Stable orbits of planets of a binary star system in the three-dimensional restricted problem (Q5960088)

The paper studies the motion of recently discovered planets around binary stars using the theory of restricted three-body problem, in which a particle of negligible mass moves under the action of two finite point masses, called primaries and revolving in circular orbits around their common center of mass. The diameter of the planetary orbits is about 4 to 4.5 times of the distance between the two stars. The author calculates the families of direct (class \(L\)) and retrogarde (class \(m\)) periodic orbits, and determines the regions of dynamical stability. The study of symmetry properties of the problem shows existence of four basic types of symmetric orbits. The author determines all types of orbits, and demonstrates that symmetry properties of periodic orbits allow to integrate only half or quarter of the resolution in dependence on the class. The initial points of the periodic orbits may be chosen arbitrarily. All numerical results are described in details and presented in figures. An overview of mostly encountered types of periodic orbits concludes the paper.