Related papers: Secular Dynamics of Compact Three-Planet Systems
The nearly circular (mean eccentricity <e>~0.06) and coplanar (mean mutual inclination <i>~3 deg) orbits of the Solar System planets motivated Kant and Laplace to put forth the hypothesis that planets are formed in disks, which has…
We investigate the non-resonant, 3-D (spatial) model of the hierarchical system composed of point-mass stellar (or sub-stellar) binary and a low-mass companion (a circumbinary planet or a brown dwarf). We take into account the leading…
The stellar spin orientation relative to the orbital planes of multiplanet systems are becoming accessible to observations. Here, we analyze and classify different types of spin-orbit evolution in compact multiplanet systems perturbed by an…
We develop a technique for estimating the inner eccentricity in hierarchical triple systems with well separated components. We investigate systems with initially circular and coplanar orbits and comparable masses. The technique is based on…
Novel method for semi-analytical solving of equations of a trapped dynamics for a planetoid m4 close to the plane of mutual motion of main bodies around each other (in case of a special type of Bi-Elliptic Restricted 4-Bodies Problem) is…
We present the secular theory of coplanar $N$-planet system, in the absence of mean motion resonances between the planets. This theory relies on the averaging of a perturbation to the two-body problem over the mean longitudes. We expand the…
Determining the orbital eccentricity of an extrasolar planet is critically important for understanding the system's dynamical environment and history. However, eccentricity is often poorly determined or entirely mischaracterized due to poor…
Extrasolar planetary systems commonly exhibit planets on eccentric orbits, with many systems located near or within mean-motion resonances, showcasing a wide diversity of orbital architectures. Such complex systems challenge traditional…
This paper studies the long term evolution of planetary systems containing short-period planets, including the effects of tidal circularization, secular excitation of eccentricity by companion planets, and stellar damping. For planetary…
We integrate the orbital solutions of the planets orbiting 55 Cnc. In the simulations, we find that not only three resonant arguments $\theta_{1}=\lambda_{1}-3\lambda_{2}+2\tilde\omega_{1}$,…
Three-body interactions are ubiquitous in astrophysics. For instance, Kozai-Lidov oscillations in hierarchical triple systems have been studied extensively and applied to a wide range of astrophysical systems. However, mildly-hierarchical…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
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…
We determine the orbital eccentricities of individual small Kepler planets, through a combination of asteroseismology and transit light-curve analysis. We are able to constrain the eccentricities of 51 systems with a single transiting…
Consider the Restricted Planar Circular Three Body Problem (RPC3BP), which models the motion of a massless particle (Asteroid) under the gravitational influence of two massive bodies (the primaries) moving on circular orbits. By considering…
In a multi-planet system, a gradual change in one planet's semi-major axis will affect the eccentricities of all the planets, as angular momentum is distributed via secular interactions. If tidal dissipation in the planet is the cause of…
In a previous paper (Gayon & Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are…
Modern applications of celestial mechanics include the study of closely packed systems of exoplanets, circumbinary planetary systems, binary-binary interactions in star clusters, and the dynamics of stars near the galactic centre. While…
The orbital dynamics of most planetary satellites is governed by the quadrupole moment from the equatorial bulge of the host planet and the tidal field from the Sun. On the Laplace surface, the long-term orbital evolution driven by 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…