Motion of dust in mean motion resonances with planets

Pástor, P.; Klačka, J.; Kómar, Ladislav

doi:10.1007/s10569-009-9202-9

Cited by 14 publications

(9 citation statements)

References 20 publications

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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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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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“…Among all papers on the subject, let us quote the following results. InPástor et al (2009a) the authors investigate the eccentricity evolution of particles under the effect of non-radial wind, while the interplay with MMRs has been treated inPástor et al (2009b).…”

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confidence: 99%

The effect of Poynting–Robertson drag on the triangular Lagrangian points

Lhotka

Celletti

2015

Icarus

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We investigate the stability of motion close to the Lagrangian equilibrium points L 4 and L 5 in the framework of the spatial, elliptic, restricted threebody problem, subject to the radial component of Poynting-Robertson drag.For this reason we develop a simplified resonant model, that is based on averaging theory, i.e. averaged over the mean anomaly of the perturbing planet. We find temporary stability of particles displaying a tadpole motion in the 1:1 resonance. From the linear stability study of the averaged simplified resonant model, we find that the time of temporary stability is proportional to β a 1 n 1 , where β is the ratio of the solar radiation over the gravitational force, and a 1 , n 1 are the semi-major axis and the mean motion of the perturbing planet, respectively. We extend previous results (Murray (1994)) on the asymmetry of the stability indices of L 4 and L 5 to a more realistic force model.Our analytical results are supported by means of numerical simulations. We implement our study to Jupiter-like perturbing planets, that are also found in extra-solar planetary systems.

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“…The Poynting-Robertson force (see also Pástor et al 2009) is a non gravitational effect acting on a particle moving around the Sun and it is due to the solar radiation incident on the particle. In the synodic frame it takes the following form (Murray and Dermott 1999):…”

Section: Equations Of Motion In the Dissipative Casementioning

confidence: 99%

Some results on the global dynamics of the regularized restricted three-body problem with dissipation

Celletti

Stefanelli

Lega

et al. 2011

Celest Mech Dyn Astr

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International audienceWe perform an analysis of the dynamics of the circular, restricted, planar three-body problem under the effect of different kinds of dissipation (linear, Stokes and Poynting-Robertson drags). Since the problem is singular, we implement a regularization technique in the style of Levi-Civita. The effect of the dissipation is often to decrease the semi-major axis; as a consequence the minor body collides with one of the primaries. In general, it is quite difficult to find non-collision orbits using random initial conditions. However, by means of the computation of the Fast Lyapunov Indicators (FLI), we obtain a global view of the dynamics. Precisely, we detect the regions of the phase space potentially belonging to basins of attraction. This investigation provides information on the different regions of the phase space, showing both collision and non-collision trajectories. Moreover, we find periodic orbit attractors for the case of linear and Stokes drags, while in the case of the Poynting-Robertson effect no other attractors are found beside the primaries, unless a fourth body is added to counterbalance the dissipative effect

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Motion of dust in mean motion resonances with planets

Cited by 14 publications

References 20 publications

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

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

The effect of Poynting–Robertson drag on the triangular Lagrangian points

Some results on the global dynamics of the regularized restricted three-body problem with dissipation

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