On Stability of the Collinear Libration Point $L_1^{}$ in the Planar Restricted Circular Photogravitational Three-Body Problem

The stability of the collinear libration point $L_1^{}$ in the photogravitational three-body problem is investigated. This problem is concerned with the motion of a body of infinitely small mass which experiences gravitational forces and repulsive forces of radiation pressure coming from two massive bodies. It is assumed that the massive bodies move in circular orbits and that the body of small mass is located in the plane of their motion. Using methods of normal forms and KAM theory, a rigorous analysis of the Lyapunov stability of the collinear libration point lying on the segment connecting the massive bodies is performed. Conclusions on the stability are drawn both for the nonresonant case and for the case of resonances through order four.