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.
References
[1]
Hassan, M.R., Hassan, Md. A., Singh, P., Kumar, V. and Thapa, R.R. (2017) Existence of Periodic Orbits of the First Kind in the Autonomous Four-Body Problem with the Case of Collision. International Journal of Astronomy and Astrophysics, 7, 91-111. https://doi.org/10.4236/ijaa.2017.72008
Giacaglia, E.O. (1967) Periodic Orbits of Collision in the Restricted Problem of Three Bodies. Astronomical Journal, 72, 386-391. https://doi.org/10.1086/110237
[4]
Bhatnagar, K.B. (1969) Periodic Orbits of Collision in the Plane Elliptic Restricted Problem of Three Bodies. National Institute of Science, 35A, 829-844.
[5]
Bhatnagar, K.B. (1971) Periodic Orbits of Collision in the Plane Circular Problem of Four Bodies. Indian Journal of Pure and Applied Mathematics, 2, 583-596.
[6]
Ceccaroni, M. and Biggs, J. (2012) Low-Thrust Propulsion in a Coplanar Circular Restricted Four Body Problem. Celestial Mechanics and Dynamical Astronomy, 112, 191-219. https://doi.org/10.1007/s10569-011-9391-x
[7]
McCuskey, C.W. (1963) Introduction to Celestial Mechanics. Addison-Wesley, Pearson Education, Massachusetts, USA.
[8]
Choudhry, R.K. (1966) Existence of Periodic Orbits of the Third kind in the Elliptic Restricted Problem of the Three Bodies and the Stability of the Generating Solution. Proceedings of the National Academy of Sciences, 36A, 249-264.
[9]
Poincare, H. (1905) Lecons de Mécanique Céleste. Gauthier-Villars, Paris, 1.
