On the stability of the Neptune Trojans

Dvořák, R.; Schwarz, Richard P.; Süli, Á.; Kotoulas, Thomas

doi:10.1111/j.1365-2966.2007.12480.x

Cited by 52 publications

(38 citation statements)

References 21 publications

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“…The stability of Neptune Trojans appears to be enhanced for high inclination values (Dvorak et al 2007), and also for low libration amplitudes. On the other hand, Plutinos seem to be essentially pushed out of their resonance by Pluto, in conformity with the results of Yu & Tremaine (1999) and .…”

Section: Discussionmentioning

confidence: 98%

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Neptune Trojans and Plutinos: colors, sizes, dynamics, and their possible collisions

Almeida

Peixinho

Correia

2009

A&A

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Neptune Trojans and Plutinos are two subpopulations of trans-Neptunian objects located in the 1:1 and the 3:2 mean motion resonances with Neptune, respectively, and therefore protected from close encounters with the planet. However, the orbits of these two kinds of objects may cross very often, allowing a higher collisional rate between them than with other kinds of trans-Neptunian objects, and a consequent size distribution modification of the two subpopulations. Observational colors and absolute magnitudes of Neptune Trojans and Plutinos show that i) there are no intrinsically bright (large) Plutinos at small inclinations; ii) there is an apparent excess of blue and intrinsically faint (small) Plutinos; and iii) Neptune Trojans possess the same blue colors as Plutinos within the same (estimated) size range do. For the present subpopulations we analyzed the most favorable conditions for close encounters/collisions and address any link there could be between those encounters and the sizes and/or colors of Plutinos and Neptune Trojans. We also performed a simultaneous numerical simulation of the outer Solar System over 1 Gyr for all these bodies in order to estimate their collisional rate. We conclude that orbital overlap between Neptune Trojans and Plutinos is favored for Plutinos with large libration amplitudes, high eccentricities, and small inclinations. Additionally, with the assumption that the collisions can be disruptive creating smaller objects not necessarily with similar colors, the present high concentration of small Plutinos with small inclinations can thus be a consequence of a collisional interaction with Neptune Trojans and such hypothesis should be further analyzed.

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Section: Discussionmentioning

confidence: 98%

“…According to Dvorak et al (2007) Trojans with low-inclined orbits are less stable. The stability area around L 4 and L 5 disappears after about 10 8 yr for small inclinations, while this stability zone is still present for about 10 9 yr for high inclinations.…”

Section: Stability Of the Neptune Trojansmentioning

confidence: 99%

Neptune Trojans and Plutinos: colors, sizes, dynamics, and their possible collisions

Almeida

Peixinho

Correia

2009

A&A

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“…Clearly, the CR3BP is an idealized case which is barely (if at all) realized in nature. Desired generalizations should include studies of the ER3BP (e.g., Pilat-Lohinger & Dvorak 2002;Szenkovits & Makó 2008) as well as of planets on inclined orbits (Dvorak et al 2007), noting that especially the former have important applications to real existing systems in consideration of the identified stellar and planetary orbital parameters (Eggenberger & Udry 2007).…”

Section: Resultsmentioning

confidence: 99%

The instability transition for the restricted 3-body problem

Eberle

Cuntz

2010

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Aims. We present a new method that allows identifying the onset of orbital instability, as well as quasi-periodicity and multiperiodicity, for planets in binary systems. This method is given for the special case of the circular restricted 3-body problem (CR3BP). Methods. Our method relies on an approach given by differential geometry that analyzes the curvature of the planetary orbit in the synodic coordinate system. The centerpiece of the method consists in inspecting the effective (instantaneous) eccentricity of the orbit based on the hodograph in rotated coordinates and in calculating the mean and median values of the eccentricity distribution. Results. Orbital stability and instability can be mapped by numerically inspecting the hodograph and/or the effective eccentricity of the orbit in the synodic coordinate system. The behavior of the system depends solely on the mass ratio μ of the binary components and the initial distance ratio ρ 0 of the planet relative to the stellar separation distance noting that the stellar components move on circular orbits. Our study indicates that orbital instability occurs when the median of the effective eccentricity distribution exceeds unity. This instability criterion can be compared to other criteria, including those based on Jacobi's integral and the zero-velocity contour of the planetary orbit. Conclusions. The method can be used during detailed numerical simulations and in contrast to other methods such as methods based on the Lyapunov exponent does not require a piece-wise secondary integration of the planetary orbit. Although the method has been deduced for the CR3BP, it is likely that it can be expanded to more general cases.

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“…Desired generalizations should include studies of the elliptical restricted 3-body problem (ER3BP) (e.g., Pilat-Lohinger & Dvorak 2002;Szenkovits & Makó 2008) as well as of planets on inclined orbits (Dvorak et al 2007), noting that especially the former have important applications to real existing systems in consideration of the identified stellar and planetary orbital parameters (Eggenberger & Udry 2010).…”

Section: Discussionmentioning

confidence: 99%

The instability transition for the restricted 3-body problem

Quarles

Eberle

Musielak

et al. 2011

A&A

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Aims. We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The criterion augments our earlier results given in the two previous papers of this series where stability criteria have been developed based on the Jacobi constant and the hodograph method.Methods. The centerpiece of our method is the concept of Lyapunov exponents, which are incorporated into the analysis of orbital stability by integrating the Jacobian of the CR3BP and orthogonalizing the tangent vectors via a well-established algorithm originally developed by Wolf et al. The criterion for orbital stability based on the Lyapunov exponents is independently verified by using power spectra. The obtained results are compared to results presented in the two previous papers of this series. Results. It is shown that the maximum Lyapunov exponent can be used as an indicator for chaotic behaviour of planetary orbits, which is consistent with previous applications of this method, particularly studies for the Solar System. The chaotic behaviour corresponds to either orbital stability or instability, and it depends solely on the mass ratio μ of the binary components and the initial distance ratio ρ 0 of the planet relative to the stellar separation distance. Detailed case studies are presented for μ = 0.3 and 0.5. The stability limits are characterized based on the value of the maximum Lyapunov exponent. However, chaos theory as well as the concept of Lyapunov time prevents us from predicting exactly when the planet is ejected. Our method is also able to indicate evidence of quasi-periodicity. Conclusions. For different mass ratios of the stellar components, we are able to characterize stability limits for the CR3BP based on the value of the maximum Lyapunov exponent. This theoretical result allows us to link the study of planetary orbital stability to chaos theory noting that there is a large array of literature on the properties and significance of Lyapunov exponents. Although our results are given for the special case of the CR3BP, we expect that it may be possible to augment the proposed Lyapunov exponent criterion to studies of planets in generalized stellar binary systems, which is strongly motivated by existing observational results as well as results expected from ongoing and future planet search missions.

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On the stability of the Neptune Trojans

Cited by 52 publications

References 21 publications

Neptune Trojans and Plutinos: colors, sizes, dynamics, and their possible collisions

Neptune Trojans and Plutinos: colors, sizes, dynamics, and their possible collisions

The instability transition for the restricted 3-body problem

The instability transition for the restricted 3-body problem

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