Periodic orbits of a Hill-tether problem originated from collinear points

A tether satellite's behavior about the collinear points of the circular-restricted three-body problem is analyzed systematically for inert tethers. The dumbbell model, which is assumed to be applicable for tethers in fast rotation, is addressed. The known periodic solutions that are modified in the case of tether satellites are discussed with a focus on the Hill problem. A conspicuous configuration is found for tethers rotating parallel to the plane of the primaries, a case in which the attitude of the tether satellite remains constant on average, and it is demonstrated that either lengthening or shortening the tether may lead to orbit stability. Promising results are found for orbits of the vertical family, but regions of stability are also found in the case of halo orbits.