<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Periodic orbits play a fundamental role in the study and deep understanding of the behavior of dynamical systems. In the current work, we investigated the periodic orbits around the triangular libration points of the restricted three-body problem. The equations of motion of the restricted problem are presented when both primaries are prolate triaxial. Periodic orbits around the triangular points are obtained and then illustrated graphically for some selected initial conditions and for the entire domain of the mass ratio <italic>μ</italic>, as well. The eccentricities of the periodic orbits are obtained and then represented graphically. It is observed that the periodic orbits about the triangular stationary points are elliptical, and the frequencies of short and long orbits of the periodic motion are influenced by the shape of the primary bodies. Furthermore, we found that the perturbing forces influence the period, the orientation, and the eccentricities of the short and long periodic orbits.</p>
</abstract>

Periodic orbits play a fundamental role in the study and deep understanding of the behavior of dynamical systems. In the current work, we investigated the periodic orbits around the triangular libration points of the restricted three-body problem. The equations of motion of the restricted problem are presented when both primaries are prolate triaxial. Periodic orbits around the triangular points are obtained and then illustrated graphically for some selected initial conditions and for the entire domain of the mass ratio μ, as well. The eccentricities of the periodic orbits are obtained and then represented graphically. It is observed that the periodic orbits about the triangular stationary points are elliptical, and the frequencies of short and long orbits of the periodic motion are influenced by the shape of the primary bodies. Furthermore, we found that the perturbing forces influence the period, the orientation, and the eccentricities of the short and long periodic orbits.

Periodic Orbits Around the Triangular Points with Prolate Primaries

Artificial Satellites

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Periodic Orbits Around the Triangular Points with Prolate Primaries"}

Periodic orbits play a fundamental role in the study and deep understanding of the behavior of dynamical systems. In the current work, we investigated the...

Periodic Orbits Around the Triangular Points with Prolate Primaries

Published Online: Apr 15, 2023

Page range: 1 - 13

Received: May 17, 2022

Accepted: Feb 02, 2023

DOI: https://doi.org/10.2478/arsa-2023-0001

Keywords
restricted three-body problem, triangular points, prolate triaxial, periodic orbits

© 2023 Nihad Abd El Motelp et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Periodic Orbits Around the Triangular Points with Prolate Primaries

Published Online: Apr 15, 2023

Page range: 1 - 13

Received: May 17, 2022

Accepted: Feb 02, 2023

DOI: https://doi.org/10.2478/arsa-2023-0001

Keywordsrestricted three-body problem, triangular points, prolate triaxial, periodic orbits

© 2023 Nihad Abd El Motelp et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
restricted three-body problem, triangular points, prolate triaxial, periodic orbits