Optimal Earth-Moon Trajectory Design Using New Initial Costate Estimation Method

Abstract

A study was conducted to propose an initial costate estimation method to construct spiral trajectories directly in the Earth-moon rotating frame for an arbitrary initial radius and transfer time and for arbitrary target-specific energy, reducing computational burden. An initial guess structure was generated in the new estimation method, which was derived according to the initial costate properties. A means of determining the duration of a spiral phase and the target-specific energy at the end of the spiral phase was also suggested for Earth-to-moon transfer trajectories, as an application of the structure of the initial guess. The new initial costate estimation method was presented for designing spiral transfer trajectories and fuel-optimal Earth-to-moon trajectories were designed using the initial guess structure and the proposed design procedure from a 315 km Earth-parking orbit to a 100 km lunar-parking orbit.