The shape of a rotating electric solar wind sail under the centrifugal forceand solar wind dynamic pressure is modeled to address the sail attitudemaintenance and thrust vectoring. The sail rig assumes centrifugally stretchedmain tethers that extend radially outward from the spacecraft in the sail spinplane. Furthermore, the tips of the main tethers host remote units that areconnected by auxiliary tethers at the sail rim. Here, we derive the equation ofmain tether shape and present both a numerical solution and an analyticalapproximation for the shape as parametrized both by the ratio of the electricsail force to the centrifugal force and the sail orientation with respect tothe solar wind direction. The resulting shape is such that near the spacecraft,the roots of the main tethers form a cone, whereas towards the rim, this coningis flattened by the centrifugal force, and the sail is coplanar with the sailspin plane. Our approximation for the sail shape is parametrized only by thetether root coning angle and the main tether length. Using the approximateshape, we obtain the torque and thrust of the electric sail force applied tothe sail. As a result, the amplitude of the tether voltage modulation requiredfor the maintenance of the sail attitude is given as a torque-free solution.The amplitude is smaller than that previously obtained for a rigid singletether resembling a spherical pendulum. This implies that less thrusting marginis required for the maintenance of the sail attitude. For a given voltagemodulation, the thrust vectoring is then considered in terms of the radial andtransverse thrust components.
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