<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we present a comprehensive analytical study on the perturbed restricted three bodies problem. We formulate the equations of motion of this problem, in the event of the asteroids belt perturbation. We find the locations of equilibrium points (collinear and triangular points) and analysis their linear stability. Furthermore the periodic orbits around both collinear and triangular points are found.</p></abstract>

In this paper, we present a comprehensive analytical study on the perturbed restricted three bodies problem. We formulate the equations of motion of this problem, in the event of the asteroids belt perturbation. We find the locations of equilibrium points (collinear and triangular points) and analysis their linear stability. Furthermore the periodic orbits around both collinear and triangular points are found.

Periodic orbit in the frame work of restricted three bodies under the asteroids belt effect

Celestial Mechanics and Space Dynamics Research Group (CMSDRG), Astronomy Department

Applied Mathematics and Nonlinear Sciences

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

In this paper, we present a comprehensive analytical study on the perturbed restricted three bodies problem. We formulate the equations of motion of this...

Periodic orbit in the frame work of restricted three bodies under the asteroids belt effect

Published Online: Aug 20, 2020

Page range: 157 - 176

Received: Jul 05, 2019

Accepted: Nov 20, 2019

DOI: https://doi.org/10.2478/amns.2020.2.00022

Keywords
Restricted three bodies problem, Asteroids belt effect, Linear Stability, Periodic orbits

© 2020 Ahmed A. Abozaid et al., published by Sciendo

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

Fig. 1

Fig. 2

Periodic orbit in the frame work of restricted three bodies under the asteroids belt effect

Published Online: Aug 20, 2020

Page range: 157 - 176

Received: Jul 05, 2019

Accepted: Nov 20, 2019

DOI: https://doi.org/10.2478/amns.2020.2.00022

KeywordsRestricted three bodies problem, Asteroids belt effect, Linear Stability, Periodic orbits

© 2020 Ahmed A. Abozaid et al., published by Sciendo

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

Fig. 1

Fig. 2

Keywords
Restricted three bodies problem, Asteroids belt effect, Linear Stability, Periodic orbits