Related papers: High inclination orbits in the secular quadrupolar…
Triple systems with low hierarchical structure are common throughout the Universe, including examples such as high-altitude lunar satellites influenced by the Earth, planetary satellites perturbed by the Sun, and stellar binaries affected…
We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of [4] is applicable. This guarantees…
Recent results by Martin et al. (2014) showed in 3D SPH simulations that tilted discs in binary systems can be unstable to the development of global, damped Kozai-Lidov (KL) oscillations in which the discs exchange tilt for eccentricity. We…
This study examines the dynamics of the third body in an elliptic restricted three-body problem (ERTBP) framework, taking into account perturbations from radiation pressure, oblateness, and elongation of the primary bodies, as well as…
In a system of particles, quasi-periodic almost-collision orbits are collisionless orbits along which two bodies become arbitrarily close to each other -- the lower limit of their distance is zero but the upper limit is strictly positive --…
It is well established that certain detached eclipsing binary stars exhibit apsidal motions whose value is in disagreement with with calculated deviations from Keplerian motion based on tidal effects and the general theory of relativity.…
We study a three dimensional continuous model of gravitating matter rotating at constant angular velocity. In the rotating reference frame, by a finite dimensional reduction, we prove the existence of non radial stationary solutions whose…
We consider the planar circular equilateral restricted four body-problem where a test particle of infinitesimal mass is moving under the gravitational attraction of three primary bodies which move on circular orbits around their common…
In the restricted three-body problem, consecutive collision orbits are those orbits which start and end at collisions with one of the primaries. Interests for such orbits arise not only from mathematics but also from various engineering…
We consider the 3-body problem of celestial mechanics in Euclidean, elliptic, and hyperbolic spaces, and study how the Lagrangian (equilateral) relative equilibria bifurcate when the Gaussian curvature varies. We thus prove the existence of…
Motivated by the dynamics of resonance capture, we study numerically the coorbital resonance for inclination180 >=I>=0 in the circular restricted three-body problem. We examine the similarities and differences between planar and three…
General properties of the three-body problem in a model of modified dynamics are investigated. It is shown that the three-body problem in this model shares some characters with the similar problem in Newtonian dynamics. Moreover, the planar…
In this letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al [1] predicts the observed stability. This seems to…
The classical two-body system with Lorentz-invariant Coulomb interaction V=-k/rho is solved in 3+1 dimensions using the manifestly covariant Hamiltonian mechanics of Stueckelberg. Particular solutions for the reduced motion are obtained…
The circular restricted three body problem, which considers the dynamics of an infinitesimal particle in the presence of the gravitational interaction with two massive bodies moving on circular orbits about their common center of mass, is a…
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…
We introduce a restricted four body problem in a 2+2 configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the planewhere the primaries…
In this article, equilibrium points and families of periodic orbits in the vicinity of the collinear equilibrium points of a binary asteroid system are investigated with respect to the angular velocity of the secondary body, the mass ratio…
In hierarchical triple systems, the inner binary is slowly perturbed by a distant companion, giving rise to large-scale oscillations in eccentricity and inclination, known as von-Zeipel-Lidov-Kozai (ZLK) oscillations. Stable systems with a…
Recent observational campaigns have shown that multi-planet systems seem to be abundant in our Galaxy. Moreover, it seems that these systems might have distant companions, either planets, brown-dwarfs or other stellar objects. These…