Abstract
We consider the motion of an infinitesimal mass under the Newtonian attraction of N point masses forming a ring plus a central body where a Manev potential (-1/r + e/r^2, e in {mathbb {R}}), is applied to the central body. More precisely, the bodies are arranged in a planar ring configuration. This configuration consists of N-1 primaries of equal mass m located at the vertices of a regular polygon that is rotating on its own plane about its center of mass with a constant angular velocity omega . Another primary of mass m_0=beta m (beta >0 parameter) is placed at the center of the ring. Moreover, we assume that the central body may be an ellipsoid, or a radiation source, which introduces a new parameter e. The existence and stability of periodic solutions of the spatial Maxwell restricted N+1-body problem is obtained using averaging theory. The determination of KAM 3-tori encasing some of the linearly stable periodic solutions is proved. The planar case is moreover considered.
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