Artificial Equilibrium Points for Electric Sail with Constant Attitude

Abstract

C REATINGandmaintaining artificial equilibrium points (AEPs) in the restricted three-body problem is a challenging mission scenario in which a propellantless propulsion system exploits its natural potential [1]. Indeed, in such a problem, the acceleration resulting from the sum of centrifugal and gravitational forces can be balanced, for a theoretically unlimited time period, by means of a suitable continuous propulsive thrust. A thorough analysis involving the location and stability of AEPs has been addressed in a recent paper [2], under the assumption that the propulsion system provides a purely radial thrust with respect to the sun, and the thrust modulus is a function of the sun–spacecraft distance only. In that way, with a unified mathematical model, it is possible to analyze the performances of different propulsion systems, as, for example, a photonic solar sail and an electric solar wind sail (ESWS). In particular, an ESWS is known to be able to provide a continuous propulsive acceleration by means of Coulomb’s interaction of a number of positively charged tethers with the solar wind plasma stream [3]. As long as the propulsive acceleration is assumed to be radial, as per [2], the ESWS nominal plane is orthogonal to the sun–spacecraft direction. However, in a more general case, the spacecraft propulsive acceleration directionmay be inclined (within prescribed limits) with respect to the radial direction, and a transverse thrust component may be generated. The latter, in turn, introduces an additional degree of freedom that can be exploited to expand the region of admissible AEPs. The study of such a region for an ESWS-based spacecraft is the subject of this Note, for which the aim is to extend the result of [2] by removing the assumption of the radial direction for the propulsive acceleration. Moreover, this work, dealing with ESWSs, complements the analysis of Baoyin and McInnes [4], which refers to photonic solar sails. More precisely, to reduce the active attitude control effort, the ESWS nominal plane is assumed here to maintain a constant orientation in an orbital reference frame, and the problem of calculating the maps of AEPs’ positions as a function of the ESWS attitude and performance is addressed within an elliptical restricted three-body problem. A linear stability analysis of AEPs near the Lagrange points L1 and L4 in the sun–[Earth moon] system is finally discussed, with the aid of Floquet’s theory.