Few-Body Systems

, Volume 57, Issue 1, pp 83–91 | Cite as

Equilibrium Points in the Restricted Four-Body Problem with Radiation Pressure

  • Jagadish Singh
  • Aguda Ekele Vincent


This paper studies numerically the photogravitational version of the restricted four-body problem, where an infinitesimal particle is moving under the gravitational attraction and radiation pressure of three bodies much bigger than the particle, the primaries. The fourth body does not affect the motion of the three bodies. These bodies are always at the vertices of an equilateral triangle (Lagrange configuration). We consider all the primary bodies (m 1, m 2, m 3) as radiation sources with radiation factors of the two bodies (m 2 and m 3) equal. In this paper we suppose the masses of the three primary bodies are equal. It is found that the involved parameters influenced the positions of the equilibrium points. The linear stability of the relative equilibrium solutions is also studied and all these points are unstable.


Equilibrium Point Radiation Pressure Equilateral Triangle Collinear Point Primary Body 
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  1. 1.
    Baltagiannis, A.N., Papadakis, K.E.: Equilibrium points and their stability in the restricted four-body problem. Int. J. Birfucat Chaos. Appl. Sci. Eng. 21, 2179–2193 (2011a)Google Scholar
  2. 2.
    Kalvouridis T.J.: The effect of radiation pressure on the particle dynamics in ring type N-body configurations. Earth Moon Planets 87, 87–102 (2001)CrossRefADSGoogle Scholar
  3. 3.
    Kalvouridis T.J, Arribas M., Elipe A.: Dynamical properties of the restricted four-body problem with radiation pressure. Mech. Res. Commun. 33, 811–817 (2006)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Kumar V., Choudhry R.K.: Linear stability and the resonance cases for the triangular libration points for the doubly photogravitational elliptic restricted problem of three bodies. Celest. Mech. Dyn. Astron. 46, 59–77 (1989)zbMATHCrossRefADSGoogle Scholar
  5. 5.
    Kunitsyn A.L., Polyakhova E.N.: The restricted photogravitational three-body problem. Astron. Astrophys. Trans. 6, 283–293 (1995)CrossRefADSGoogle Scholar
  6. 6.
    Luk’yanov L.G.: Stability of Coplanar libration points in the restricted photogravitational three-body problem. Sov. Astron. 31, 677–681 (1987)zbMATHMathSciNetADSGoogle Scholar
  7. 7.
    Markellos V.V., Perdios E., Papadakis K.E.: The stability of inner collinear equilibrium points in the photogravitational elliptic restricted problem. Astrophys. Space Sci. 199, 139–146 (1993)zbMATHCrossRefADSGoogle Scholar
  8. 8.
    Markellos V.V., Roy A.E., Velgakis M.J., Kanavos S.S.: A photogravitational Hill problem and radiation effects on Hill stability of orbits. Astrophys. Space Sci. 271, 293–301 (2000)zbMATHCrossRefADSGoogle Scholar
  9. 9.
    Papadouris J.P., Papadakis K.E.: Equilibrium points in the photogravitational restricted four-body problem. Astrophys. Space Sci. 344, 21–38 (2013)zbMATHCrossRefADSGoogle Scholar
  10. 10.
    Radzievskii V.V.: The restricted problem of three-bodies taking account of light pressure. Astron. J. 27, 250–256 (1950)MathSciNetGoogle Scholar
  11. 11.
    Radzievskii, V.V.: Zadacha dvuh gravitiruyoushih I izluchayoushih tel. Astron. J. 28, 363–372 (1951)Google Scholar
  12. 12.
    Radzievskii V.V.: The space photogravitational restricted three-body. Astron. J. 30, 265 (1953)MathSciNetGoogle Scholar
  13. 13.
    Ragos O., Zafiropoulos F.A.: A numerical study of the influence of the Poynting–Robertson effect on the equilibrium points of the photo-gravitational restricted three-body problem. Astron. Astrophys. 300, 568 (1995)ADSGoogle Scholar
  14. 14.
    Simmons J., McDonald A., Brown J.: The restricted 3-body problem with radiation pressure. Celest. Mech. 35, 145–187 (1985)zbMATHMathSciNetCrossRefADSGoogle Scholar
  15. 15.
    Singh J.: Combined effects of oblateness and radiation on the nonlinear stability of L4 in the restricted three-body problem. Astron. J. 137, 3286 (2009)CrossRefADSGoogle Scholar
  16. 16.
    Singh J., Leke O.: Stability of the photogravitational restricted three-body with variable masses. Astrophys. Space Sci. 326, 305 (2010)zbMATHCrossRefADSGoogle Scholar

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© Springer-Verlag Wien 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceAhmadu Bello UniversityZariaNigeria
  2. 2.Department of Mathematics and Statistics, School of TechnologyFederal Polytechnic, IdahIdahNigeria

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