# Advances in Astrophysics

### Effect of Oblateness of the More Massive Primary on Periodic Orbits in the Restricted Three-Body Problem

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### Author(s)

**A. Safiya Beevi**

Department of Mathematics, College of Engineering, Thiruvananthapuram - 695016, India**Ram Krishan Sharma**^{*}

Department of Aerospace Engineering, Karunya University, Coimbatore - 641114, Tamilnadu, India

### Abstract

### Keywords

### References

[1] E. Stromgren, “Connaissance Actualle des Orbites dans le Problem des Trois Corps” Publications and Minor communications of Copenhagen Observatory, Publication 100, Copenhagen University, Astronomical Observatory, Denmark, 1935.

[2] F. R. Moulton, “Periodic orbits”, Carnegie Institute of Washington Publications, No.161, pp. 299-324, 1920.

[3] G. H. Darwin, “Periodic orbits”, Scientific Papers, Cambridge University Press, Cambridge, Mass, Vol 4, 1911.

[4] R.A. Broucke, “Periodic orbits in the restricted three-body problem with Earth– Moon masses”. Jet Propulsion Lab. Technical Report, 32-1168, Pasadena, CA, 1968.

[5] V. G. Szebehely, “Theory of orbits”, Academic press, New York, 1967.

[6] S. W. McCuskey, “Introduction to Celestial Mechanics”, New-York: Addison – Wesley, 1963.

[7] A. H. Nayfeh, “Introduction to Perturbation Techniques”, John Wiley and Sons, Inc. New York, 1981.

[8] J. Guckenheimer and P. Holmes, “Nonlinear oscillations, dynamical systems, and bifurcations of vector fields”, Springer-Verlag, New York, 1983.

[9] J. W. Jordan, and P. Smith, “Nonlinear ordinary differential equations. An introduction to dynamical systems”, 3rd ed. Oxford University Press Inc., New York, 1999.

[10] J. Pelaez and M. Lara, “Periodic solutions in Electrodynamic Tethers on inclined orbits”, Journal of Guidance, Control, and Dynamics, vol. 26. no.3, pp. 395-406, 2003.

[11] S. S. Huang, “Preliminary study of orbits of interest for Moon Probes” Astron. J., vol. 67, pp 304-310, 1962.

[12] S. S. Huang and C. Wade Jr., “Preliminary study of periodic orbits of interest for Moon Probes. II”, Astron J., vol. 68, pp. 388-391, 1963.

[13] S. S. Huang, “A Series solution for some periodic orbits in the restricted three-body problem according to the perturbation method”, Technical Report, Goddard Space Flight Centre, NASA technical note, D-2488, 1964.

[14] E. I. Abouelmagd, M. S. Alhothuali, Juan L. G. Guirao, and H. M. Malaikah, “Periodic and secular solutions in the restricted three–body problem under the effect of zonal harmonic parameters”, Appl. Math. Inf. Sci., vol. 9, no. 4, pp. 1659-1669, 2015.

[15] R. K. Sharma and P. V. Subba Rao, “Stationary solutions and their characteristic exponents in the restricted three-body problem when the more massive primary is an oblate spheroid” Celestial Mechanics, vol. 13, pp. 137- 149,1976.