra

Lan

Volk

et al. 2018

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Observations of Kuiper belt objects (KBOs) in Neptune's 5:2 resonance present two puzzles: this third order resonance hosts a surprisingly large population, comparable to the prominent populations of Plutinos and Twotinos in the first order 3:2 and 2:1 resonances, respectively; secondly, their eccentricities are concentrated near 0.4. To shed light on these puzzles, we investigate the phase space near this resonance with use of Poincaré sections of the circular planar restricted three body model. We find several transitions in the phase space structure with increasing eccentricity, which we explain with the properties of the resonant orbit relative to Neptune's. The resonance width is narrow for very small eccentricities, but widens dramatically for e 0.2, reaching a maximum near e ≈ 0.4, where it is similar to the maximum widths of the 2:1 and 3:2 resonances. We confirm these results with N-body numerical simulations, including the effects of all four giant planets and a wide range of orbital inclinations of the KBOs. We find that the boundaries of the stable resonance zone are not strongly sensitive to inclination and remain very similar to those found with the simplified three body model, with the caveat that orbits of eccentricity above ∼ 0.53 are unstable; higher eccentricity orbits are phase-protected from destabilizing encounters with Neptune but not with Uranus. These results show that the 5:2 resonant KBOs are not more puzzling than the Plutinos and Twotinos; however, detailed understanding of the origins of eccentric, inclined resonant KBOs remains a challenge.

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Section: Resonance Width In the Planar Circular Restricted Three Body...mentioning

confidence: 99%

Neptune's 5:2 Resonance in the Kuiper Belt

Malhotra

Lan

Volk

et al. 2018

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“…This allows us to obtain the so-called maps of dynamical stability (Celletti et al 2007) 1 by drawing through a color scale the LCN values in the plane defined by the two variable parameters. We performed the numerical integrations for t max = 30000 planetary revolutions.…”

Section: Dynamical Stability Mapsmentioning

confidence: 99%

Regions of stability in rotational dynamics

Celletti

Voyatzis

2010

Celest Mech Dyn Astr

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We investigate the rotational dynamics of a triaxial planet moving on a Keplerian orbit around its star. The dynamics is ruled by several parameters, like the eccentricity, the obliquity, the non-principal rotation, the angular momentum, etc. We consider two specific cases in which the planet is symmetric or asymmetric, according to whether two moments of inertia coincide or differs from each other. We study the dynamics by constructing maps of dynamical stability based on the computation of the maximum Lyapunov characteristic number versus some typical parameters. The results show that only specific resonances appear in the symmetric case, while the asymmetric case shows a much richer phenomenology.

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“…Finally, we present the applicability of the RLI to map the high order resonances in the restricted three-body problem, which might have relevance when studying the behavior of Kuiper belt objects [15]. We note that close relatives to our investigations are the works of [50] computing the stability maps of the system 55 Cancri by using various indicators (LI, SALI and FLI), and of [7] studying the dynamical stability of the Kuiper-Belt using the LI indicator. In all of the above problems the mean motion resonances (MMR) play an essential role, therefore we shortly summarize their properties.…”

Section: A Short Discussion On the Computing Timesmentioning

confidence: 83%

The Relative Lyapunov Indicators: Theory and Application to Dynamical Astronomy

Sándor

Maffione

2016

Chaos Detection and Predictability

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A recently introduced chaos detection method, the Relative Lyapunov Indicator (RLI) is investigated in the cases of symplectic mappings and continuous Hamiltonian systems. It is shown that the RLI is an efficient numerical tool in determining the true nature of individual orbits, and in separating ordered and chaotic regions of the phase space of dynamical systems. A comparison between the RLI and some other variational indicators are presented, as well as the recent applications of the RLI to various problems of dynamical astronomy.

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The dynamical stability of a Kuiper Belt-like region

Cited by 8 publications

References 25 publications

Neptune's 5:2 Resonance in the Kuiper Belt

Neptune's 5:2 Resonance in the Kuiper Belt

Regions of stability in rotational dynamics

The Relative Lyapunov Indicators: Theory and Application to Dynamical Astronomy

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