Astronomy and Astrophysics – Astronomy
Scientific paper
Mar 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003arep...47..254o&link_type=abstract
Astronomy Reports, vol. 47, Issue 3, p.254-262
Astronomy and Astrophysics
Astronomy
1
Scientific paper
The motions in the rectilinear three-body problem are analyzed for the case of unequal masses. At the initial time, the central body is equidistant from the outer bodies. The initial conditions for a fixed ratio of the body masses are determined by two parameters: the virial coefficient of the triple system and the ratio of the differences in the velocities of the central body and the two outer bodies. The domains of the initial conditions corresponding to the escape of one of the outer bodies after some number n={1, 2, 3, 4, 5} of passes of the central body through the barycenter of the triple system are identified. When n≤2, these domains are continuous manifolds. When n≥3, structures consisting of “scattered” points begin to emerge. The changes in the topological properties and in the areas of the continuous domains are determined by the variation of the ratios of the body masses. The domains of the initial conditions for long-lived triple systems are also found, as well as areas within these corresponding to stable systems with bound motions.
Martynova Alija I.
Orlov Valeri
Petrova Anna V.
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