New phenomenons in the spatial isosceles three-body problem

In this work, we study the periodic orbits in the spatial isosceles three-body problem. These periodic orbits form a one-parameter set with a rotation angle $θ$ as the parameter. Some new phenomenons are discovered by applying our numerical method. The periodic orbit coincides with the planar Euler orbit when $0 < θ\leq 0.32 π$ and it changes to a spatial orbit when $0.33 π\leq θ< π$. Eventually, the spatial orbit becomes a planar collision orbit when $θ=π$. Furthermore, an oscillated behavior is found when $θ=π/2$, which is chaotic but bounded under a small perturbation. As another application of our numerical method, 7 new periodic orbits are presented in the end.

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