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.
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
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.
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.
![\"\"](\"Edit_7f0ba34e-c287-4d6d-ba69-85428441b262.bmp\")
(h is energy constant; μ is mass ratio of the two primaries; ![\"\"](\"Edit_9e1dd54f-b316-4e82-a993-27e69e0401d0.bmp\")
are parameters of triaxial rigid bodies and are ![\"\"](\"Edit_29589071-a72b-4daf-8c88-f5b4f68b8184.bmp\")
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.
