Periodic orbits in the concentric circular restricted four-body problem and their invariant manifolds

We give numerical calculations of periodic orbits in the planar concentric restricted four-body problem. It is assumed that the motion of a massless body is governed by three primaries m 1 , m 2 and m 3 . We suppose that m 1 ≫ m 2 , m 3 and that, in an m 1 centered inertial reference frame, m 2 and m 3 move in different circles about m 1 and m 1 is fixed. Although the motion of the primaries m 1 , m 2 , m 3 does not satisfy Newton’s equations of motion, this approximation is a good to model, for instance, the Jupiter–Europa–Ganymede–spacecraft system. We compute periodic orbits in both the m 1 – m 2 and m 1 – m 3 rotating frames. Periodic orbits that orbit around one of the primaries are found. Using a method that is based on the well-known Laplace resonance we also find unstable periodic orbits about the collinear libration points near m 2 and m 3 . Since the periodic orbits near the collinear libration points are unstable they have stable/unstable manifolds, which we compute. We observe a lack of intersection of the stable and unstable manifolds of different periodic orbits.