Related papers: A semi-empirical stability criterion for real plan…
Recent work on the equilibrium and stability of ellipsoidal stellar systems is reviewed. The absence of constant-density cores in early-type galaxies implies that chaos and high-order resonances are generic features of the motion in…
Many multi-planet systems have been discovered in recent years. Some of them are in mean-motion resonances (MMR). Planet formation theory was successful in explaining the formation of 2:1, 3:1 and other low resonances as a result of…
We present an approach that is able to both rapidly assess the dynamical stability of multiple planet systems, and determine whether an exoplanet system would be capable of hosting a dynamically stable Earth-mass companion in its habitable…
The relationship between the boundaries for Hill and Lagrange stability in orbital element space is modified in the case of resonantly interacting planets. Hill stability requires the ordering of the planets to remain constant while…
We have previously introduced the parameter `alpha' as an indicator of stability to m=2 nonaxisymmetric modes in rotating, self-gravitating, axisymmetric, gaseous and stellar systems. This parameter can be written as a function of the total…
The dynamical excitation of asteroids due to mean motion resonant interactions with planets is enhanced when their parent star leaves the main sequence. However, numerical investigation of resonant outcomes within post-main-sequence…
Our concern here is the nature of secondary resonances--commensurabilities between apsidal and libration periods lying within first-order mean motion resonances [mmr] in the solar system. At the 4/3 and 3/2 mmr in the asteroid belt, we find…
We propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time…
The orbits in the HD 160691 planetary system at first appeared highly unstable, but using the MEGNO and FLI techniques of global dynamics analysis in the orbital parameter space we have found a stabilizing mechanism that could be the key to…
Hundreds of giant planets have been discovered so far and the quest of exo-Earths in giant planet systems has become intriguing. In this work, we aim to address the question of the possible long-term coexistence of a terrestrial companion…
Motivated by the large number of extrasolar planetary systems that are near mean motion resonances, this paper explores a related type of dynamical behavior known as "nodding". Here, the resonance angle of a planetary system executes…
In previous papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. We considered systems with well separated components and different initial…
Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital…
A number of multiplanet systems are observed to contain planets very close to mean motion resonances, although there is no significant pileup of precise resonance pairs. We present theoretical and numerical studies on the outcome of capture…
Planets around binary stars and those in multiplanet systems may experience resonant eccentricity excitation and disruption due to perturbations from a distant stellar companion. This "evection resonance" occurs when the apsidal precession…
While not detected yet, pairs of exoplanets in the 1:1 mean motion resonance probably exist. Low eccentricity, near-planar orbits, which in the comoving frame follow the horseshoe trajectories, are one of the possible stable configurations.…
For strictly entropic Riemann shock solutions of strictly hyperbolic systems of balance laws, we prove that exponential spectral stability implies large-time asymptotic orbital stability. As a preparation, we also prove similar results for…
One possible diagnostic of planet formation, orbital migration, and tidal evolution is the angle psi between a planet's orbital axis and the spin axis of its parent star. In general, psi cannot be measured, but for transiting planets one…
Analyzing system trajectory from the perspective of individual machines provides a distinctive angle to analyze the transient stability of power systems. This two-paper series propose a direct-time-domain method that is based on the…
A widely considered characteristic of extra-solar planetary systems has been a seeming tendency for major axes of adjacent orbits to librate in stable configurations. Based on a new catalog of extra-solar planets (Butler et al. 2006) and…