<p>The dynamics of classical mass-point orbits is changed when using cable-connected satellites. If long enough, tethers in fast rotation have stabilizing characteristics that make them appealing for satellite missions involving unstable dynamics. Using Hamiltonian formulation and with the help of perturbation methods, we reduce the dynamics about the collinear points of the Hill problem approximation to the restricted three-body problem to just one degree of freedom. The integrable dynamics maps orbits of the tether’s center of mass onto points on the sphere, and demonstrates the haloing effect stemming from the orbit-attitude coupling of the fast-rotating configuration. Indeed, it is shown that halo orbits are generated in regions in which the natural dynamics would prevent them to exist, by modifying the tether’s length.</p>