On the Validity of the “Hill Radius Criterion” for the Ejection of Planets From Stellar Habitable Zones

Cuntz, M.; Yeager, Katherine E.

doi:10.1088/0004-637x/697/2/l86

Cited by 35 publications

(14 citation statements)

References 28 publications

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“…The border between the regular and chaotic regions is at the place where the apocentre of the test particle is one and a half Hill's radius from the orbit of the second primary. In a recent paper Cuntz and Yeager (2009) investigated the role of the Hill's radius criterion in stability investigations of planetary systems and concluded that it is invalid for the prediction of ejection. Our results, however, show that approaching or entering the sphere of influence of the perturbing body, described by the Hill's radius, results in changing regular behaviour into chaotic.…”

Section: Discussionmentioning

confidence: 99%

Stability of higher order resonances in the restricted three-body problem

Érdi

Rajnai

Sándor

et al. 2012

Celest Mech Dyn Astr

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Third and fourth order mean motion resonances are studied in the model of the restricted three-body problem by numerical methods for mass parameters corresponding approximately to the Sun-Jupiter and Sun-Neptune systems. In the case of inner resonances, it is shown that there are two regions of libration in the 8:5 and 7:4 resonances, one at low, the other at high eccentricities. In the 9:5 and 7:3 resonances libration can exist only in one region at high eccentricities. The 5:2 and 4:1 resonances are very regular, with one librational zone existing for all eccentricities. There is no visible region of libration at any eccentricities in the 5:1 resonance, the transition between the regions of direct and retrograde circulation is very sharp. In the case of outer resonances, the 8:5 and 7:4 resonances have also two regions of libration, but the 9:5 resonance has three, the 7:3 resonance two librational zones. The 5:2 resonance is again very regular, but it is parted for two regions of libration at high eccentricities. Libration is possible in the 4:1 resonance only at high eccentricities. The 5:1 resonance is very symmetric. In the case of outer resonances, a comparison is made with trans-Neptunian objects (TNO) in higher order mean motion resonances. Several new librating TNOs are identified.

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Section: Discussionmentioning

confidence: 99%

Stability of higher order resonances in the restricted three-body problem

Érdi

Rajnai

Sándor

et al. 2012

Celest Mech Dyn Astr

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“…A recent study byCuntz & Yeager (2009) notes that the Hill-radius criterion for ejection of a Earth mass planet around a giant planet may not be valid. Our stability maps shown here are, therefore, accurate to within the constraint highlighted by that study.…”

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confidence: 99%

Stability Analysis of Single-Planet Systems and Their Habitable Zones

Kopparapu

Barnes

2010

ApJ

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We study the dynamical stability of planetary systems consisting of one hypothetical terrestrial mass planet (1 or 10 M ⊕ ) and one massive planet (10 M ⊕ − 10 M jup ). We consider masses and orbits that cover the range of observed planetary system architectures (including non-zero initial eccentricities), determine the stability limit through N-body simulations, and compare it to the analytic Hill stability boundary. We show that for given masses and orbits of a two planet system, a single parameter, which can be calculated analytically, describes the Lagrange stability boundary (no ejections or exchanges) but which diverges significantly from the Hill stability boundary. However, we do find that the actual boundary is fractal, and therefore we also identify a second parameter which demarcates the transition from stable to unstable evolution. We show the portions of the habitable zones of ρ CrB, HD 164922, GJ 674, and HD 7924 which can support a terrestrial planet. These analyses clarify the stability boundaries in exoplanetary systems and demonstrate that, for most exoplanetary systems, numerical simulations of the stability of potentially habitable planets are only necessary over a narrow region of parameter space. Finally we also identify and provide a catalog of known systems which can host terrestrial planets in their habitable zones.

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“…This criterion has been refined statistically through numerical simulation with estimates indicating a limit of ∼ 3.2R H , where R H denotes the Hill Radius given by Gladman, 1993]. Limitations of this criterion in applications two extrasolar planetary systems were pointed out by Cuntz and Yeager [2009]. Recently, Satyal et al [2013] used a method proposed by Szenkovits and Makó [2008] that utilizes the Hill stability criterion; we discuss this approach in Section 8.6.…”

Section: The Sun-earth-moon Systemmentioning

confidence: 99%

The three-body problem

Musielak

Quarles

2014

Rep. Prog. Phys.

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Abstract. The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more than 300 years. In this paper, we present a review of the three-body problem in the context of both historical and modern developments. We describe the general and restricted (circular and elliptic) three-body problems, different analytical and numerical methods of finding solutions, methods for performing stability analysis, search for periodic orbits and resonances, and application of the results to some interesting astronomical and space dynamical settings. We also provide a brief presentation of the general and restricted relativistic three-body problems, and discuss their astronomical applications.

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On the Validity of the “Hill Radius Criterion” for the Ejection of Planets From Stellar Habitable Zones

Cited by 35 publications

References 28 publications

Stability of higher order resonances in the restricted three-body problem

Stability of higher order resonances in the restricted three-body problem

Stability Analysis of Single-Planet Systems and Their Habitable Zones

The three-body problem

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