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Search for periodic orbits in Agekyan and Anosova’s region D for the general three-body problem

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The goal of this study is to search for close-to-periodic orbits in the general three-body problem with equal masses and zero initial velocities. This search was carried out by scanning region D for all possible configurations of triple systems specified by coordinates (ξ, η). Points in region D whose vicinities could contain the initial conditions for exactly periodic orbits were identified. This was done by requiring that two conditions be satisfied: (1) the minimum of the sum of the squares of the differences between the initial and current coordinates and velocities of the bodies is less than a specified value; (2) the time T when this minimum is attained does not exceed 10τ, where τ is the mean crossing time. This analysis reveals 22 regions with initial coordinates (ξ, η) corresponding to periodic orbits. The trajectories of bodies with initial conditions in these regions are constructed. Some properties of the structure of the orbits found are described.

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Correspondence to P. P. Yasko.

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Original Russian Text © P.P. Yasko, V.V. Orlov, 2015, published in Astronomicheskii Zhurnal, 2015, Vol. 92, No. 5, pp. 447–456.

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Yasko, P.P., Orlov, V.V. Search for periodic orbits in Agekyan and Anosova’s region D for the general three-body problem. Astron. Rep. 59, 404–413 (2015).

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