Related papers: Secular instability in the spatial three-body prob…
We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic…
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…
We study the secular, hierarchical three-body problem to first-order in a post-Newtonian expansion of General Relativity. We expand the first-order post-Newtonian Hamiltonian to leading-order in the ratio of the semi-major axis of the two…
In this paper we consider the circular restricted three body problem which models the motion of a masless body under the influence of the Newtionan gravitational force caused by two other bodies, the primaries, which move along cicular…
We consider a curved Sitnikov problem, in which an infinitesimal particle moves on a circle under the gravitational influence of two equal masses in Keplerian motion within a plane perpendicular to that circle. There are two equilibrium…
I consider the dynamics of mean motion resonances between pairs of co-planar planets and derive a new integrable Hamiltonian model for planets' resonant motion. The new model generalizes previously-derived integrable Hamiltonians for…
The aim of the present work is to reduce the secular solution around the triangular equilibrium points to periodic solution in the frame work of the generalized restricted thee-body problem. This model is generalized in sense that both the…
As shown by Johannes Kepler in 1609, in the two-body problem, the shape of the orbit, a given ellipse, and a given non-vanishing constant angular momentum determines the motion of the planet completely. Even in the three-body problem, in…
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…
The results of an extensive numerical study of the periodic orbits of planar, elliptic restricted three-body planetary systems consisting of a star, an inner massive planet and an outer mass-less body in the external 1:2 mean-motion…
Stability of Hilda Asteroids in the solar system around the 3:2 resonance point is analyzed in terms of the Sun-Jupiter-asteroid elliptic restricted three-body problem. We show that the Hamiltonian of the system is well-approximated by a…
The hierarchical triple body approximation has useful applications to a variety of systems from planetary and stellar scales to supermassive black holes. In this approximation, the energy of each orbit is separately conserved and therefore…
Massive bodies undergo orbital eccentricity oscillations when embedded in an axisymmetric disk of smaller mass orbits. These eccentricity oscillations are driven by secular torques that seek to equalize the apsidal precession rates of all…
The behavior of an interior test particle in the secular 3-body problem has been studied extensively. A well-known feature is the Lidov-Kozai resonance in which the test particle's argument of periapse librates about $\pm 90^\circ$ and…
More than 10% of extra-solar planets (EPs) orbit in a binary or multiple stellar system. We investigated the motion of planets revolving in binary systems in the frame of the particular case of the three body problem. We carried out an…
This paper presents a study of the isosceles problem resulting by a perturbation of Euler's collinear solution under Newtonian gravitational attraction of three bodies in space. After the Hamiltonian was obtained, a circumference of…
The long-term stability of the evolution of two-planet systems is considered by using the general three body problem (GTBP). Our study is focused on the stability of systems with adjacent orbits when at least one of them is highly…
We present a numerical study on the stability of all fourth- and fifth-order retrograde mean motion resonances (1/3, 3/1, 1/4, 4/1, 2/3, and 3/2) in the 3-body problem composed of a solar mass star, a Jupiter mass planet, and an additional…
We study the nonholonomic motion of a point particle on the Heisenberg group around the fixed "sun" whose potential is given by the fundamental solution of the sub-Laplacian. Unlike arXiv:1212.2713 where the variational problem is studied…
We present a numerical study on the stability of the 1/2, 2/1 and 1/1 retrograde mean motion resonances in the 3-body problem composed of a solar mass star, a Jupiter mass planet and an additional body with zero mass (elliptic restricted…