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The planar circular restricted three-body problem with modified Newtonian gravity is used in order to determine the Newton-Raphson basins of attraction associated with the equilibrium points. The evolution of the position of the five…

Chaotic Dynamics · Physics 2018-03-30 Euaggelos E. Zotos

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

Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…

Astrophysics · Physics 2007-05-23 Douglas C. Heggie

The circular restricted three-body problem (CR3BP) with solar radiation pressure (SRP) has often been analyzed with assumptions made on a spacecraft's attitude, such that the problem remains Hamiltonian. These assumptions are…

Dynamical Systems · Mathematics 2024-02-13 Hailee Hettrick , David W. Miller , Begum Cannataro

There are periodic solutions to the equal-mass three-body (and N-body) problem in Newtonian gravity. The figure-eight solution is one of them. In this paper, we discuss its solution in the first and second post-Newtonian approximations to…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Carlos O. Lousto , Hiroyuki Nakano

The general relativistic Poynting-Robertson (PR) effect is a very important dissipative phenomenon occurring in high-energy astrophysics. Recently, it has been proposed a new model, which upgrades the two-dimensional (2D) description in the…

General Relativity and Quantum Cosmology · Physics 2023-03-28 Vittorio De Falco

In this paper, we extend the basic model of the restricted four-body problem introducing two bigger dominant primaries $m_1$ and $m_2$ as oblate spheroids when masses of the two primary bodies ($m_2$ and $m_3$) are equal. The aim of this…

Earth and Planetary Astrophysics · Physics 2013-11-20 Reena Kumari , Badam Singh Kushvah

We revisit the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particles move periodically in a single closed…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Tatsunori Imai , Takamasa Chiba , Hideki Asada

We consider the modified restricted three body problem with power-law density profile of disk, which rotates around the center of mass of the system with perturbed mean motion. Using analytical and numerical methods we have found…

Dynamical Systems · Mathematics 2015-05-28 Badam Singh Kushvah , Ram Kishor , Uday Dolas

The case of the planar circular restricted three-body problem where one of the two primaries has a stronger gravitational field with respect to the classical Newtonian field is investigated. We consider the case where two primaries have the…

Chaotic Dynamics · Physics 2017-09-28 Euaggelos E. Zotos

We demonstrate how to separate the rotational degrees of freedom in a quantum N-body problem completely from the internal ones. It is shown that any common eigenfunction of the total orbital angular momentum ($\ell$) and the parity in the…

Atomic Physics · Physics 2007-05-23 Zhong-Qi Ma , Bing Duan , Xiao-Yan Gu

The problem of describing the free motions of three gravitating bodies under each others gravitational influence is one of the oldest of unsolved problems of classical mechanics. Henry Poincare proved in his dictum that due to the nature of…

Mathematical Physics · Physics 2016-09-07 AbuBakr Mehmood , Syed Umer Abbas Shah , Ghulam Shabbir

The planar linear restricted four-body problem is used in order to determine the Newton-Raphson basins of convergence associated with the equilibrium points. The parametric variation of the position as well as of the stability of the…

Chaotic Dynamics · Physics 2017-09-28 Euaggelos E. Zotos

In this paper we consider the planar circular restricted three body problem (PCRTBP), which models the motion of a massless body under the attraction of other two bodies, the primaries, which describe circular orbits around their common…

Dynamical Systems · Mathematics 2024-07-25 Marcel Guardia , José Lamas , Tere M. Seara

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

We study the Robe's restricted three-body problem. Such a motion was firstly studied by A. G. Robe in \cite{Robe}, which is used to model small oscillations of the earth's inner core taking into account the moon attraction. For the linear…

Dynamical Systems · Mathematics 2019-08-02 Qinglong Zhou , Yongchao Zhang

The restricted planar elliptic three body problem models the motion of a massless body under the Newtonian gravitational force of the two other bodies, the primaries, which evolve in Keplerian ellipses. A trajectory is called oscillatory if…

Dynamical Systems · Mathematics 2016-08-08 Marcel Guardia , Pau Martín , Lara Sabbagh , Tere M. Seara

Within the framework of restricted four-body problem, we study the motion of an infinitesimal mass by assuming that the primaries of the system are radiating-oblate spheroids surrounded by a circular cluster of material points. In our…

Earth and Planetary Astrophysics · Physics 2014-11-06 Babatunde J. Falaye

In my doctoral thesis, I have focussed my attention on radiation processes in high-energy astrophysics connected with the accretion flow physics around compact objects. Generally, a radiation field beside to exert an outward radiation…

General Relativity and Quantum Cosmology · Physics 2019-04-03 Vittorio De Falco

The Newton-Raphson basins of attraction, associated with the libration points (attractors), are revealed in the pseudo-Newtonian planar circular restricted three-body problem, where the primaries have equal masses. The parametric variation…

Chaotic Dynamics · Physics 2018-01-05 Euaggelos E. Zotos