Abstract
The stability of the collinear libration points in the photogravitational elliptical three-body problem is investigated. The distribution of the inner collinear libration points located between the principal bodies in the system is revealed. A method of finding collinear libration points for particles with specified reduction coefficients is given. Stability diagrams are constructed for an entire heterogeneous ensemble of particles (cloud) at libration points, which, in particular, make it possible to trace cloud subdivision scenarios. The characteristics (the number of clusters, the diameter of each cluster and the distances to the components of a binary system) are determined for a binary star system similar to α–Centauri.
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