Trajectory design and optimization for elliptical lunar frozen orbit mission

Abstract

The elliptical lunar frozen orbit (ELFO) is the preferred orbit type for providing relay and navigation services to the lunar south pole, yet limited research exists on the design and optimization of transfer trajectories to ELFO. For engineering applications, several new challenges must be addressed, including the control over the ascending/descending characteristics of Earth-Moon transfer trajectories, the improvement of trajectory shooting convergence success rate, and the optimization of transfer trajectories to ELFO. A systematical trajectory design methodology for missions to ELFO is established in this paper. For the Earth-to-Moon transfer, a bidirectional integration model based on the eccentricity vector shooting is proposed, enabling precise control of trajectory ascending/descending characteristics with a simple solution process and high shooting success rate. For the optimization of transfer trajectories after lunar capture to ELFO, a three-impulse transfer framework is proposed, accompanied by a parameter offset design to expand the design space. Simulation results validate that the proposed bidirectional integration model with eccentricity vector shooting successfully controls ascending/descending characteristics, achieving a 100 % shooting success rate in simulations. The three-impulse transfer framework can effectively optimize the velocity increment and achieve the insertion to ELFO. Additionally, frozen parameter offset is demonstrated to reduce velocity increment requirements while preserving orbit frozen characteristics. The methodologies proposed herein have been successfully applied to the in-orbit operations of Chinese Tiandu satellite—the first spacecraft to operate in ELFO—confirming the effectiveness of the proposed methods.