Impact of solar wind fluctuations on Electric Sail mission design

The Electric Solar Wind Sail (E-sail) is a propellantless propulsion system that generates thrust by exploiting the interaction between a grid of tethers, kept at a high electric potential, and the charged particles of the solar wind. Such an advanced propulsion system allows innovative and exotic mission scenarios to be envisaged, including non-Keplerian orbits, artificial Lagrange point maintenance, and heliostationary condition attainment. In the preliminary mission analysis of an E-sail-based spacecraft, the local physical properties of the solar wind are usually specified and kept constant, while the E-sailpropulsive acceleration is assumed to vary with the heliocentric distance, the sail attitude, and the grid electric voltage. However, the solar wind physical properties are known to be characterized by a marked variability, which implies a non-negligible uncertainty as to whether or not the solutions obtained with a deterministic approach are representative of the actual E-sail trajectory. The aim of this paper is to propose an effective method to evaluate the impact of solar wind variability on the E-Sail trajectory design, by considering the solar wind dynamic pressure as a random variable with a gamma distribution. In particular, the effects of plasma property fluctuations on E-sail trajectory are calculated with an uncertainty quantification procedure based on the generalized polynomial chaos method. The paper also proposes a possible control strategy that uses suitable adjustments of grid electric voltage. Numerical simulations demonstrate the importance of such a control system for missions that require a precise modulation of the propulsive acceleration magnitude.