17 research outputs found
Resonant planetary dynamics: Periodic orbits and long-term stability
Many exo-solar systems discovered in the last decade consist of planets
orbiting in resonant configurations and consequently, their evolution should
show long-term stability. However, due to the mutual planetary interactions a
multi-planet system shows complicated dynamics with mostly chaotic
trajectories. We can determine possible stable configurations by computing
resonant periodic trajectories of the general planar three body problem, which
can be used for modeling a two-planet system. In this work, we review our model
for both the planar and the spatial case. We present families of symmetric
periodic trajectories in various resonances and study their linear horizontal
and vertical stability. We show that around stable periodic orbits there exist
regimes in phase space where regular evolution takes place. Unstable periodic
orbits are associated with the existence of chaos and planetary
destabilization.Comment: Proceedings of 10th HSTAM International Congress on Mechanics,
Chania, Crete, Greece, 25-27 May, 201
Multi-Planet Destabilisation and Escape in Post-Main Sequence Systems
Discoveries of exoplanets orbiting evolved stars motivate critical
examinations of the dynamics of -body systems with mass loss. Multi-planet
evolved systems are particularly complex because of the mutual interactions
between the planets. Here, we study the underlying dynamical mechanisms which
can incite planetary escape in two-planet post-main sequence systems. Stellar
mass loss alone is unlikely to be rapid and high enough to eject planets at
typically-observed separations. However, the combination of mass loss and
planet-planet interactions can prompt a shift from stable to chaotic regions of
phase space. Consequently, when mass loss ceases, the unstable configuration
may cause escape. By assuming a constant stellar mass loss rate, we utilize
maps of dynamical stability to illustrate the distribution of regular and
chaotic trajectories in phase space. We show that chaos can drive the planets
to undergo close encounters, leading to the ejection of one planet. Stellar
mass loss can trigger the transition of a planetary system from a stable to
chaotic configuration, subsequently causing escape. We find that mass loss
non-adiabatically affects planet-planet interaction for the most massive
progenitor stars which avoid the supernova stage. For these cases, we present
specific examples of planetary escape.Comment: Accepted for publication in MNRAS (2013
The 1:1 resonance in Extrasolar Systems: Migration from planetary to satellite orbits
We present families of symmetric and asymmetric periodic orbits at the 1/1
resonance, for a planetary system consisting of a star and two small bodies, in
comparison to the star, moving in the same plane under their mutual
gravitational attraction. The stable 1/1 resonant periodic orbits belong to a
family which has a planetary branch, with the two planets moving in nearly
Keplerian orbits with non zero eccentricities and a satellite branch, where the
gravitational interaction between the two planets dominates the attraction from
the star and the two planets form a close binary which revolves around the
star. The stability regions around periodic orbits along the family are
studied. Next, we study the dynamical evolution in time of a planetary system
with two planets which is initially trapped in a stable 1/1 resonant periodic
motion, when a drag force is included in the system. We prove that if we start
with a 1/1 resonant planetary system with large eccentricities, the system
migrates, due to the drag force, {\it along the family of periodic orbits} and
is finally trapped in a satellite orbit. This, in principle, provides a
mechanism for the generation of a satellite system: we start with a planetary
system and the final stage is a system where the two small bodies form a close
binary whose center of mass revolves around the star.Comment: to appear in Cel.Mech.Dyn.Ast
On the dynamics of Extrasolar Planetary Systems under dissipation. Migration of planets
We study the dynamics of planetary systems with two planets moving in the
same plane, when frictional forces act on the two planets, in addition to the
gravitational forces. The model of the general three-body problem is used.
Different laws of friction are considered. The topology of the phase space is
essential in understanding the evolution of the system. The topology is
determined by the families of stable and unstable periodic orbits, both
symmetric and non symmetric. It is along the stable families, or close to them,
that the planets migrate when dissipative forces act. At the critical points
where the stability along the family changes, there is a bifurcation of a new
family of stable periodic orbits and the migration process changes route and
follows the new stable family up to large eccentricities or to a chaotic
region. We consider both resonant and non resonant planetary systems. The 2/1,
3/1 and 3/2 resonances are studied. The migration to larger or smaller
eccentricities depends on the particular law of friction. Also, in some cases
the semimajor axes increase and in other cases they are stabilized. For
particular laws of friction and for special values of the parameters of the
frictional forces, it is possible to have partially stationary solutions, where
the eccentricities and the semimajor axes are fixed.Comment: Accepted in Celestial Mechanics and Dynamical Astronom