Where are the Uranus Trojans?

Dvořák, R.; Bazsó, Ákos; Zhou, Li-Yong

doi:10.1007/s10569-010-9261-y

Cited by 50 publications

(38 citation statements)

References 33 publications

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“…For Uranus a similar study by Dvorak, Bazsó & Zhou (2010) concluded that Trojans on low inclination orbits could survive over timescales of 10 9 ⋆ Corresponding author: e-mail: akos.bazso@univie.ac.at years. Both studies used as dynamical model the outer Solar system including all four gas planets, thus accounting for mutual perturbations of the planets; but a more complex model can also obscure the fundamental features of Trojan motion.…”

Section: Solar Systemmentioning

confidence: 97%

Stability of librational motion in the spatial circular restricted three‐body problem for high inclinations and mass ratios

et al. 2013

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In the spatial circular restricted three-body problem librational motion around the Lagrangian points L4 and L5 exists up to high inclinations of the massless object. We report the results of numerical investigations on the stability of this librational motion for systematic variations in the inclination of the Trojan and the mass-ratio µ of the two massive bodies. We show that stable motion prevails for inclinations below 60 degrees and mass-ratios µ < 0.04 for typical integration times up to 10 6 revolution periods. At even higher mass-ratios -beyond the critical mass-ratio for the planar case -stable orbits were found to exist for up to 10 7 periods at moderate inclinations. We extracted the librational frequencies on a grid in the parameter space from the Fourier spectra and traced their variation. Several resonances between the short and long period librational frequency as well as the vertical frequency lie inside the investigated region. The application of the Lyapunov characteristic indicator and spectral number methods also reveals the chaotic regions. This simple model is equally applicable in the Solar system for low mass ratios for Trojans of the planets, as well as to Trojan-type exoplanets in binary star systems at high mass-ratios.

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Section: Solar Systemmentioning

confidence: 97%

Stability of librational motion in the spatial circular restricted three‐body problem for high inclinations and mass ratios

et al. 2013

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“…The most important are the low order resonances. Recent studies indicate the ever increasing interest in resonances in the Solar System (Pástor et al 2009;Cachucho et al 2010;Dvorak et al 2010) and in exoplanetary systems (Gayon et al 2009;Schwarz et al 2009;Hadjidemetriou et al 2009;Voyatzis 2010, 2011;Libert and Tsiganis 2011). However, higher order resonances can also become important, especially at high eccentricities.…”

Section: Introductionmentioning

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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“…Our results suggest that, contrary to this view and in spite of the destabilizing role of Saturn, Uranus still can actively capture temporary co-orbitals. Regarding the question of stability, (83982) Crantor's orbital inclination is close to the edge of one of the stability islands in i identified by Dvorak et al (2010), but 2010 EU 65 moves outside the stability islands proposed in that study, yet it seems to be more stable than (83982) Crantor. This comparatively better stability strongly suggests that not only inclination but also eccentricity play an important role in the longterm dynamics of these objects.…”

Section: Discussionmentioning

confidence: 56%

“…However, Uranus appears not to be able to efficiently capture objects into the 1:1 commensurability today even for short periods of time (Horner & Evans 2006). The stability of hypothetical Uranus co-orbitals, specifically those moving in tadpole orbits, has been studied by Dvorak et al (2010), who have found that the orbital A&A 551, A114 (2013) inclination is the key parameter regarding stability, only the inclination intervals (0, 7) • , (9, 13) • , (31, 36) • and (38, 50) • appear to be stable. This scarcity of Uranus co-orbitals seems to be confirmed by current observational results.…”

Section: Introductionmentioning

confidence: 99%

Crantor, a short-lived horseshoe companion to Uranus

Marcos

2013

A&A

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Context. Stable co-orbital motion with Uranus is vulnerable to planetary migration, but temporary co-orbitals may exist today. So far, only two candidates have been suggested, both moving on horseshoe orbits: 83982 Crantor (2002 GO 9 ) and 2000 SN 331 . Aims. (83982) Crantor is currently classified in the group of the Centaurs by the MPC although the value of its orbital period is close to that of Uranus. Here we revisit the topic of the possible 1:1 commensurability of (83982) Crantor with Uranus, explore its dynamical past, and look into its medium-term stability and future orbital evolution. Methods. Our analysis is based on the results of N-body calculations that use the most updated ephemerides and include perturbations by the eight major planets, the Moon, the barycenter of the Pluto-Charon system, and the three largest asteroids. Results. (83982) Crantor currently moves inside Uranus' co-orbital region on a complex horseshoe orbit. The motion of this object is primarily driven by the influence of the Sun and Uranus, although Saturn plays a significant role in destabilizing its orbit. The precession of the nodes of (83982) Crantor, which is accelerated by Saturn, controls its evolution and short-term stability. Although this object follows a temporary horseshoe orbit, more stable trajectories are possible and we present 2010 EU 65 as a long-term horseshoe librator candidate in urgent need of follow-up observations. Available data indicate that the candidate 2000 SN 331 is not a Uranus' co-orbital. Conclusions. Our calculations confirm that (83982) Crantor is currently trapped in the 1:1 commensurability with Uranus but it is unlikely to be a primordial 1:1 librator. Although this object follows a chaotic, short-lived horseshoe orbit, longer term horseshoe stability appears to be possible. We also confirm that high-order resonances with Saturn play a major role in destabilizing the orbits of Uranus co-orbitals.

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Where are the Uranus Trojans?

Cited by 50 publications

References 33 publications

Stability of librational motion in the spatial circular restricted three‐body problem for high inclinations and mass ratios

Stability of librational motion in the spatial circular restricted three‐body problem for high inclinations and mass ratios

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

Crantor, a short-lived horseshoe companion to Uranus

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