Dynamics of a 3D Rotating Tethered Formation Flying Facing the Earth

Several on-going studies indicate interest in large, light orbiting structures, shaped like fishnets or webs: along the ropes of the web small spacecraft can move to position and relocate, at will, pieces of hardware devoted to specific missions.12 The presence of hard links adds the advantage of a simpler control strategy to the typical benefits of formation flying. Unfortunately, there is no stable configuration for an orbiting two dimensional web made by light, flexible tethers: in fact it cannot support compression forces caused by the gravity gradient. The proposed solution is to make use of centrifugal forces to pull the net, with a reduced number of simple thrusters located at the tips of the tethers to initially acquire the required spin. A sequence of simulations has been carried out to investigate the dynamic behavior of such a system. The numerical model adopted overlaps simpler elements, each of them given by a tether connecting two extreme bodies which accommodate the spinning thrusters. The combination of these "diameter-like" elements provides the web, shaped according to the specific requirements. The net is initially considered as rotating in the orbital plane, which is demonstrated to be the only configuration leading to a stable motion. However, as the earth-facing orientation can be of greater interest for earth observation and telecommunication missions, we have searched for a possible solution to stabilize the web. The solution has been identified by several authors with connecting two additional masses along the orbital radius, in a spinning double-pyramid configuration. Numerical analysis of the proper three dimensional web properties, namely spin rate and boom-to-corner mass ratio, is performed in this paper, showing regions where the structure satisfies the requirements both of earth-pointing accuracy and of shape integrity. Two kinds of motion are analyzed separately: the first one follows the conditions for relative equilibrium of a spinning axisymmetrical rigid body, which requires a non zero angle between the nadir direction and the spin axis; a number of different configurations for the central web have been proposed, highlighting the possible advantages. Stability has been proved also in the second case, namely zero off-nadir angle configurations, even though limited to a simplified orbital environment including the sole gravity gradient action. Extensive plots of the stable regions, considered as a useful baseline for more detailed mission design, are reported.