## Tethered Satellites at Lagrangian Points

For long enough tethers the effect of the higher-order terms of the mutual gravity field play a role in the dynamics and stability of the satellite near a Lagrangian point. These terms can be exploited (by changing the tether length) to stabilize the orbit of a tethered satellite in the proximity of a collinear Lagrangian point that would be otherwise unstable for a compact-body satellite. Also the non-negligible angular momentum of a spinning tether can be used to stabilize the system at Lagrangian collinear points.

Halo orbits around teh collinear point L2 provide excellent opportunities for scientific and exploration missions, most of the times taking advantage of their unstable character. However, this unstable character can be changed when instead of a point mass satellite a rotating tether system is considered.

Specifically, work inside SDG-UPM research group stablishes the existence and stability of periodic orbits associated with rotating inert tethers. From a qualitative point of view, these orbits are the natural continuation of periodic motios characteristic of the Circular Restricted Three Body Problem.

Even though the unstable character of collinear Lagrangian points does not changes with the presence of a tether, following the ideas of Farquhar, the Lagrangian points become stable if an appropriate variation of the tether length is accomplished.

For the case of electrodynamic tethers, whenever they are applicable in the neighborhood of a collinear Lagrangian point, numerical explorations show that the modifications in the dynamics introduced by fast-rotating inert tethers can mitigate the instabilities of periodic orbits. Thus, halo orbits can be stabilized in some regions. Moreover, the tether’s length required to stabilize halo orbits can be small, and the tether-stabilized orbit retains most of the haloing characteristics.