Related papers: Periodic orbits in the restricted four-body proble…
We generalize the Newtonian n-body problem to spaces of curvature k=constant, and study the motion in the 2-dimensional case. For k>0, the equations of motion encounter non-collision singularities, which occur when two bodies are antipodal.…
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…
For a body with negligible mass moving in the gravitational field of a star and one planet in a circular orbit (the circular restricted three-body problem) five equilibrium points exist and are known as the Lagrangian points. The positions…
We consider $(n+1)$ bodies moving under their mutual gravitational attraction in spaces with constant Gaussian curvature $\kappa$. In this system, $n$ primary bodies with equal masses form a relative equilibrium solution with a regular…
In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving near the planet in case of the elliptic restricted problem…
In the framework of the planar restricted three body problem we study a considerable number of resonances associated to the Kuiper Belt dynamics and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic…
In this article, I discuss the motion of $N$ point masses in non-relativistic mechanics, when the interaction between them is purely the Newtonian gravitational interaction, with $N$ greater than or equal to 2. The dynamical equations of…
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 --…
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…
In the circular case of the coplanar Restricted Three-body Problem, we studied how the family of quasi-satellite (QS) periodic orbits allows to define an associated libration center. Using the averaged problem, we highlighted a validity…
In this paper, we consider the elliptic relative equilibria of the restricted $N$-body problems, where the $N-1$ primaries form an Euler-Moulton collinear central configuration or a $(1+n)$-gon central configuration. We obtain the…
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…
Although the free-fall three-body problem have been investigated for more than one century, however, only four collisionless periodic orbits have been found. In this paper, we report 234 collisionless periodic orbits of the free-fall…
The size distribution of the stability region around the Lagrangian point L4 is investigated in the elliptic restricted three-body problem as the function of the mass parameter and the orbital eccentricity of the primaries. It is shown that…
For the Newtonian (gravitational) $n$-body problem in the Euclidean $d$-dimensional space, the simplest possible solutions are provided by those rigid motions (homographic solutions) in which each body moves along a Keplerian orbit and the…
By introducing a new coordinate system, we prove that there are abundant new periodic orbits near relative equilibrium solutions of the N-body problem. We consider only Lagrange relative equilibrium of the three-body problem and…
In the helium case of the classical Coulomb three-body problem in two dimensions with zero angular momentum, we develop a procedure to find periodic orbits applying two symbolic dynamics for one-dimensional and planar problems. A sequence…
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…
The quest of exo-Earths has become a prominent field. In this work, we study the stability of non-coplanar planetary configurations consisting of an inclined inner terrestrial planet in mean-motion resonance with an outer giant planet. We…
This paper demonstrates the existence of twistless tori and the associated reconnection bifurcations and meandering curves in the planar circular restricted three-body problem. Near the Lagrangian equilibrium $\mathcal{L}_4$ a twistless…