Detailed survey of the phase space around Nix and Hydra

Süli, Á.; Zsigmond, Zsuzsa

doi:10.1111/j.1365-2966.2009.15274.x

Cited by 13 publications

(11 citation statements)

References 22 publications

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“…For this quite low eccentric regime, earlier studies have already shown that a good agreement can generally be found with the results of chaos indicators (e.g. Dvorak et al 2003; Süli, Dvorak & Freistetter 2005; Nagy, Süli & Érdi 2006; Süli & Zsigmond 2008).…”

Section: Dynamical Model and Methodssupporting

confidence: 78%

On the stability of possible Trojan planets in the habitable zone: an application to the systems HD 147513 and HD 210277

Funk

Schwarz

Süli

et al. 2012

Monthly Notices of the Royal Astronomical Society

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In this paper, we study the dynamical stability of fictitious terrestrial planets in the 1:1 mean‐motion resonance with a gas giant moving in the habitable zone (HZ). We investigate the stability of Trojan planets both in a general study and for two specific known extrasolar planetary systems (HD 147513 and HD 210277). In the general study, we determine the stability of the Lagrangian point L4. The numerical simulations have been carried out using the spatial elliptic‐restricted three‐body problem, where we placed the test particles (TPs) exactly at L4, which is located 60° ahead of the gas giant at the same distance to the star. In the stability study, we have concentrated on the dependences between the eccentricity and the inclination of the Trojan planet. Going a step further, we have investigated two specific systems where the known gas giant moves in the HZ. The two specific extrasolar systems are investigated by using the general study to define the region in eccentricity and inclination where, in principle, stable motion is possible. To find out whether the existence of a Trojan planet is possible, in addition we have calculated the stable area in the semimajor axis (aTP) and the argument of perihelion (ωTP) for an actual planetary mass (2 M⊕). Thus, we can conclude that the region around the Lagrangian points L4 and L5 allows stable motion in the system HD 147513, because the gas giant of this system has an eccentricity of 0.26, which lies well within the stable region. The known planet in the system HD 210277 has a much higher eccentricity and thus it cannot harbour any terrestrial planets in the Lagrangian points.

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Section: Dynamical Model and Methodssupporting

confidence: 78%

On the stability of possible Trojan planets in the habitable zone: an application to the systems HD 147513 and HD 210277

Funk

Schwarz

Süli

et al. 2012

Monthly Notices of the Royal Astronomical Society

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“…For very low values (e < 0.2) and very high values (e > 0.8) of ME, a good agreement can generally be found with the results of chaos indicators (see e.g. Dvorak et al 2003;Süli et al 2005;Nagy et al 2006;Süli et al 2008). For intermediate values of ME a confident distinction between stable and unstable motion is not possible, since high eccentric orbits (0.2 < e < 0.8) can be stable in the long-term.…”

Section: The Dynamical Model and The Methodssupporting

confidence: 64%

On the influence of the Kozai mechanism in habitable zones of extrasolar planetary systems

Funk

Libert

Süli

et al. 2011

A&A

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Aims. We investigate the long-term evolution of inclined test particles representing a small Earth-like body with negligible gravitational effects (hereafter called massless test-planets) in the restricted three-body problem, and consisting of a star, a gas giant, and a massless test-planet. The test-planet is initially on a circular orbit and moves around the star at distances closer than the gas giant. The aim is to show the influences of the eccentricity and the mass of the gas giant on the dynamics, for various inclinations of the test-planet, and to investigate in more detail the Kozai mechanism in the elliptic problem. Methods. We performed a parametric study, integrating the orbital evolution of test particles whose initial conditions were distributed on the semi-major axis -inclination plane. The gas giant's initial eccentricity was varied. For the calculations, we used the Lie integration method and in some cases the Bulirsch-Stoer algorithm. To analyze the results, the maximum eccentricity and the Lyapunov characteristic indicator were used. All integrations were performed for 10 5 periods of the gas giant. Results. Our calculations show that inclined massless test-planets can be in stable configurations with gas giants on either circular or elliptic orbits. The higher the eccentricity of the gas giant, the smaller the possible range in semi-major axis for the test-planet. For gas giants on circular orbits, our results illustrate the well-known results associated with the Kozai mechanism, which do not allow stable orbits above a critical inclination of approximately 40 • . For gas giants on eccentric orbits, the dynamics is quite similar, and the massless companion exhibits limited variations in eccentricity. In addition, we identify a region around 35 • consisting of longtime stable, low eccentric orbits. We show that these results are also valid for Earth-mass companions, therefore they can be applied to extrasolar systems: for instance, the extrasolar planetary system HD 154345 can possess a 35 • degree inclined, nearly circular, Earth-mass companion in the habitable zone.

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“…Two bodies are in mean motion resonance when n / n ′= p /( p + q ), where n and n ′ are their mean motions, p and q are small integers and q is of the order of the resonance. The mean motions are measured in the sidereal system (Sülli & Zsigmond 2009).…”

Section: Diagrams (A‐e)mentioning

confidence: 99%

“…An extension of this work has been presented by Sülli & Zsigmond (2009) through an analysis of the spatial elliptic restricted three‐body problem for a time‐span of 10 4 orbital periods of the binary. They generated stability maps for the ( a − e ) and ( a − I ) orbital element spaces near the satellites Nix and Hydra (taken as massless bodies) using three different complementary methods.…”

Section: Introductionmentioning

confidence: 99%

Gravitational effects of Nix and Hydra in the external region of the Pluto-Charon system

Santos¹,

Winter²,

Sfair³

2010

Monthly Notices of the Royal Astronomical Society

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Two new companions to the Pluto–Charon binary system have been detected in 2005 by Weaver et al. These small satellites, named Nix and Hydra, are located beyond Charon's orbit. Although they are small when compared to Charon, their gravitational perturbations can decrease the stability of the external region (beyond Charon's orbit). The dynamical structure of this external region is analysed by numerically simulating a sample of particles under the gravitational effects of Pluto, Charon, Nix and Hydra. As expected the effects of Nix and Hydra decrease the external stable region. Agglomerates of particles can survive even after 105 orbital periods of the binary in some regions, such as coorbital to Nix and Hydra and between their orbits. We also analysed the effects of hypothetical satellites on the orbital evolution of Nix and Hydra in order to constrain an upper limit size. Some hypothetical satellites can be coorbital to Nix or Hydra without provoking any significant gravitational effects on them.

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Detailed survey of the phase space around Nix and Hydra

Cited by 13 publications

References 22 publications

On the stability of possible Trojan planets in the habitable zone: an application to the systems HD 147513 and HD 210277

On the stability of possible Trojan planets in the habitable zone: an application to the systems HD 147513 and HD 210277

On the influence of the Kozai mechanism in habitable zones of extrasolar planetary systems

Gravitational effects of Nix and Hydra in the external region of the Pluto-Charon system

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