TITLE:
Periodic Orbits of the First Kind in the CR4BP When the Second Primary Is a Triaxial Rigid Body
AUTHORS:
M. R. Hassan, Payal Singh, Md. Aminul Hassan
KEYWORDS:
Autonomous Four-Body Problem, CR4BP, Triaxial Rigid Body, Regularization, Generating and General Solution, Periodicity
JOURNAL NAME:
International Journal of Astronomy and Astrophysics,
Vol.7 No.3,
July
24,
2017
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.