Nonlinear stability analysis of a collinear libration point in the planar circular restricted photogravitational three-body problem

Abstract

Abstract We investigate the problem on stability of collinear libration point in the photogravitational three-body problem. That is, we study the stability of stationary motion of an infinitesimal small body (particle) in gravitational field of two bodies (primaries) acting on the particle with radiation pressure repulsive forces. The primaries move in circular coplanar orbits about their barycenter and the particle lies in the plane of primaries motion. By using the method of normal forms and applying theorems of the Kolmogorov-Arnold-Moser theory we perform nonlinear stability study of collinear point, which located on the line connecting the primaries. Rigorous conclusions on stability in the sense of Lyapunov have been obtained both for non-resonant case and for cases of third and fourth order resonances. These results can be interesting for spaceflight and astronomical applications such as studies of dynamics of artificial satellites and observations of cosmic dust.