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In this paper, the L1-minimization for the translational motion of a spacecraft in a circular restricted three-body problem (CRTBP) is considered. Necessary con- ditions are derived by using the Pontryagin Maximum Principle, revealing the…

Optimization and Control · Mathematics 2016-06-22 Zheng Chen

We propose a closed-form (i.e. without expansion in the orbital eccentricities) scheme for computations in perturbation theory in the restricted three-body problem (R3BP) when the massless particle is in an orbit exterior to the one of the…

Mathematical Physics · Physics 2023-07-26 Mattia Rossi , Christos Efthymiopoulos

An approach is developed to find approximate solutions to the restricted circular three body problem. The solution is useful in approximately describing the position vectors of three spherically symmetric masses, one of which has a much…

Mathematical Physics · Physics 2007-05-23 Abu Bakr Mehmood , S. Umer Abbas , Ghulam Shabbir

In the present work a systematic study has been presented in the context of the existence of libration points, their linear stability, the regions of motion where the third particle can orbit and the domain of basins of convergence linked…

Chaotic Dynamics · Physics 2020-05-22 Md Sanam Suraj , Rajiv Aggarwal , Amit Mittal , Om Prakash Meena , Md Chand Asique

We introduce a circular restricted charged three-body problem on the plane. In this model, the gravitational and Coulomb forces, due to the primary bodies, act on a test particle; the net force exerted by some primary body on the test…

Dynamical Systems · Mathematics 2015-03-31 Abimael Bengochea , Claudio Vidal

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

Gravitational scattering of small bodies (planetesimals) by a planet remains a fundamental problem in celestial mechanics. It is traditionally modeled within the circular restricted three-body problem (CR3BP), where individual particle…

Earth and Planetary Astrophysics · Physics 2026-02-11 Yukun Huang , Brett Gladman , Eiichiro Kokubo

Extreme mass-ratio inspirals, in which solar-mass compact bodies spiral into supermassive black holes, are an important potential source for gravitational wave detectors. Because of the extreme mass-ratio, one can model these systems using…

General Relativity and Quantum Cosmology · Physics 2010-06-22 Adam Pound

This paper introduces the Circular Restricted n-Body Problem (CRNBP), an extension of the bicircular restricted four-body problem (BCR4BP) designed to describe the dynamics of an n-body system. In the CRNBP, each massive body in the system…

Systems and Control · Electrical Eng. & Systems 2023-07-21 Rodolfo Batista Negri , Antonio Fernando Bertachini de Almeida Prado

A major question in dynamical systems is to understand the mechanisms driving global instability in the 3 Body Problem (3BP), which models the motion of three bodies under Newtonian gravitational interaction. The 3BP is called restricted if…

Dynamical Systems · Mathematics 2025-06-23 Marcel Guardia , Jaime Paradela , Tere M. Seara

The 2:1 mean motion resonance orbit was integrated at the restricted planar 3-body problem in absolute frame. Orbit of Jupiter was assumed circular. Initial Jupiter longitude was assumed zero. The Runge-Kutta method was used. The start of…

Astrophysics · Physics 2007-05-23 A. E. Rosaev

We consider a planetary system consisting of two primaries, namely a star and a giant planet, and a massless secondary, say a terrestrial planet or an asteroid, which moves under their gravitational attraction. We study the dynamics of this…

Earth and Planetary Astrophysics · Physics 2018-05-23 Kyriaki I. Antoniadou , Anne-Sophie Libert

The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more…

Earth and Planetary Astrophysics · Physics 2015-08-11 Z. E. Musielak , B. Quarles

The dynamics of the planar circular restricted three-body problem with Kerr-like primaries in the context of a beyond-Newtonian approximation is studied. The beyond-Newtonian potential is developed by using the Fodor-Hoenselaers-Perj\'es…

General Relativity and Quantum Cosmology · Physics 2020-12-09 Shounak De , Suparna Roychowdhury , Roopkatha Banerjee

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

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…

Instrumentation and Methods for Astrophysics · Physics 2021-04-07 Cristina Blaga , Paul A. Blaga , Tiberiu Harko

In the last decades a peculiar family of solutions of the Circular Restricted Three Body Problem has been used to explain the temporary captures of small bodies and spacecrafts by a planet of the Solar System. These solutions, which transit…

Earth and Planetary Astrophysics · Physics 2021-09-01 Rocío Isabel Páez , Massimiliano Guzzo

The equations of the restricted three-body problem describe the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$, $0\leq \mu \leq 1/2$, that circle each other with period equal to $2\pi$. When…

Dynamical Systems · Mathematics 2014-08-28 D. Viswanath

The problem of nonintegrability of the circular restricted three-body problem is very classical and important in the theory of dynamical systems. It was partially solved by Poincare in the nineteenth century: He showed that there exists no…

Dynamical Systems · Mathematics 2024-03-05 Kazuyuki Yagasaki

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