Periodic orbits in the generalized perturbed restricted three-body problem

Abstract

This paper studies the existence of periodic orbits around the triangular points of the restricted three-body problem (R3BP) in the range of linear stability. The problem is generalized in the sense that the bigger and smaller primaries are considered as triaxial and oblate spheroidal bodies, respectively and is perturbed due to the introduction of small perturbations in the Coriolis and the centrifugal forces. It is observed that long and short periodic orbits exist around these points and that their period, orientation and eccentricities are affected by the above parameters.

The effect of zonal harmonic coefficients in the framework of the restricted three-body problem

“…It is used the definition of Karimov and Sokolsky (1989) for mobile coordinates to determine these orbits and the predictor method to draw them. Singh and Begha (2011) studied the existence of periodic orbits around the triangular points in the restricted threebody problem when the bigger primary is triaxial and the smaller one is considered as an oblate spheroid. In the range of linear stability under the effects of the perturbed forces of Coriolis and centrifugal, it is deduced that long and short periodic orbits exist around these points and are stated their periods, orientation and eccentricities affected by the non sphericity and the perturbations in the Coriolis and centrifugal forces.…”

Existence and stability of triangular points in the restricted three-body problem with numerical applications

“…Other studies are focused on the restricted problem, taking the primaries as source of radiation, oblate spheroids, and the influence of Coriolis and centrifugal forces are considered, see and Singh and Begha (2011). Abouelmagd and El-Shaboury (2012) studied the existence of libration points and their linear stability when the three participating bodies are axisymmetric and the primaries are radiating, they found that the collinear points remain unstable, and the triangular points are stable for region 0 < μ < μ c ; the range of stability for these points decrease.…”

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

“…The most important features of "restricted three-body problem" are the existence of libration points and their stability as well as the periodic motion around these points. There are many authors devoted their research to investigate the aforementioned properties within frame work of the "perturbed restricted three-body problem" [3,5,6,10,11,15,17,33]. Furthermore, the analysis of lower or higher order of resonant periodic orbits with in frame of the photogravitational "restricted three-body problem" are studied by [28,29].…”