176 research outputs found
Resonant capture of multiple planet systems under dissipation and stable orbital configurations
Migration of planetary systems caused by the action of dissipative forces may
lead the planets to be trapped in a resonance. In this work we study the
conditions and the dynamics of such resonant trapping. Particularly, we are
interested in finding out whether resonant capture ends up in a long-term
stable planetary configuration. For two planet systems we associate the
evolution of migration with the existence of families of periodic orbits in the
phase space of the three-body problem. The family of circular periodic orbits
exhibits a gap at the 2:1 resonance and an instability and bifurcation at the
3:1 resonance. These properties explain the high probability of 2:1 and 3:1
resonant capture at low eccentricities. Furthermore, we study the resonant
capture of three-planet systems. We show that such a resonant capture is
possible and can occur under particular conditions. Then, from the migration
path of the system, stable three-planet configurations, either symmetric or
asymmetric, can be determined.Comment: 10 ages, 13 figures, 5th Ph.D. School on Mathematical Modeling for
Complex System
Resonant periodic orbits in the exoplanetary systems
The planetary dynamics of , , , and mean motion
resonances is studied by using the model of the general three body problem in a
rotating frame and by determining families of periodic orbits for each
resonance. Both planar and spatial cases are examined. In the spatial problem,
families of periodic orbits are obtained after analytical continuation of
vertical critical orbits. The linear stability of orbits is also examined.
Concerning initial conditions nearby stable periodic orbits, we obtain
long-term planetary stability, while unstable orbits are associated with
chaotic evolution that destabilizes the planetary system. Stable periodic
orbits are of particular importance in planetary dynamics, since they can host
real planetary systems. We found stable orbits up to of mutual
planetary inclination, but in most families, the stability does not exceed
-, depending on the planetary mass ratio. Most of these
orbits are very eccentric. Stable inclined circular orbits or orbits of low
eccentricity were found in the and resonance, respectively.Comment: Accepted for publication in Astrophysics and Space Science. Link to
the published article on Springer's website was inserte
Inclined asymmetric librations in exterior resonances
Librational motion in celestial mechanics is generally associated with the
existence of stable resonant configurations and signified by the existence of
stable periodic solutions and oscillation of critical (resonant) angles. When
such an oscillation takes place around a value different than 0 or , the
libration is called asymmetric. In the context of the planar circular
restricted three-body problem (CRTBP), asymmetric librations have been
identified for the exterior mean-motion resonances (MMRs) 1:2, 1:3 etc. as well
as for co-orbital motion (1:1). In exterior MMRs the massless body is the outer
one. In this paper, we study asymmetric librations in the 3-dimensional space.
We employ the computational approach of Markellos (1978) and compute families
of asymmetric periodic orbits and their stability. Stable, asymmetric periodic
orbits are surrounded in phase space by domains of initial conditions which
correspond to stable evolution and librating resonant angles. Our computations
were focused on the spatial circular restricted three-body model of the
Sun-Neptune-TNO system (TNO= trans-Neptunian object). We compare our results
with numerical integrations of observed TNOs, which reveal that some of them
perform 1:2-resonant, inclined asymmetric librations. For the stable 1:2 TNOs
librators, we find that their libration seems to be related with the vertically
stable planar asymmetric orbits of our model, rather than the 3-dimensional
ones found in the present study.Comment: Accepted for publication in CeMD
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