Related papers: Stability Limits in Extra-solar Planetary Systems
Approximately 60 percent of all stars in the solar neighbourhood (up to 80 percent in our Milky Way) are members of binary or multiple star systems. This fact led to the speculations that many more planets may exist in binary systems than…
The minimum orbital separation of planets in long-stable planetary systems is often modeled as a step function, parameterized with a single value $\Delta_{min}$ (measured in mutual Hill radius of the two neighboring planets). Systems with…
With the help of the Laplace-Lagrange solution of the secular perturbation theory in a double-planet system, we study the occurrence and the stability of apsidal secular resonance between the two planets. The explicit criteria to predict…
Star-planet interactions play, among other things, a crucial role in planetary orbital configurations by circularizing orbits, aligning the star and planet spin and synchronizing stellar rotation with orbital motions. This is especially…
The stability of a system of $N$ equal sized mutually gravitating spheres resting on each other in a straight line and rotating in inertial space is considered. This is a generalization of the "Euler Resting" configurations previously…
The long-term evolution of astrophysical systems is driven by a Hamiltonian that is independent of the fast angle. As this Hamiltonian may contain explicitly time-dependent parameters, the conservation of mechanical energy is not guaranteed…
The possible observations of Trojan-like extrasolar planets stimulate the deeper understanding of the stability behaviour of the co-orbital resonant motion. By using Hill's equations and the energy-rate method an analysis of the stability…
Simple ``solar systems'' are generated with planetary orbital radii r distributed uniformly random in log(r) between 0.2 and 50 AU. A conservative stability criterion is imposed by requiring that adjacent planets are separated by a minimum…
The stability of planets in the alpha-Centauri AB stellar system has been studied extensively. However, most studies either focus on the orbital plane of the binary or consider inclined circular orbits. Here, we numerically investigate the…
We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional…
We consider the planar Hill's lunar problem with a homogeneous gravitational potential. The investigation of the system is twofold. First, the starting conditions of the trajectories are classified into three classes, that is bounded,…
Some tests of gravity theories - periastron shift, geodetic precession, change in mean motion and gravitational redshift - are applied in solar and stellar systems to constrain the cosmological constant. We thus consider a length scale…
A longstanding belief has been that the semimajor axes, in the Newtonian planetary problem, are stable. In the course of the XIX century, Laplace, Lagrange and others gave stronger and stronger arguments in this direction, thus culminating…
In this new era of gravitational wave astrophysics, observations have indicated the likely existence of black holes with significant spin. In order to better understand the potential imprint orbital dynamics have on the multi-messenger…
The new discoveries of circumbinary planetary systems shed light on the understanding of planetary system formation. Learning the architectural properties of these systems is essential for constraining the different formation mechanisms. We…
We consider a 2 d.o.f. Hamiltonian system with one degree of freedom corresponding to fast motion and the other corresponding to slow motion. The ratio of the time derivatives of slow and fast variables is of order $0<\eps \ll 1$. At frozen…
Because of the high eccentricities (~0.3) of two of the possible planets about the star Upsilon Andromeda, the stability of the system requires careful study. We present results of 1000 numerical simulations which explore the orbital…
A new era of directly imaged extrasolar planets has produced a three-planet system (Marois et al. 2008), where the masses of the planets have been estimated by untested cooling models. We point out that the nominal circular, face-on orbits…
Context. The presence of a stellar companion can strongly influence the architecture and long-term stability of planetary systems. Motivated by the discovery of exoplanets exhibiting extremely high eccentricities (e >= 0.8) in systems with…
Nearly half of the exoplanets found within binary star systems reside in very wide binaries with average stellar separations beyond 1,000 AU (1 AU being the Earth-Sun distance), yet the influence of such distant binary companions on…