Optimal Earth Gravity-Assist Maneuvers with an Electric Solar Wind Sail

Propellantless propulsive systems such as Electric Solar Wind Sails are capable of accelerating a deep-space probe, only requiring a small amount of propellant for attitude and spin-rate control. However, the generated thrust magnitude is usually small when compared with the local Sun's gravitational attraction. Therefore, the total velocity change necessary for the mission is often obtained at the expense of long flight times. A possible strategy to overcome this issue is offered by an Earth gravity-assist maneuver, in which a spacecraft departs from the Earth's sphere of influence, moves in the interplanetary space, and then re-encounters the Earth with an increased hyperbolic excess velocity with respect to the starting planet. An Electric Solar Wind Sail could effectively drive the spacecraft in the interplanetary space to perform such a particular maneuver, taking advantage of an augmented thrust magnitude in the vicinity of the Sun due to the increased solar wind ion density. This work analyzes Earth gravity-assist maneuvers performed with an Electric Solar Wind Sail based probe within an optimal framework, in which the final hyperbolic excess velocity with respect to the Earth is maximized for a given interplanetary flight time. Numerical simulations highlight the effectiveness of this maneuver in obtaining a final heliocentric orbit with high energy.