Equilibrium state of axially symmetric electric solar wind sail at arbitrary sail angles

This paper studies the equilibrium state and trajectory dynamics of an axially symmetric Electric solar wind sail (E-sail) at arbitrary sail angles. The E-sail is assumed operating in a heliocentric-ecliptic orbit at approximately one astronomic unit (au) from the Sun, and experiencing various dynamic disturbances like solar wind pressure, tether tension oscillations, and centrifugal forces. The study derives analytical expressions for the E-sail's equilibrium state and its maximal coning angle under small coning angle assumption. Subsequently, an improved propulsion model is developed for the E-sail in this equilibrium state. To assess the precision of these formulations, a high-fidelity E-sail dynamic model is constructed using the nodal position finite element method, where the tethers are modeled as two-noded tensile elements and the central spacecraft and remote units are simplified as lumped masses. Through thorough parametric analyses, this paper conclusively demonstrates that the operation of the E-sail at the equilibrium state can be achieved in accordance with the derived analytical prediction of the equilibrium state. Furthermore, the improved propulsion model is employed in trajectory analyses for a mission to reach the solar system's boundary. The study provides valuable insights and findings and foundation for the practical application and further advancement of the E-sail technology.