Periodic Orbits of the First Kind in the CR4BP When the Second Primary Is a Triaxial Rigid Body

M R Hassan,Payal Singh,Md Aminul Hassan

doi:10.4236/ijaa.2017.73011

Abstract

The present paper deals with the existence of periodic orbits in the Circular Restricted Four-Body Problem (CR4BP) in two-dimensional co-ordinate system when the second primary is a triaxial rigid body and the third primary of inferior mass (in comparison of the other primaries) is placed at triangular libration point L4 of the Circular Restricted Three-Body Problem (CR3BP). With the help of generating solutions, we formed a basis for the existence of periodic orbits, then an analytical approach given by Hassan et al. [1], was applied to our model of equilateral triangular configuration. It is found that in general solution also; the character of periodic orbits is conserved. For verification of the existence of periodic orbits, we have applied the criterion of Duboshin [2] and found satisfied.

Highlights

Giacaglia [3] applied the method of analytic continuation to examine the existence of periodic orbits of collision of the first kind in the CR3BP
Using the concept of Ceccaroni and Biggs [6] and the method of Hassan et al [1], we have proposed to study the existence of periodic orbits of the first kind in the autonomous R4BP by considering the second primary as a triaxial rigid body
In order to prove the existence of periodic orbits of the first kind in the CR4BP, we have discussed the problem into five sections starting with introduction about the historical evolution of the topic

Summary

Introduction

Giacaglia [3] applied the method of analytic continuation to examine the existence of periodic orbits of collision of the first kind in the CR3BP. Ceccaroni and Biggs [6] studied the autonomous coplanar CR4BP with an extension to low-thrust propulsion for application to the future science mission. In their problem, they studied the stability region of the artificial and natural equilibrium points in the Sun-Jupiter Trojan Asteroid-Spacecraft system. Using the concept of Ceccaroni and Biggs [6] and the method of Hassan et al [1], we have proposed to study the existence of periodic orbits of the first kind in the autonomous R4BP by considering the second primary as a triaxial rigid body

Equations of Motion of the Infinitesimal Mass

Regularization

An 2 a 2 r25

Discussions and Conclusions