The stability of triangular libration points in the photogravitational three-body problem

Abstract

The photogravitational restricted three-body problem in which a passively gravitating point, in addition to the Newtonian force of gravitation the main bodies, also experiences the force of light pressure from each of them is considered. This problem provides a fairly adequate model, for example, of the motion of a particle of a gas-dust cloud which is in the field of two gravitating and radiating stars. In the case of the elliptic restricted problem when the main bodies are rotating about one another in elliptic orbits, the existence of a family of positions of relative equilibrium is established which are analogous to the Lagrangian libration points of the classical restricted three-body problem. The necessary conditions for the orbital stability of the triangular libration points which have been found are derived using the linearized equations of motion. It is shown that, in the configuration space of the system, the stability domain has a fairly simple geometrical meaning in the circular version of the problem. Conditions for the existence of parametric resonance, which lead to instability in the elliptic version of the problem, are established for small values of the eccentricity.