New phenomenons in the spatial isosceles three-body problem

Abstract

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 $\theta$ as the parameter. Some new phenomenons are discovered by applying our numerical method. The periodic orbit coincides with the planar Euler orbit when $0 < \theta \leq 0.32 \pi$ and it changes to a spatial orbit when $0.33 \pi \leq \theta < \pi$. Eventually, the spatial orbit becomes a planar collision orbit when $\theta=\pi$. Furthermore, an oscillated behavior is found when $\theta=\pi/2$, 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.