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Astrophysics and Space Science

, Volume 351, Issue 2, pp 491–497 | Cite as

Motion around L4 in the perturbed relativistic R3BP

  • Jagadish Singh
  • Nakone Bello
Original Article

Abstract

This paper studies the motion of a test particle (infinitesimal mass) in the neighborhood of the triangular point L4 in the framework of the perturbed relativistic restricted three-body problem (R3BP). The problem is perturbed in the sense that a small perturbation is given to the centrifugal force. It is found that the position and stability of the triangular point are affected by both the relativistic factor and a small perturbation in the centrifugal force.

Keywords

Celestial mechanics Perturbation Centrifugal force Relativity R3BP 

References

  1. AbdulRaheem, A., Singh, J.: Astron. J. 131, 1880 (2006) ADSCrossRefGoogle Scholar
  2. Ahmad, M.K., Abd El-Salam, F.A., Abd El-Bar, S.E.: Am. J. Appl. Sci. 3, 1993 (2006) CrossRefGoogle Scholar
  3. Bhatnagar, K.B., Hallan, P.P.: Celest. Mech. 18, 105 (1978) ADSCrossRefGoogle Scholar
  4. Bhatnagar, K.B., Hallan, P.P.: Celest. Mech. Dyn. Astron. 69(3), 271 (1998) ADSCrossRefGoogle Scholar
  5. Brumberg, V.A.: Relativistic Celestial Mechanics. Moscow, Nauka (1972) zbMATHGoogle Scholar
  6. Brumberg, V.A.: Essential Relativistic Celestial Mechanics. Hilger, New York (1991) zbMATHGoogle Scholar
  7. Contopoulos, G.: In: Kotsakis, D. (ed.) In Memoriam D. Eginitis, p. 159 (1976). Athen Google Scholar
  8. Contopoulos, G.: Order and Chaos in Dynamical Astronomy, p. 543. Springer, Berlin (2002) CrossRefzbMATHGoogle Scholar
  9. Douskos, C.N., Perdios, E.A.: Celest. Mech. Dyn. Astron. 82, 317 (2002) ADSCrossRefGoogle Scholar
  10. Ichita, T., Yamada, K., Asada, H.: Phys. Rev. D 83, 084026 (2011) ADSCrossRefGoogle Scholar
  11. Klioner, S.A.: Astron. J. 125, 1580 (2003) ADSCrossRefGoogle Scholar
  12. Krefetz, E.: Astron. J. 72, 471 (1967) ADSCrossRefGoogle Scholar
  13. Lucas, F.W.: Z. Naturforsch. 58a, 13 (2003) Google Scholar
  14. Maindl, T.I., Dvorak, R.: Astron. Astrophys. 290, 335 (1994) ADSGoogle Scholar
  15. Ragos, O., Perdios, E.A., Kalantonis, V.S., Vrahatis, M.N.: Nonlinear Anal. 47, 3413 (2001) MathSciNetCrossRefGoogle Scholar
  16. Singh, J.: Astrophys. Space Sci. 132, 123 (2009) Google Scholar
  17. Singh, J.: Astrophys. Space Sci. 332, 331 (2011) ADSCrossRefGoogle Scholar
  18. Singh, J.: Astrophys. Space Sci. 346, 41 (2013) ADSCrossRefGoogle Scholar
  19. Singh, J., Begha, J.M.: Astrophys. Space Sci. 331, 511 (2011) ADSCrossRefGoogle Scholar
  20. SubbaRao, P.V., Sharma, R.K.: Astron. Astrophys. 43, 381 (1975) ADSGoogle Scholar
  21. Szebehely, V.: Theory of Orbits. The Restricted Problem of Three Bodies. Academic Press, New York (1967a) zbMATHGoogle Scholar
  22. Szebehely, V.: Astron. J. 27, 7 (1967b) ADSMathSciNetCrossRefGoogle Scholar
  23. Will, C.M.: Theory and Experiment in Gravitational Physics. Cambridge University Press, Cambridge (1993) CrossRefzbMATHGoogle Scholar
  24. Wintner, A.: The Analytical Foundations of Celestial Mechanics, p. 372. Princeton University press, Princeton (1941) zbMATHGoogle Scholar
  25. Yamada, K., Asada, H.: Phys. Rev. D 86, 124029 (2012) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceAhmadu Bello UniversityZariaNigeria
  2. 2.Department of Mathematics, Faculty of ScienceUsmanu Danfodiyo UniversitySokotoNigeria

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