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Astrophysics and Space Science

, Volume 326, Issue 2, pp 305–314 | Cite as

Stability of the photogravitational restricted three-body problem with variable masses

  • Jagadish Singh
  • Oni Leke
Original Article

Abstract

This paper investigates the stability of equilibrium points in the restricted three-body problem, in which the masses of the luminous primaries vary isotropically in accordance with the unified Meshcherskii law, and their motion takes place within the framework of the Gylden–Meshcherskii problem. For the autonomized system, it is found that collinear and coplanar points are unstable, while the triangular points are conditionally stable. It is also observed that, in the triangular case, the presence of a constant κ, of a particular integral of the Gylden–Meshcherskii problem, makes the destabilizing tendency of the radiation pressures strong. The stability of equilibrium points varying with time is tested using the Lyapunov Characteristic Numbers (LCN). It is seen that the range of stability or instability depends on the parameter κ. The motion around the equilibrium points L i (i=1,2,…,7) for the restricted three-body problem with variable masses is in general unstable.

Keywords

Celestial mechanics Variable masses 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceAhmadu Bello UniversityZariaNigeria

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