Abstract
This paper investigates the motion of a test particle around the out-of-plane equilibrium points in the circular photogravitational restricted three-body problem when the effect of radiation pressure from the smaller primary and its Poynting-Robertson (P-R) drag are taken into account, and the bigger primary is modeled as an oblate spheroid. These points lie in the xz-plane almost directly above and below the center of the oblate primary. The equilibrium points are sought, and we observe that, there are two coordinate points L 6,7 which depend on the oblateness of the bigger primary, and the radiation pressure force and P-R drag of the smaller primary. The positions and linear stability of the problem are investigated both analytically and numerically for the binary system Cen X-4. The out-of-plane equilibrium points are found to be unstable in the sense of Lyapunov due to the presence of a positive real root.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
AbdulRaheem, A., Singh, J. 2006, Astron. J., 131, 1880–1885.
Alain Chenciner 2007, Scholarpedia, 2 (10), 2111.
Anand, S. P. S. 1965, Proceedings of the National Academy of Sciences of the United States of America, 54 (1), 23–26.
Arutyunyan, G. G., Sedrakyan, D. M., Chubaryan, É. V. 1971, Astrophysics, 7 (3), 274–280.
Boshkayev et al. 2013, The Astrophys. J., 762 (2), article id. 117, 14 pp.
Bruno, A. D. 1994, de Gruyter (1994).
Chernikov, Yu. A. 1970, Sov. Astron. A. J, 14, 175–176.
Damiani, C. et al. 2011, J. Atmos. Solar-Terrestrial Phys., 73, 241.
Das, M. K. et al. 2009, JAA, 30, 177–185.
Douskos, C. N., Markellos, V. V. 2006, A&A, 446, 357–360.
Ershkov, S. V. 2012, IJPAM, 78 (3).
Fienga, A. et al. 2014, arXiv: 1409.4932 [astro-ph.EP].
Fokker, A. D. 1921, Proceedings, 23, 729–738.
Gutzwiller, M. 1998, Moon–Earth–Sun Reviews of Modern Physics, 70 (2).
Hamilton, D. P., Burns, J. A. 1992, Icarus, 96, 43–64.
Hartle, James, B. 1967, Astrophys. J., 150, 1005.
Iorio, L. 2007a, AP&SS, 310 (1-2), 73–76.
Iorio, L. 2007b, AP&SS, 312 (3-4), 337–341.
Iorio, L. 2011, Physical Review D, 84 (12), 124001.
Iorio, L. 2013a, Classical and Quantum Gravity, 30 (19), article id 195011.
Iorio, L. et al. 2013b, Acta Astronautica, 91, 141–148.
Iorio, L. 2014, Frontiers in Astronomy and Space Sciences, 1 (3).
Jonker, P. G. et al. 2007, The Astrophysical Journal, 665, 147.
Kushvah, B. S. 2008, Ap&SS, 315, 231–241.
Kushvah, B. S. 2009, Res. Astron. Astrophys., 9, 1049–1060.
Kushvah, B. S, Sharma, J. P, Ishwar, B. 2007a, Bulletin of the Astronomical Society of India, 35, 319–338.
Kushvah, B. S, Sharma, J. P., Ishwar, B 2007c, Earth Moon and Planets, 101, 55–64.
Langer, N. et al. 2002, in: ASP Conf. Ser (2002) 252–261.
Murray, C. D. 1994, Icarus (1994), 122, 465–484.
Narayan, A. et al. 2015, IJAA, 3 (1), 8–16.
Nordvedt, K. 1968, Phys. Rev., 170 (5), 1186.
Oberti, P., Vienne, A. 2003, Astron. Astrophys., 397, 353–359.
Pinto, R. F. et al. 2011, Astrophys. J., 737, 72.
Pitjeva, E. V., Pitjev, N. P. 2012, Solar Syst. Res., 46, 78.
Pitjeva, E. V. Pitjev, N. P. 2014, Celest. Mech. Dyn. Astr., 119, 237.
Poynting, J. H. 1903, PTSLA, 202, 525–552.
Radzievsky, V. V. 1950, Astron Zh, 27, 250.
Ragos, O. et al. 2001, Nonlinear Analysis, 47, 3413–3418.
Ragos, O., Zafiropoulos, F. A. 1995, A&A, 300, 568.
Renzetti, G. 2012, Earth, Moon, and Planets, 109 (1–4), 55–59.
Renzetti, G. 2013, JOAA, 34 (4), 341–348.
Renzetti, G. 2014, AP&SS, 352 (2), 493–496.
Robertson, H. P. 1937, MNRAS, 97, 423–438.
Rozelot, J. P., Fazel, Z. 2013, Solar Physics, 287, 161–170.
Schuerman, D. W. 1980, Astrophys J, 238, 337–342.
Shahbaz, T. et al. 2014, MNRAS.
Shankaran et al. 2011, Ap&SS, 332, 115.
Sharma, R. K. 1987, Ap&SS, 135, 271–281.
Sharma, R. K., SubbaRao, P. V. 1967, Celest. Mech., 13, 137–149.
Singh Jagadish 2009, The Astronomical Journal, 137, 3286–3292.
Singh Jagadish 2012, Ap&SS, 342, 303.
Singh, J., Mohammed, H. L. 2012, E.M.P, 109, 1–11.
Singh, J., Umar, A. 2012, The Astronomical Journal, 143, 109.
Singh, J., Umar, A. 2013, Ap&SS, 341, 349.
Singh, J., Amuda, T. O. 2014, Ap&SS, 350, 119–126.
Singh, J., Leke, O. 2014, Ap&SS, 350, 109–117.
Soffel, M. et al. 1988, Celestial Mechanics, 42 (1–4), 81–89.
Valtonen, M., Karttunen, H. 2006, Cambridge University Press.
Xuetang, Z., Lizhong, Y. 1993, Chinese Phys. Lett., 10 (1), 61–64.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Singh, J., Amuda, T.O. Out-of-Plane Equilibrium Points in the Photogravitational CR3BP with Oblateness and P-R Drag. J Astrophys Astron 36, 291–305 (2015). https://doi.org/10.1007/s12036-015-9336-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12036-015-9336-y