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Journal of Dynamical Systems and Geometric Theories

(Since 2002)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X

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Journal of Dynamical Systems and Geometric Theories
Open Access Article

On the stability of the triangular points in the relativistic R3BP with a bigger triaxial primary

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pp. 119–136Vol. 14Issue 2July 2016DOI: 10.1080/1726037X.2016.1250499XML
Received:
21 Aug 2015
Accepted:
06 Jan 2016
Published Online:
28 Oct 2016
Article type:
Article
Language:
EN
Article no.:
1726037X.2016.1250499
Pages:
119–136

Abstract

This paper studies the motion of a third body (test particle) in the vicinity of the triangular points L4,5 by considering the more massive as a triaxial body in the frame work of the relativistic restricted three-body problem (R3BP). It is seen that the positions and stability of the triangular points are affected by both relativistic and triaxiality factors. It turns out both the coordinates of the infinitesimal mass axe affected. It is seen that for these points, the range of stability region increases or decreases according as p>0 or p

Keywords

Celestial MechanicsTriaxialityRelativityR3BP

Subject Classifications

70F15

References

  1. E.I.Abouelmagd, S.M.El-Shaboury, Periodic orbits under combined effects of oblateness and radiation in the restricted problem of three bodies . Astrophys Space Sci. 341 , 331 – 341 ( 2012 ). doi: 10.1007/s10509-012-1093-7
  2. K.B.Bhatnagar, P.P.Hallan, Existence and stability of L4,5 in the relativistic restricted three-body problem . Celest. Mech. Dyn. Astron. 69 , 271 – 281 ( 1998 ). doi: 10.1023/A:1008271021060
  3. V.A.Brumberg, Relativistic Celestial Mechanics . Moscow, Nauka , 1972 .
  4. V.A.Brumberg, Essential Relativistic Celestial Mechanics . Adam Hilger Ltd , New York, 1991 .
  5. A.Chenciner, Scholarpedia , 2111 ( 2007 ).
  6. C.N.Douskos, E.A.Perdios, On the stability of equilibrium points in the relativistic restricted three-body problem , Celest. Mech. Dyn. Astron. 82 , 317 – 321 ( 2002 ). doi: 10.1023/A:1015296327786
  7. S.M.El-Shaboury, M.O.Shaker, A.E.El-Dessoky, M.A.Tantawy, The libration points of axissymmetric satellite in the gravitational field of two triaxial rigid body , Earth-Moon-Planets 52 , 69 – 81 ( 1991 ). doi: 10.1007/BF00113832
  8. S.M.El-Shaboury, M.O.Shaker, M.A.El-Tantawy, Eulerian libration points of restricted problem of three oblate spheroid , Earth-Moon Planets 63 : 23 – 28 ( 1993 ). doi: 10.1007/BF00572136
  9. A.Elipe, S.Ferrer, On the equilibrium solution in the circular plannar restricted three rigid bodies problem , Celest. Mech. 37 , 59 – 70 ( 1985 ). doi: 10.1007/BF01230341
  10. P.P.Hallan, S.Jain, K.B.Bhatnagar, Non linear stability of L4 in the restricted three-body problem when the primaries are triaxial rigid bodies . 32 ( 3 ), 413 – 445 ( 2001 ).
  11. L.Iorio, An assessment of the symmetric uncertainty in present and future tests of the Lense-Thirring effect with satellite Laser ranging : Space Science Reviews 148 ( 1–4 ), 363 – 381 ( 2009 ). doi: 10.1007/s11214-008-9478-1
  12. L.Iorio, Orbital motions as gradiometers for post-Newtonian tidal effects , Front. Astron. Space. Sci. Vol 1 ( 3 ) ( 2014 ).
  13. D.A.Katour, F.A.AbdEl-salam, M.O.Shaker, Relativistic restricted three-body problem with oblateness and photo-gravitational corrections to triangular equilibrium points . Astrophys Space Sci. 351 ( 1 ), 143 – 149 ( 2014 ). doi: 10.1007/s10509-014-1826-x
  14. M.Khanna, K.B.Bhatnagar, Existence and stability of libration points in the restricted three-body problem when the smaller primary is a triaxial rigid body and the bigger one an oblate spheroid , Indian . J. pure Appl. Math. 7 , 721 – 733 ( 1999 ).
  15. S.W.McCuskey, Introduction to celestial mechanics . Addison-Wesley , New York, 1963 .
  16. C.W.Misner, K.S.Thorne, J.A.wheeler, Gravitation, freeman , New York, 1973 .
  17. G.Renzetti, Exact geodesic precession of the orbit of two-body gyroscope in geodesic motion about a third mass , Earth-Moon and Planets 109 ( 1–4 ), 55 – 59 ( 2012 ). doi: 10.1007/s11038-012-9402-2
  18. R.K.Sharma, Z.A.Taqvi, K.B.Bhatnagar, Existence and stability of the libration points in the restricted three-body problem when the primaries are triaxial rigid bodies and source of radiations , Indian J. Pure Appl. Math. 32 ( 7 ), 981 – 944 ( 2001 ).
  19. R.K.Sharma, Z.A.Taqvi, K.B.Bhatnagar, Existence and stability of the libration points in the restricted three-body problem when the primaries are triaxial rigid bodies , Celest. Mech. Dyn. Astron. 79 , 119 – 133 ( 2001 ). doi: 10.1023/A:1011168605411
  20. J.Singh, The equilibrium points in the perturbed R3BP with triaxial and luminous primaries , Astrophys Space Sci. 346 , 41 – 50 ( 2013 ). doi: 10.1007/s10509-013-1420-7
  21. P.V.SubbaRao, R.K.Sharma, A note on the stability of the triangular points of equilibrium in the restricted three-body problem , Astron. Astrophys 43 , 381 – 383 ( 1975 ).
  22. V.Szebehely, Theory of orbits, The restricted problem of three-bodies . Academic Press . New York, 1967 .
  23. M.Valtonen, H.Karttunen, The three-body problem , Cambridge University Press , 2006 .
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