On the stability of L4,5 in the perturbed relativistic R3BP with a triaxial bigger primary

 
 
 
  • Abstract
  • Keywords
  • References
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  • Abstract


    In the present paper, we endeavor to study the stability of triangular points under the influence of small perturbations in the Coriolis and centrifugal forces, together with the triaxiality of the bigger primary in the framework of the relativistic R3BP. It is observed that the locations of these points are affected by the relativistic factor, triaxiality and a small perturbation in the centrifugal force, but are unaffected by that of the Coriolis force. It is also seen that for these points the range of stability region increases or decreases according as equation (14) without is greater or less than zero.


  • Keywords


    Celestial Mechanics; Perturbation; Relativity; Triaxiality; R3BP.

  • References


      [1] Szebehely V (1967), Theory of orbits. The restricted problem of three- bodies. Academic Press. New York.

      [2] Wintner A (1941),The Analytical foundations of celestial mechanics, Princeton University press, Princeton

      [3] Contopolous G (2002), Order and Chaos in Dynamical Astronomy Spring, Berlin. http://dx.doi.org/10.1007/978-3-662-04917-4.

      [4] Szebehely V (1967), Stability of the points of equilibrium in the restricted problem, Astronomical Journal, 27, 7-9. http://dx.doi.org/10.1086/110195.

      [5] Bhatnagar KB& Hallan PP (1978), Effect of perturbations in the Coriolis and centrifugal forces on the stability of libration points in restricted problem,Celestial Mechanics, 18,105-112. http://dx.doi.org/10.1007/BF01228710.

      [6] AbdulRaheem A & Singh J (2006), Combined effects of perturbations, radiation and oblateness on the stability of equilibrium points in the restricted three-body problem,Atronomical Journal,131, 1880-1885. http://dx.doi.org/10.1086/499300.

      [7] Singh J &Begha JM (2011), Stability of equilibrium points in the generalized perturbed restricted three-body problem, Astrophysics & Space Science, 331, 511-519. http://dx.doi.org/10.1007/s10509-010-0464-1.

      [8] Abouelmagd E I,Asiri HM & Sharaf MA (2013), The effects of oblateness in the perturbed restricted three-body problem, Meccanica,48, 2479-2490. http://dx.doi.org/10.1007/s11012-013-9762-3.

      [9] Singh J (2013), the equilibrium points in the perturbed R3BP with triaxial and luminous primaries Astrophys & Space Science, 346, 41-50. http://dx.doi.org/10.1007/s10509-013-1420-7.

      [10] Brumberg VA (1972), Relativistic Celestial Mechanics. Moscow, Nauka.

      [11] Brumberg VA (1991), Essential Relativistic Celestial Mechanics. Adam Hilger Ltd, New York.

      [12] Bhatnagar KB &Hallan PP (1998), Existence and stability of L 4, 5 in the relativistic restricted three-body problem. Celestial Mechanics &Dynamical Astronomy, 69, 271-281. http://dx.doi.org/10.1023/A:1008271021060.

      [13] Douskos CN &Perdios EA (2002), “On the stability of equilibrium points in the relativistic restricted three-body problem”, Celestial Mechanics &Dynamical Astronomy, 82, 317-321. http://dx.doi.org/10.1023/A:1015296327786.

      [14] Katour DA, Abd El-Salam FA & Shaker MO (2014), Relativistic restricted three-body problem with oblateness and photo-gravitational corrections to triangular equilibrium points, Astrophysics & Space Science, 351(1), 143-149. http://dx.doi.org/10.1007/s10509-014-1826-x.

      [15] Singh J & Bello N (2014), Motion around L4 in the perturbed relativistic R3BP, Astrophysics & Space Science, 351(2), 491-497. http://dx.doi.org/10.1007/s10509-014-1870-6.

      [16] Singh J & Bello N (2014), Effect of perturbations in the Coriolis and centrifugal forces on the stability of L4 in the relativistic R3BP, Journal of Astrophysics &Astronomy, 35 (4) 701-713. http://dx.doi.org/10.1007/s12036-014-9307-8.

      [17] McCuskey SW (1963), Introduction to celestial mechanics, Addison, Wesley.


 

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Article ID: 6251
 
DOI: 10.14419/ijaa.v4i2.6251




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