Abstract
The planar restricted four-body problem is considered. That is, motion of an infinitesimal body P in the gravitational field of three attracting bodies is studied. It is supposed, that the above three body form a stable equilateral Lagrange triangle and all four bodies move in a plane. In this case there are eight central configurations formed by the bodies. An analysis of stability and bifurcation of the central configurations is performed. In particular, it is shown that the bifurcation is only possible in cases of degeneracy, when mass of an attracting body vanishes. It is also established that in non-degenerate cases five central configurations are unstable and three central configurations can be both stable and unstable. Domains of stability in linear approximation are constructed in the plane of parameters.
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