The Hill stability of inclined bound triple star and planetary systems

Donnison, J. R.

doi:10.1016/j.pss.2009.01.014

Cited by 40 publications

(29 citation statements)

References 28 publications

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“…This theory was originally applied only to coplanar systems where all three bodies moved on bound orbits (Szebehely and Zare 1977;Walker et al 1980;Walker and Roy 1981;Marchal and Bozis 1982;Donnison and Williams 1983).The theory was extended to unbound coplanar orbits by Donnison (1984a, b) and to inclined unbound orbits by Donnison (2006Donnison ( , 2008 and to bound inclined orbits by Veras and Armitage (2004) and Donnison (2009). The basic theory was applied to extrasolar planetary systems.…”

Section: Full Three Body Hill Stabilitymentioning

confidence: 99%

“…0 in order for the system not to be disrupted or any exchange of components to occur. To solve this condition generally for the critical value of ða 2 =a 1 Þ in terms of the orbital elements e 1 ; e 2 and i, Donnison (2009) showed that the critical condition can be solved numerically as a fourth order algebraic equation of the form…”

Section: Full Three Body Hill Stabilitymentioning

confidence: 99%

“…It should be noted that in Donnison (2009Donnison ( , 2010a this equation had a typographical error in the sign of A, which should be defined as positive. Equations (11) and (12) use the same basic parameters as Szebehely and Zare (1977) did for a completely bound coplanar three body system but now with the inclusion of the inclination.…”

Section: Full Three Body Hill Stabilitymentioning

confidence: 99%

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Limits on the Orbits of Possible Eccentric and Inclined Moons of Extrasolar Planets Orbiting Single Stars

Donnison

2014

Earth Moon Planets

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Limits are placed on the range of orbits and masses of possible moons orbiting extrasolar planets which orbit single central stars. The Roche limiting radius determines how close the moon can approach the planet before tidal disruption occurs; while the Hill stability of the star-planet-moon system determines stable orbits of the moon around the planet. Here the full three-body Hill stability is derived for a system with the binary composed of the planet and moon moving on an inclined, elliptical orbit relative the central star. The approximation derived here in Eq. (17) assumes the binary mass is very small compared with the mass of the star and has not previously been applied to this problem and gives the criterion against disruption and component exchange in a closed form. This criterion was applied to transiting extrasolar planetary systems discovered since the last estimation of the critical separations (Donnison in Mon Not R Astron Soc 406:1918, 2010a) for a variety of planet/ moon ratios including binary planets, with the moon moving on a circular orbit. The effects of eccentricity and inclination of the binary on the stability of the orbit of a moon is discussed and applied to the transiting extrasolar planets, assuming the same planet/moon ratios but with the moon moving with a variety of eccentricities and inclinations. For the non-zero values of the eccentricity of the moon, the critical separation distance decreased as the eccentricity increased in value. Similarly the critical separation decreased as the inclination increased. In both cases the changes though very small were significant.

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Section: Full Three Body Hill Stabilitymentioning

confidence: 99%

Section: Full Three Body Hill Stabilitymentioning

confidence: 99%

Section: Full Three Body Hill Stabilitymentioning

confidence: 99%

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Limits on the Orbits of Possible Eccentric and Inclined Moons of Extrasolar Planets Orbiting Single Stars

Donnison

2014

Earth Moon Planets

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“…Many researchers discussed the analytical criteria for different systems based on different assumption on the systems Williams 1983, 1985;Donnison 1984Donnison , 1988Donnison , 2010Donnison , 2011Walker et al 1980Walker et al , 1981Walker 1983;Walker and Roy 1983;Valsecchi et al 1984;Georgakarakos 2008;Li et al 2010;Liu et al 2012). The dependence of the stability on the orbital inclination in the spatial three body system was also studied widely Khodykin et al 2004;Donnison 2006Donnison , 2009Donnison , 2014Georgakarakos 2013). The analytic criteria give only sufficient conditions for dynamical stability.…”

Section: Introductionmentioning

confidence: 99%

Analytical criteria of Hill stability in the elliptic restricted three body problem

Gong

2015

Astrophys Space Sci

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Due to the time-dependent Jacobi integral in the elliptic restricted three body problem, it is difficult to develop analytical criteria of Hill stability. In this paper, the Hill stability of the orbit around the one primary is concerned. Several analytical criteria are established based on the bifurcation of the extremum of the Jacobi integral. One criterion is used to judge the Hill stability of the orbit with orbit size known. One criterion is used to judge the Hill stability of the orbit with orbital element completely known. These criteria are applied to the judge the Hill stability of Jupiter's moons and planets in three stellar binaries.

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“…However, he did not give any quantitive description of this perspective. More recently, Donnison (2006Donnison ( , 2008 applied the c 2 H criterion to a binary during its encounter with a third body moving on an inclined parabolic/hyperbolic orbit, and there followed a consideration of inclined bound triple star and planetary systems (Donnison 2009). The c 2 H criterion involves a high order algebraic equation, which does not in general have closed-form solutions.…”

Section: Introductionmentioning

confidence: 99%

The Hill stability of low mass binaries in hierarchical triple systems

Sun

2010

Celest Mech Dyn Astr

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The Hill stability of the low mass binary system in the presence of a massive third body moving on a wider inclined orbit is investigated analytically. It is found that, in the case of the third body being on a nearly circular orbit, the region of Hill stability expands as the binary/third body mass ratio increases and the inclination (i) decreases. This i-dependence decreases very quickly with increasing eccentricity (e 2 ) of the third body relative to the binary barycentre. In fact, if e 2 is not extremely small, the Hill stable region can be approximately expressed in a closed form by setting i = 90 • , and it contracts with increasing e 2 as e 2 2 for sufficiently low mass binary. Our analytic results are then applied to the observed triple star systems and the Kuiper belt binaries.

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The Hill stability of inclined bound triple star and planetary systems

Cited by 40 publications

References 28 publications

Limits on the Orbits of Possible Eccentric and Inclined Moons of Extrasolar Planets Orbiting Single Stars

Limits on the Orbits of Possible Eccentric and Inclined Moons of Extrasolar Planets Orbiting Single Stars

Analytical criteria of Hill stability in the elliptic restricted three body problem

The Hill stability of low mass binaries in hierarchical triple systems

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