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 IJAA  Vol.6 No.1 , March 2016
Periodic Orbits in the Photogravitational Restricted Problem When the Primaries Are Triaxial Rigid Bodies
Abstract: We have studied periodic orbits generated by Lagrangian solutions of the restricted three-body problem when both the primaries are triaxial rigid bodies and source of radiation pressure. We have determined periodic orbits for different values of  (h is energy constant; μ is mass ratio of the two primaries; are parameters of triaxial rigid bodies and are radiation parameters). These orbits have been determined by giving displacements along the tangent and normal at the mobile co-ordinates as defined in our papers (Mittal et al. [1]-[3]). These orbits have been drawn by using the predictor-corrector method. We have also studied the effect of triaxial bodies and source of radiation pressure on the periodic orbits by taking fixed value of μ.
Cite this paper: Jain, P. , Aggarwal, R. , Mittal, A. and Abdullah, &. (2016) Periodic Orbits in the Photogravitational Restricted Problem When the Primaries Are Triaxial Rigid Bodies. International Journal of Astronomy and Astrophysics, 6, 111-121. doi: 10.4236/ijaa.2016.61009.
References

[1]   Mittal, A., Aggarwal, R. and Bhatnagar, K.B. (2011) Periodic Orbits around L4in the Photogravitational Restricted Problem with Oblate Primaries.WSEAS 6th International Conference Proceedings on Optics Astrophysics and Astrology,Article ID: 650927.

[2]   Mittal, A., Iqbal, A. and Bhatnagar, K.B. (2008) Periodic Orbits Generated by Lagrangian Solutions of the Restricted Three-Body Problem When One of the Primaries Is an Oblate Body.Astrophysics and Space Science, 319, 63-73.
http://dx.doi.org/10.1007/s10509-008-9942-0

[3]   Mittal, A., Iqbal, A. and Bhatnagar, K.B. (2009) Periodic Orbits in the Photogravitational Restricted Problem with the Smaller Primary an Oblate Body.Astrophysics and Space Science, 323, 65-73.
http://dx.doi.org/10.1007/s10509-009-0038-2

[4]   Charlier, C.L. (1899) Die Mechanik des Himmels.Walter de Gryter and Co., Berlin and Leipzig.

[5]   Plummer, H.C. (1901) On Periodic Orbits in the Neighborhood of Centres of Liberation. Monthly Notices of the Royal Astronomical Society, 62, 6-17.
http://dx.doi.org/10.1093/mnras/62.1.6

[6]   Riabov, U.A. (1952) Preliminary Orbits Trojan Asteroids. Soviet Astronomy, 29, 5.

[7]   Szebehely, V. (1967) Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press, NewYork.

[8]   Deprit, A. and Henrard, J. (1968)Advances in Astronomy and Astrophysics.Academic Press, NewYork, London.

[9]   Markeev, A.P. and Sokolsky, A.G. (1975) Investigation of Periodic Motions near the Lagrangian Solutions of Restricted Three-Body Problem.Publ. Inst. of Appl. Math. Acad. Sci., Moscow.

[10]   Hadjidemetriou, J.D. (1984) Periodic Orbits.Celestial Mechanics,34, 379-393.
http://dx.doi.org/10.1007/BF01235816

[11]   Karimov, S.R. and Sokolsky, A.G. (1989) Periodic Motions Generated by Lagrangian Solutions of the Circular Restricted Three-Body Problem.Celestial Mechanics and Dynamical Astronomy, 46, 335-381.
http://dx.doi.org/10.1007/BF00051487

[12]   Taqvi, Z.A.A.R. and Iqbal, A. (2006) Non-Linear Stability of L4 in the Restricted Three-Body Problem for Radiated Axes Symmetric Primaries with Resonances. Bulletin of Astronomical Society of India,35, 1-29.

[13]   Abouelmagd, E.I., Alhothuali, M.S., Guirao, J.L.G. and Malaikah, H.M. (2015) Periodic and Secular Solutions in the Restricted Three-Body Problem under the Effect of Zonal Harmonic Parameters. Applied Mathematics & Information Sciences, 9, 1659-1669.

[14]   Perdios, E.A., Kalantonis, V.S.,Perdiou, A.E.andNikaki, A.A. (2015) Equilibrium Points and Related Periodic Motions in the Restricted Three-Body Problem with Angular Velocity and Radiation Effects. Advances in Astronomy, 2015, 1-21.

[15]   Jain, M. and Aggarwal, R. (2015) A Study of Non-Collinear Libration Points in Restricted Three-Body Problem with Stokes Drag Effect When Smaller Primary Is an Oblate Spheroid. Astrophysics and Space Science, 358, 1-8.

 
 
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