Optimal Circle-to-Ellipse Orbit Transfer for Sun-Facing E-Sail

The transfer between two coplanar Keplerian orbits of a spacecraft with a continuous-thrust propulsion system is a classical problem of astrodynamics, in which a numerical procedure is usually employed to find the transfer trajectory that optimizes (i.e., maximizes or minimizes) a given performance index such as, for example, the delivered payload mass, the propellant mass, the total flight time, or a suitable combination of them. In the last decade, this class of problem has been thoroughly analyzed in the context of heliocentric mission scenarios of a spacecraft equipped with an Electric Solar Wind Sail as primary propulsion system. The aim of this paper is to further extend the existing related literature by analyzing the optimal transfer of an Electric Solar Wind Sail-based spacecraft with a Sun-facing attitude, a particular configuration in which the sail nominal plane is perpendicular to the Sun-spacecraft (i.e., radial) direction, so that the propulsion system is able to produce its maximum propulsive acceleration magnitude. The problem consists in transferring the spacecraft, which initially traces a heliocentric circular orbit, into an elliptic coplanar orbit of given eccentricity with a minimum-time trajectory. Using a classical indirect approach for trajectory optimization, the paper shows that a simplified version of the optimal control problem can be obtained by enforcing the typical transfer constraints. The numerical simulations show that the proposed approach is able to quantify the transfer performance in a parametric and general form, with a simple and efficient algorithm.