E-Sail Optimal Trajectories to Heliostationary Points

Abstract

The aim of this paper is to investigate the performance of a robotic spacecraft, whose primary propulsion system is an electric solar wind sail (E-sail), in a mission to a heliostationary point (HP)—that is, a static equilibrium point in a heliocentric and inertial reference frame. A spacecraft placed at a given HP with zero inertial velocity maintains that heliocentric position provided the on-board thrust is able to counterbalance the Sun’s gravitational force. Due to the finite amount of storable propellant mass, a prolonged mission toward an HP may be considered as a typical application of a propellantless propulsion system. In this respect, previous research has been concentrated on the capability of high-performance (photonic) solar sails to reach and maintain such a static equilibrium condition. However, in the case of a solar-sail-based spacecraft, an HP mission requires a sail design with propulsive characteristics that are well beyond the capability of current or near-future technology. This paper shows that a medium-performance E-sail is able to offer a viable alternative to the use of photonic solar sails. To that end, we discuss a typical HP mission from an optimal viewpoint, by looking for the minimum time trajectory necessary for a spacecraft to reach a given HP. In particular, both two- and three-dimensional scenarios are considered, and the time-optimal mission performance is analyzed parametrically as a function of the HP heliocentric position. The paper also illustrates a potential mission application involving the observation of the Sun’s poles from such a static inertial position.

Circular Orbit Flip Trajectories Generated by E-Sail

“…The DT and SWA are two types of transfers introduced by the authors [42] by drawing parallels with similar concepts used in an interstellar mission based on a photonic solar sail [43][44][45][46]. In the recent literature, this two concepts have also been used to analyze the optimal transfer to heliostationary points using a very high-performance E-sail [37].…”

“…More precisely, in a DT the radial distance increases continuously with time until the spacecraft reaches the aphelion point (subscript a), as shown in Figure 2a. Instead, a trajectory with a (single) SWA contains an initial phase where the spacecraft approaches the Sun to increase its propulsive acceleration magnitude, and then rapidly grows its radial distance to reach the aphelion point [37]; see the scheme of Figure 2b. Note that the mathematical model discussed in the previous section does not include a constraint on the minimum solar distance, that is, a constraint on the perihelion (subscript p) distance, as was considered in the model described in Ref.…”

“…Note that the mathematical model discussed in the previous section does not include a constraint on the minimum solar distance, that is, a constraint on the perihelion (subscript p) distance, as was considered in the model described in Ref. [37]. Therefore, the (unconstrained) perihelion distance r p is an output of the optimization process in a transfer with a single SWA.…”

“…The approach used to solve the problem, which is similar to that used by the authors in recent works [36,37], is now summarized for the sake of completeness.…”