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 IJAA  Vol.6 No.3 , September 2016
Halo Orbits around Sun-Earth L1 in Photogravitational Restricted Three-Body Problem with Oblateness of Smaller Primary
Abstract: This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. Both the terms due to oblateness of the smaller primary are considered. Numerical as well as analytical solutions are obtained around the Lagrangian point L1, which lies between the primaries, of the Sun-Earth system. A comparison with the real time flight data of SOHO mission is made. Inclusion of oblateness of the smaller primary can improve the accuracy. Due to the effect of radiation pressure and oblateness, the size and the orbital period of the halo orbit around L1 are found to increase.
Cite this paper: Chidambararaj, P. and Sharma, R. (2016) Halo Orbits around Sun-Earth L1 in Photogravitational Restricted Three-Body Problem with Oblateness of Smaller Primary. International Journal of Astronomy and Astrophysics, 6, 293-311. doi: 10.4236/ijaa.2016.63025.
References

[1]   Farquhar, R. (1968) The Control and Use of Libration Point Satellites. Ph.D Thesis, MIT, California.

[2]   Breakwell, J.V. and Brown, J.V. (1979) “Halo” Family of 3-Dimensional Periodic Orbits in the Earth-Moon Restricted 3-Body Problem. Celestial Mechanics, 20, 389-404.
http://dx.doi.org/10.1007/BF01230405

[3]   Richardson, D. (1980) Analytical Construction of Periodic Orbits about the Collinear Points. Celestial Mechanics, 22, 241-253.
http://dx.doi.org/10.1007/BF01229511

[4]   Howell, K.C. (1984) Three-Dimensional, Periodic, “Halo” Orbits. Celestial Mechanics, 32, 53-71.
http://dx.doi.org/10.1007/BF01358403

[5]   Howell, K.C. and Pernicka, H.J. (1988) Numerical Determination of Lissajous Trajectories in the Restricted Three-Body Problem. Celestial Mechanics, 41, 107-124, 1988.
http://dx.doi.org/10.1007/BF01238756

[6]   Folta, D. and Richon, K. (1998) Libration Orbit Mission Design at L2: A MAP and NGST Perspective. AIAA Paper, AIAA 98-4469.
http://dx.doi.org/10.2514/6.1998-4469

[7]   Howell, K.C., Beckman, M., Patterson, C. and Folta, D. (2006) Representations of Invariant Manifolds for Applications in Three-Body Systems. The Journal of the Astronautical Sciences, 54, 25 p.

[8]   Radzievskii, V. (1950) The Restricted Problem of Three Bodies Taking Account of Light Pressure. Astronomicheskii Zhurnal, 27, 250.

[9]   Dutt, P. and Sharma, R.K. (2011) Evolution of Periodic Orbits in the Sun-Mars System. Journal of Guidance, Control and Dynamics, 34, 635-644.
http://dx.doi.org/10.2514/1.51101

[10]   Sharma, R.K. and Subba Rao, P.V. (1976) Stationary Solutions and Their Characteristic Exponents in the Restricted Three-Body Problem When the More Massive Primary Is an Oblate Spheroid. Celestial Mechanics, 13, 137-149.
http://dx.doi.org/10.1007/BF01232721

[11]   Sharma, R.K. (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 Science, 135, 271-281.
http://dx.doi.org/10.1007/BF00641562

[12]   Tiwary, R.D. and Kushvah, B.S. (2015) Computation of Halo Orbits in the Photogravitational Sun-Earth System with Oblateness. Astrophysics and Space Science, 357, 1-16.
http://dx.doi.org/10.1007/s10509-015-2243-5

[13]   Szebehely, V. (1967) Theory of Orbits. Academic Press, New York.

[14]   Koon, W.S., Lo, M.W., Marsden, J.E. and Ross, S. (2008) Dynamical Systems, the Three-Body Problem and Space Mission Design.
http://www.cds.caltech.edu/~marsden/volume/missiondesign/KoLoMaRo_DMissionBk.pdf

[15]   Thurman, R. and Worfolk, P.A. (1996) The Geometry of Halo Orbits in the Circular Restricted Three Body Problem. Univ. Minnesota, Minneapolis, MN, Tech. Rep. GCG 95.

[16]   Eapen, R.T. and Sharma, R.K. (2014) A Study of Halo Orbits at the Sun-Mars L1 Lagrangian Point in the Photogravitational Restricted Three-Body Problem. Astrophysics and Space Science, 352, 437-441.
http://dx.doi.org/10.1007/s10509-014-1951-6

 
 
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