Three-body orbital stability criteria for circular retrograde orbits

Donnison, J. R.; Mikulskis, D. F.

doi:10.1093/mnras/266.1.25

Cited by 23 publications

(13 citation statements)

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“…The disk is significantly thicker than observed. stability was also found in hierarchical triple systems (Donnison & Mikulskis 1994).…”

Section: Retrograde Runsmentioning

confidence: 73%

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Dynamics of the young multiple system GG Tauri

Beust¹,

Dutrey

2006

A&A

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The quadruple young system GG Tauri is an example of a multiple T Tauri system. Its consists of two binaries, the brighter one (GG Tau A) being surrounded by a ring-shape circumbinary disk. In a recent paper, we performed a dynamical study of circumbinary and showed that there is an apparent discrepancy between the orbital fit of GG Tau A and the observed inner edge of the disk. In this paper, we now investigate the dynamics of the whole quadruple system together with the disk. We show that it is possible to design an orbital configuration between the two binaries in such a way that the outer profile of the circumbinary ring may be explained by tidal interaction with repeated periastron passages of the outer binary GG Tau B. We show that the observed characteristics of the disk are not compatible with some orbital configurations, such as those giving rise to the Kozai resonance. Surprisingly, the outer binary GG Tau B appears only marginally stable against tidal disruption by GG Tau A. GG Tau B appears stable only if its internal orbit is retrograde with respect to the motion of its center of mass around GG Tau A. We also find that the CB disk should be almost coplanar with the inner binary.

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“…The disk is significantly thicker than observed. stability was also found in hierarchical triple systems (Donnison & Mikulskis 1994).…”

Section: Retrograde Runsmentioning

confidence: 73%

“…He gave an empirical analytical stability criterion, q out /a in required to be above a critical value to ensure stability. This question was reinvestigated by Donnison & Mikulskis (1994, 1995, and more recently by Fig. 19.…”

Section: Stability Analysismentioning

confidence: 99%

Dynamics of the young multiple system GG Tauri

Beust¹,

Dutrey

2006

A&A

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“…Donnison and Mikulskis (1992) found numerically that for prograde three body systems moving on circular orbits that there was a good correspondence between the results obtained for the critical orbital or Lagrange stability and the full three-body Hill stability method employed here (see also Donnison and Mikulskis 1995 for eccentric orbits). Donnison and Mikulskis (1994) and Eggleton and Kiseleva (1995) have also shown numerically that retrograde circular orbits tend to be more stable than their prograde counterparts. Domingos et al (2006), using numerical simulations of the orbits using the restricted elliptic three-body problem, with the moon assumed to be massless examined the boundary of the stable regions for a fixed planet/star mass ratio of 10 À3 .…”

Section: Stability Limitsmentioning

confidence: 90%

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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“…Recently in an article by [50], the authors investigated the stability of retrograde orbits in extrasolar planetary systems with multiple planets and showed that in systems were prograde orbits are unstable (e.g., HD 73256), retrograde orbits may survive for long times. The stability of retrograde orbits in planetary systems has been known for many years [60,61,62,27]. Such long-term stable orbits have also been observed among Jupiter's retrograde irregular satellites [71].…”

Section: Stability Of Tp-i and Tp-o Orbitsmentioning

confidence: 99%