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The proposal of increasingly complex and innovative space endeavours poses growing demands for mission designers. In order to meet the established requirements and constraints while maintaining a low fuel cost, the use of low-energy…

Earth and Planetary Astrophysics · Physics 2020-06-09 Rita Neves

Near-rectilinear halo orbits (NRHOs) around Earth-Moon L2 in the Circular Restricted 3-Body Problem (CR3BP) exhibit a complex dynamical landscape, featuring a band of normally elliptic orbits embedded within regions of strong instability.…

Dynamical Systems · Mathematics 2026-04-14 Joan Gimeno , Luke T. Peterson

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 prove, under suitable non-resonance and non-degeneracy ``twist'' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic…

Dynamical Systems · Mathematics 2007-05-23 Massimiliano Berti , Luca Biasco , Enrico Valdinoci

We consider the special case of the restricted circular three-body problem, when the two primaries are of equal mass, while the third body of negligible mass performs oscillations along a straight line perpendicular to the plane of the…

Earth and Planetary Astrophysics · Physics 2011-02-17 Vladislav Sidorenko

We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…

Chaotic Dynamics · Physics 2009-11-10 J. Mellenthin , S. Russ

Context: The Circular Restricted Three-Body Problem provides a fundamental framework for understanding resonant dynamics in binary star systems. Aims: We develop a unified Hamiltonian formulation for mean-motion resonances that encompasses…

Earth and Planetary Astrophysics · Physics 2026-05-08 R. Capuzzo-Dolcetta

This paper employs an alternate dynamical model of the circular restricted three body problem to quantify uncertainties associated with spacecraft thrusting maneuvers. A non-product quadrature scheme known as Conjugate Unscented Transform…

Optimization and Control · Mathematics 2025-04-01 Sharad Sharan , Amit Jain , Roshan T. Eapen , Puneet Singla

A classical approach to the restricted three-body problem is to analyze the dynamics of the massless body in the synodic reference frame. A different approach is represented by the perturbative treatment: in particular the averaged problem…

Earth and Planetary Astrophysics · Physics 2021-06-29 Alexandre Pousse , Elisa Maria Alessi

We present a numerical study on the stability of the 1/2, 2/1 and 1/1 retrograde mean motion resonances in the 3-body problem composed of a solar mass star, a Jupiter mass planet and an additional body with zero mass (elliptic restricted…

Earth and Planetary Astrophysics · Physics 2022-06-15 G. A. Caritá , A. C. Signor , M. H. M. Morais

A family of periodic orbits is proven to exist in the spatial lunar problem that are continuations of a family of consecutive collision orbits, perpendicular to the primary orbit plane. This family emanates from all but two energy values.…

Dynamical Systems · Mathematics 2019-02-13 Edward Belbruno , Urs Frauenfelder , Otto van Koert

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 construct a highly-symmetric periodic orbit of eight bodies in three dimensions. In this orbit, each body collides with its three nearest neighbors in a regular periodic fashion. Regularization of the collisions in the orbit is achieved…

Dynamical Systems · Mathematics 2021-11-08 Skyler Simmons

In the preliminary design of space missions it can be useful to identify regions of dynamics that drive the system's behaviour or separate qualitatively different dynamics. The Lagrangian Coherent Structure (LCS) has been widely used in the…

Earth and Planetary Astrophysics · Physics 2022-09-26 Jack Tyler , Alexander Wittig

Planetary, stellar and galactic physics often rely on the general restricted gravitational N-body problem to model the motion of a small-mass object under the influence of much more massive objects. Here, I formulate the general restricted…

Earth and Planetary Astrophysics · Physics 2015-06-18 Dimitri Veras

Many binary systems of interest for gravitational-wave astronomy are orbited by a third distant body, which can considerably alter their relativistic dynamics. Precision computations are needed to understand the interplay between…

General Relativity and Quantum Cosmology · Physics 2023-02-22 Adrien Kuntz , Francesco Serra , Enrico Trincherini

In the framework of multi-body dynamics, successive encounters with a third body, even if well outside of its sphere of influence, can noticeably alter the trajectory of a spacecraft. Examples of these effects have already been exploited by…

Space Physics · Physics 2017-09-14 J. P. Sanchez , C. Colombo , E. M. Alessi

We consider the Earth-Moon planar circular restricted three body problem and present a proof of the existence orbits, which approach arbitrarily close to one of the primary masses, and at the same time after each approach they move away…

Dynamical Systems · Mathematics 2024-01-24 Maciej J. Capiński , Aleksander Pasiut

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…

Earth and Planetary Astrophysics · Physics 2026-01-21 M. B. Saputra , H. S. Ramadhan , Ibnu N. Huda , Leonardus B. Putra

This study investigates the problem of areostationary orbits around Mars in the three-dimensional space. Areostationary orbits are expected to be used to establish a future telecommunication network for the exploration of Mars. However, no…

Earth and Planetary Astrophysics · Physics 2012-05-07 Xiaodong Liu , Hexi Baoyin , Xingrui Ma
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