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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…

Earth and Planetary Astrophysics · Physics 2017-02-10 Kyriaki I. Antoniadou , George Voyatzis

We present a diffusion mechanism for time-dependent perturbations of autonomous Hamiltonian systems introduced in [25]. This mechanism is based on shadowing of pseudo-orbits generated by two dynamics: an `outer dynamics', given by…

Dynamical Systems · Mathematics 2016-12-20 Maciej J. Capinski , Marian Gidea , Rafael de la Llave

A novel approach for solving equations of motion of finite-sized satellite supposed to be moving in a proximity and around the planet in the elliptic restricted three-body problem, ER3BP is presented in this semi-analytical investigation.…

General Physics · Physics 2023-06-26 Sergey Ershkov , Dmytro Leshchenko , Alla Rachinskaya

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…

Dynamical Systems · Mathematics 2012-10-08 Marcel Guardia , Pau Martin , Tere M. Seara

We consider the problem of orbital stability of the motion of a test particle in the restricted three-body problem, by using the orbital moment and its time derivative. We show that it is possible to get some insight into the stability…

General Relativity and Quantum Cosmology · Physics 2016-03-16 M. Abishev , H. Quevedo , S. Toktarbay , B. Zhami

We consider the planar three body problem of planetary type and we study the generation and continuation of periodic orbits and mainly of asymmetric periodic orbits. Asymmetric orbits exist in the restricted circular three body problem only…

Earth and Planetary Astrophysics · Physics 2011-11-03 K. I. Antoniadou , G. Voyatzis , T. Kotoulas

We herein utilize the general three-body problem (GTBP) as a model, in order to simulate resonant systems consisting of a star and two planets, where at least one of them is highly eccentric. We study them in terms of their long-term…

Earth and Planetary Astrophysics · Physics 2015-09-10 K. I. Antoniadou , G. Voyatzis

The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.

Mathematical Physics · Physics 2012-08-06 Donglun Wu , Shiqing Zhang

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…

General Physics · Physics 2021-04-19 Sergey Ershkov , Alla Rachinskaya

The restricted planar four body problem describes the motion of a massless body under the Newtonian gravitational force of other three bodies (the primaries), of which the motion gives us general solutions of the three body problem. A…

Dynamical Systems · Mathematics 2020-12-02 Tere Seara , Jianlu Zhang

The Circular Restricted Three-Body Problem (CR3BP) models the motion of a massless body under the gravitational influence of two primaries. We present a method for approximating a given family of periodic orbits by low-degree implicit…

Algebraic Geometry · Mathematics 2026-04-30 Ruiqi Huang , Anton Leykin

We consider the elliptic three body problem as a perturbation of the circular problem. We show that for sufficiently small eccentricities of the elliptic problem, and for energies sufficiently close to the energy of the libration point L2,…

Dynamical Systems · Mathematics 2015-03-13 Maciej J. Capinski , Piotr Zgliczynski

In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…

Dynamical Systems · Mathematics 2026-02-24 Joshua Fitzgerald , Shane Ross

The description of unstable motions in the Restricted Planar Circular 3-Body Problem, modeling the dynamics of a Sun-Planet-Asteriod system, is one of the fundamental problems in Celestial Mechanics. The goal of this paper is to analyze…

Dynamical Systems · Mathematics 2023-12-22 Inmaculada Baldomá , Mar Giralt , Marcel Guardia

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…

Astrophysics · Physics 2008-11-26 Nader Haghighipour , Jocelyn Couetdic , Ferenc Varadi , William B. Moore

We present a method for proving the existence of symmetric periodic, heteroclinic or homoclinic orbits in dynamical systems with the reversing symmetry. As an application we show that the Planar Restricted Circular Three Body Problem…

Dynamical Systems · Mathematics 2009-11-10 D. Wilczak , P. Zgliczynski

The goal of this paper is to obtain an approximate solution of the restricted three-body problem in the case of small perturbations in the vicinity of, but not in exact resonance. In this paper, we study the restricted threebody problem…

Earth and Planetary Astrophysics · Physics 2025-11-11 Alexey Rosaev , Eva Plavalova , Pavel Nesterov

We study the secular effects in the motion of an asteroid with negligible mass in a spatial restricted elliptic three body problem with arbitrary inclination. Averaging over mean anomalies of the asteroid and the planet are applied to…

Dynamical Systems · Mathematics 2024-09-20 Xiumin Huang , Yan Luo , Kaicheng Sheng , Yiru Ye

We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating…

Dynamical Systems · Mathematics 2025-10-28 Alessandra Celletti , Christoph Lhotka , Giuseppe Pucacco

We study the dynamics of the 3-D three-body problem of a small body moving under the attractions of a star and a giant planet which orbits the star on a much wider and elliptic orbit. In particular, we focus on the influence of an eccentric…

Earth and Planetary Astrophysics · Physics 2015-06-04 A. -S. Libert , N. Delsate