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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

We develop a framework based on energy kicks for the evolution of high-eccentricity long-period orbits with Jacobi constant close to 3 in the restricted circular planar three-body problem where the secondary and primary masses have mass…

Astrophysics · Physics 2009-11-07 Margaret Pan , Re'em Sari

We analyze in this paper the existence of the "out-of-plane" equilibrium points in the restricted three-body problem with oblateness. From the series expansion of the potential function of an oblate asteroid, we show analytically all…

Earth and Planetary Astrophysics · Physics 2018-03-20 Xuefeng Wang , Nan Wu , Liyong Zhou , Bo Xu

This paper is devoted to the study of secondary resonances and the stability of the Lagrangian point L4 in the spatial restricted three-body problem for moderate mass ratios (mu), meaning that mu is smaller than 0.0045. However, we…

Earth and Planetary Astrophysics · Physics 2017-08-23 Richard Schwarz , Akos Bazso , Balint Erdi , Barbara Funk

The multi-dissipative photogravitational triaxial elliptic restricted three body problem is treated. The perturbed locations of triangular points are computed. The stability of the triangular points under changing one or more perturbing…

Earth and Planetary Astrophysics · Physics 2015-06-10 F. A. Abd El-Salam

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…

Dynamical Systems · Mathematics 2016-12-21 Florin Diacu

The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of…

Dynamical Systems · Mathematics 2018-08-07 Amadeu Delshams , Vadim Kaloshin , Abraham de la Rosa , Tere M. Seara

This paper describes design of the trajectory and analysis of the stability of collinear point $L_2$ in the Sun-Earth system. The modified restricted three body problem with additional gravitational potential from the belt is used as the…

Earth and Planetary Astrophysics · Physics 2011-04-07 Badam Singh Kushvah

Since the discovery in 1772 of the triangular Lagrange points L4 and L5 in the gravitational field of two bodies moving under the sole influence of mutual gravitational forces, astronomers found a large number of minor celestial bodies…

Earth and Planetary Astrophysics · Physics 2019-10-17 Judit Slíz-Balogh , András Barta , Gábor Horváth

In the spatial circular restricted three-body problem librational motion around the Lagrangian points $L_4$ and $L_5$ exists up to high inclinations of the massless object. We report the results of numerical investigations on the stability…

Earth and Planetary Astrophysics · Physics 2017-08-10 Ákos Bazsó , Richard Schwarz , Bálint Érdi , Barbara Funk

Consider the Restricted Planar Circular Three Body Problem (RPC3BP), which models the motion of a massless particle (Asteroid) under the gravitational influence of two massive bodies (the primaries) moving on circular orbits. By considering…

Mathematical Physics · Physics 2025-12-24 Marcel Guardia , José Lamas , Tere M-Seara

The Roche potential is the sum of the gravitational and rotational potentials experienced by a massless body rotating alongside two massive bodies in a circular orbit. The Lagrangian points are five stationary points in the Roche potential.…

Solar and Stellar Astrophysics · Physics 2023-09-28 John Southworth

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 restricted three body problem is well-known and very important for dynamics of binary, multiple stars and also planetary systems. We extend the classical version of this problem to the situation that there are some external forces from…

Astrophysics · Physics 2007-05-23 Ing-Guey Jiang , Li-Chin Yeh

In this new era of gravitational wave astrophysics, observations have indicated the likely existence of black holes with significant spin. In order to better understand the potential imprint orbital dynamics have on the multi-messenger…

General Relativity and Quantum Cosmology · Physics 2020-07-22 Martin D. Strong , Michael Crescimanno

The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion…

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

We study the problem of minimal resistance for a body moving with constant velocity in a rarefied medium of chaotically moving point particles, in Euclidean space R^d. The particles distribution over velocities is radially symmetric. Under…

Optimization and Control · Mathematics 2007-05-23 Alexander Yu. Plakhov , Delfim F. M. Torres

We present a numerical study on the stability of all fourth- and fifth-order retrograde mean motion resonances (1/3, 3/1, 1/4, 4/1, 2/3, and 3/2) in the 3-body problem composed of a solar mass star, a Jupiter mass planet, and an additional…

Earth and Planetary Astrophysics · Physics 2023-03-14 Alan Cefali Signor , Gabriel Antonio Carita , Maria Helena Moreira Morais

Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is…

Dynamical Systems · Mathematics 2016-09-07 Alain Chenciner , Richard Montgomery

Trojans are defined as objects that share the orbit of a planet at the stable Lagrangian points $L_4$ and $L_5$. In the Solar System, these bodies show a broad size distribution ranging from micrometer($\mu$m) to centimeter(cm) particles…