Electric Sail Trajectory Design with Bezier Curve-based Shaping Approach

The aim of this paper is to propose a shape-based method in which the concept of Bezier curve is used to efficiently design the three-dimensional interplanetary trajectory of a spacecraft whose primary propulsion system is an Electric Solar Wind Sail. The latter is a propellantless propulsion concept that consists of a spinning grid of tethers, kept at a high positive potential by a power source and maintained stretched by the centrifugal force. The proposed approach approximates the time variation of the components of the spacecraft position vector using a Bezier curve function, whose geometric coefficients are calculated by optimizing the total flight time with standard numerical methods and enforcing the boundary conditions of a typical interplanetary rendezvous mission. The paper also discusses a geometrical approach to include, in the optimization process, the propulsive acceleration vector constraints obtained with the latest Electric Solar Wind Sail thrust model.