Detection that a satellite in a two-satellite tethered system is tethered using observations of that satellite alone over a relatively short time is more difficult when the system has a relatively short tether and/or significant libration. The estimation of the sate of the system using the same information is also more difficult under these conditions. In this paper, two different formulations of the equations of motion of a two-body tethered satellite system with a massless tether are used to see which resutls in the best performance of detection and sate estimation algorithms. The two formulations involve the use of differnet state variables. In the first, the position and velocity of the observed satellite are used. In the second formulation, we use the position and velocity of the observed satellite and its position and velocity relative to the center of mass of the system as variables. The second formulation provides equations that may be solved approximately for small libration angles to obtain an analytical solution that describes the motion better than a similar solution based on the first formulation. However, both formulations appear to provide essentially the same detection/state estimation results.
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