# Advances in Astrophysics

### Periodic Orbits in the Photogravitational Elliptic Restricted Three-Body Problem

Download PDF (931.7 KB) PP. 154 - 170 Pub. Date: August 1, 2018

### Author(s)

**Y. SHARON RUTH**^{*}

Department of Aerospace Engineering, Karunya Institute of Technology and Sciences, Coimbatore, 641114, India**RAM KRISHAN SHARMA**^{*}

Department of Aerospace Engineering, Karunya Institute of Technology and Sciences, Coimbatore, 641114, India

### Abstract

### Keywords

### References

[1] Danby, (1964). "Stability of the Triangular Points in the Elliptic Restricted Problem", The Astronomical Journal, 69, No. 2

[2] R.K.Sharma (1987). "The Linear stability of Libration Points of the Photogravitational Restricted Three-Body Problem when the smaller primary is an oblate spheroid", Astrophysics and Space Sciences 135 (1987) 271-281.

[3] S.K.Sahoo and B.Ishwar (2000). "Stability of collinear equilibrium points in the generalized photogravitational elliptic restricted three-body problem". Astronomical Society of India,28, 579-586.

[4] J. Singh, A. Umar (2012). "On out of plane equilibrium points in the ER3BP with radiating and oblate primaries". Astrophys, Space Science, 344:13-19.

[5] P.V. Subba Rao and R.K. Sharma (1975). "A note on the Stability of the Triangular Points of the Equilibrium in

[6] R.K.Sharma and P.V.Subba Rao, "Stationary solutions and their characteristic exponents in the restricted threebody problem when the more massive primary is an oblate spheroid". Celestial Mechanics 13 (1976) 137-149.

[7] E.A.Grebenikov, "On the Stability of The Lagrangian Triangle Solutions of the Restricted Elliptic Three Body Problem," Soviet Astronomy- AJ, 1964, vol 8, No.3.

[8] C. D. Murray and S. F. Dermott. (1999). "Solar System Dynamics", Cambridge University Press, Cambridge.

[9] R. A. Broucke (1969), "Periodic orbits in the Elliptic Restricted Three-body problem". Technical Report 32-1360.

[10] Szebehely, V.:1967, Theory of Orbits, "The Restricted Problem of Three bodies", Academic Press, New York..

[11] R. A. Broucke, “Stability of Periodic Orbits in the Elliptic Restricted Three-body Problem”, Paper 68-086, presented at the AAS/AIAA Astrodynamics Specialist Conference, Jackson, Wyo., Sept- 3-5,1968.

[12] K. T. Alfriend and R. H. Rand. (1969)." Stability of the Triangular Points in the Elliptic Restricted Problem of Three bodies", AIAA Journal, 7, No 6, 1024-1028.

[13] V. Kumar, R. K. Choudhary, Non linear stability of the triangular libration points for the photogravitational elliptic restricted problem of three bodies, Celestial Mech. and Dyn. Astro.,48, No. 4(1990), 299-317.

[14] V. V. Markellos, E. Perdios and P. Labropoulou (1992)."Linear stability of the triangular equilibrium points in the photogravitational elliptic restricted problem I", Astrophysics and Space Science 194, 207-213.

[15] Raheem & Singh. (2006). "Combined effects of perturbations, radiation, and oblateness on the stability of equilibrium points in the restricted three-body problem." The Astronomical Journal, 131:1880–1885, 2006 March.

[16] A. Narayan and C. R. Kumar. (2011). "Stability of Triangular Equilibrium points in elliptical restricted threebody problem under the effects of photogravitational and oblateness of primaries", International Journal of Pure and Applied Mathematics, Volume 70 No. 5 2011, 735-754.

[17] A. Bennett. (1965), "Analytical determination of characteristic exponents", The Boeing Company Huntsville, Alabama, AIAA Paper, NO. 65-685.

[18] A. Narayan and N.Singh (2015), "Characteristics Exponents of the Triangular Solutions in the Elliptical Restricted Three-Body Problem under Radiating Primaries", Differ Equ Dyn Syst 24(3):329-–343.

[19] R. Rajnai, L. Nagy and B. Erdi. (2002), "Frequencies and resonances around L4 in the elliptic restricted threebody problem", Mon. Not. R. Astron. Soc. 000, 1–10.

[20] P. Gurfil, D. Meltzer (2006), "Stationkeeping on unstable orbits: Generalization to the elliptic restricted threebody problem", The Journal of the Astronautical Sciences, Vol. 54, 29-51.

[21] J. Singh and A. Umar (2014). "The collinear libration points in the elliptic restricted three-body problem with a triaxial primary and an oblate secondary", Astronomy and Astrophysics 4, 391-398.

[22] A. G. Anderlecht, "Tadpole orbits in the L4/L5 region: Construction and links to other families of periodic orbits", Thesis (2016), Purdue University, West Lafayette, Indiana.

[23] E.I. Abouelmagd et al. (2016) "Periodic orbits around the collinear libration points", Journal of Nonlinear Science and Applications, 9, 1716-1727.

[24] V. V. Radzievsky (1950). "The restricted problem of three bodies taking account of light pressure", Astron Zh, 27, pp.250.

[25] J. H. Poynting (1903) "The pressure of light, The Inquirer", pp. 195-196.

[26] J. M. A. Danby., (1988), "Fundamentals of Celestial Mechanics", (pg 346).

[27] S. Kumar, S. and B. Ishwar (2009), "Solutions of Generalized Photogravitational Elliptic Restricted Three-Body Problem." AIP Conference Proceedings, 1146, 456-460.