Rapid Capture Trajectories from Parabolic Orbit with Modulated Radial Thrust

The aim of this paper is to analyze the performance of a radially-accelerated spacecraft in a capture mission scenario, in which a space vehicle transfers from a parabolic approaching trajectory of assigned semilatus rectum to a target circular orbit around a generic celestial body. The radial propulsive acceleration provided by the spacecraft propulsion system can be modulated within a suitable given range, and the radial thrust can be either inward- or outward-directed. The transfer mission performance is analyzed in an optimal framework, by minimizing the total flight time with an indirect approach. In this context, the paper proposes a semi-analytical method to reduce the computation time required to solve the optimal control problem. Using a proper description of the spacecraft dynamics in a dimensionless form, the paper reports a set of graphs and tables that allow the designer to obtain a rapid approximation of the optimal mission performance with an accuracy consistent with that of a preliminary trajectory design. Finally, the proposed approach is used to describe the minimum time capture trajectories in a mission scenario towards Ceres.