Advertisement

Few-Body Systems

, Volume 56, Issue 1, pp 29–40 | Cite as

Effect of Oblateness, Radiation and a Circular Cluster of Material Points on the Stability of Equilibrium Points in the Restricted Four-Body Problem

  • Babatunde J. Falaye
Article

Abstract

Within the framework of restricted four-body problem, we study the motion of an infinitesimal mass by assuming that the primaries of the system are radiating-oblate spheroids surrounded by a circular cluster of material points. In our model, we assume that the two masses of the primaries m 2 and m 3 are equal to μ and the mass m 1 is 1−2μ. By using numerical approach, we have obtained the equilibrium points and examined their linear stability. The effect of potential created by the circular cluster and oblateness coefficients for the more massive primary and the less massive primary, on the existence and linear stability of the libration point have been critically examine via numerical computation. The stability of these points examined shows that the collinear and the non-collinear equilibrium points are unstable. The result presented in this paper have practical application in astrophysics.

Keywords

Equilibrium Point Linear Stability Material Point Libration Point Collinear Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Singh J., Taura J.J.: Effects of zonal harmonics and a circular cluster of material points on the stability of triangular equilibrium points in the R3BP. Astrophys. Space Sci. 350, 127 (2014)ADSCrossRefGoogle Scholar
  2. 2.
    Singh J., Taura J.J.: Combined effect of oblateness, radiation and a circular cluster of material points on the stability of triangular liberation points in the R3BP. Astrophys Space Sci. 351, 499 (2014)ADSCrossRefGoogle Scholar
  3. 3.
    Baltagiannis A.N., Papadakis K.E.: Families of periodic orbits in the restricted four-body problem. Astrophys. Space Sci. 336, 357 (2011)ADSCrossRefMATHGoogle Scholar
  4. 4.
    Kumari R., Kushvah B.S.: Stability regions of equilibrium points in restricted four-body problem with oblateness effects. Astrophys. Space Sci. 349, 693 (2014)ADSCrossRefGoogle Scholar
  5. 5.
    Papadouris J.P., Papadakis K.E.: Equilibrium points in the photogravitational restricted four-body problem. Astrophys. Space Sci. 344, 21 (2013)ADSCrossRefMATHGoogle Scholar
  6. 6.
    Alvarez, M., Vidal C.: Dynamical aspects of an equilateral restricted four-body problem. Math. Prob. Eng. doi: 10.1155/2009/181360
  7. 7.
    Radzievskii V.V.: The restricted three-body problem including radiation pressure. Astron. J. 27, 250 (1950)MathSciNetGoogle Scholar
  8. 8.
    Miyamoto M., Nagai R.: Three-dimensional models for the distribution of mass in galaxies. Publ. Astron. Soc. Jpn. 27, 533 (1975)ADSGoogle Scholar
  9. 9.
    Peter I.D., Lissauer J.J.: Planetary Science. Cambridge University Press, New York (2001)Google Scholar

Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  1. 1.Applied Theoretical Physics Division, Department of PhysicsFederal University LafiaLafiaNigeria

Personalised recommendations