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

The photogravitational restricted three-body problem in which a passively g ravitating point, in addition to the Newtonian force of gravitation the mai n 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 pro blem when the main bodies are rotating about one another in elliptic orbits , the existence of a family of positions of relative equilibrium is establi shed which are analogous to the Lagrangian libration points of the classica l restricted three-body problem. The necessary conditions for the orbital s tability of the triangular libration points which have been found are deriv ed using the linearized equations of motion. It is shown that, in the confi guration space of the system, the stability domain has a fairly simple geom etrical meaning in the circular version of the problem. Conditions for the existence of parametric resonance, which leads to instability in the ellipt ic version of the problem, are established for small values of the eccentri city. (C) 2001 Elsevier Science Ltd. All rights reserved.