Abstract
The collinear equilibrium position of the circular restricted problem with the two primaries at unit distance and the massless body at the pointL 3 is extended to the planar three-body problem with respect to the massm 3 of the third body; the mass ratio μ of the two primaries is considered constant and the constant angular velocity of the straight line on which the three masses stay at rest is taken equal to 1.
As regards periodic motions ‘around’ the equilibrium pointL 3, four possible extensions from the restricted to the general problem are presented each of them starting with a simple or a doubly periodic orbit of the family α of the Copenhagen category (μ=0.50).
Form 3=0.10, μ=0.50 (i.e. for fixed masses of all three bodies) the characteristic curve of the extended family α is found. The qualitative differences of the families corresponding tom 3=0 andm 3=0.10 are discussed.
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Bozis, G., Christides, T. Periodic motions around a collinear equilibrium solution of the general three-body problem. Celestial Mechanics 12, 277–295 (1975). https://doi.org/10.1007/BF01228564
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DOI: https://doi.org/10.1007/BF01228564