On stability of a collinear libration point in the planar circular restricted photogravitational three-body problem in the cases of first and second order resonances

Abstract

We deal with the planar circular photogravitational three-body problem. That is, we consider the motion of a particle under influence of gravitational and radiation forces acting from two bodies, which move in circular orbits. The stability of collinear point L1 , which located on the line between the bodies, is investigated. By using the method of normal forms and applying theorems of KAM theory we perform a nonlinear stability study for parameter values corresponding to the cases of first and second order resonances. Rigorous conclusions on instability and stability in the sense of Lyapunov have been obtained.