A Simple Strategy for Computing Time Optimal Earth-Return Trajectories for Lunar and Cislunar Flight

Abstract

A simple strategy is presented for computing Earth-return trajectories with a minimum time of flight. The simplicity and robustness of this particular algorithm makes it wellsuited for on-board use during contingency and abort operations. Rather than attempting to create fuel-optimal trajectories, the algorithm presented in this paper focuses on computing a trajectory from low lunar orbit to direct atmospheric Earth entry that minimizes the time of flight but does not violate the fuel constraint. This strategy is applicable for both trans-lunar, and trans-Earth portions of the mission. In addition the strategy allows for return from any bounded lunar orbit. Some examples demonstrating the eectiveness of the targeting algorithm are also presented. The goal of the paper is to present a simple method for computing Earth return trajectories for manned lunar missions. The techniques presented in this paper were developed for use in contingency and abort scenarios where the spacecraft must unexpectedly return to the Earth without the aid of Earth-based trajectory calculations. In these situations a return trajectory must be calculated on-board the spacecraft without the aid of the vast computational resources available to Earth-based mission planners. The limited computing power available on-board the craft and the limited time available for performing the computations, demand that procedures for calculating the Earth return sequence must be simple yet robust. The algorithms found in this paper strive to be simple and robust by using the amount of available propellant as a constraint while minimizing the time-of-flight. The methods outlined in this paper are intended to generate Earth-return trajectories during two phases of a typical lunar mission. First, abort from cislunar flight is considered. In this paper cislunar flight refers to the portion of the trajectory between low earth orbit (LEO) and bounded lunar orbit. This includes the trans-lunar portion of the mission, which begins with trans-lunar injection (TLI) and ends with lunar orbit insertion (LOI). It also includes the trans-Earth portion of the mission, which begins with trans-Earth injection (TEI) and ends with direct atmospheric entry at the Earth. Techniques for computing abort trajectories from bounded lunar orbits are also considered. During the Apollo missions the capabilities for executing returns without the aid of the ground were very limited. These limits were caused by the relative lack of on-board computational capability. Due to this, and other reasons, the Apollo missions were limited to a very narrow window of lunar access. These limits on mission scope greatly simplify abort planning, thus helping to alleviate the diculty imposed by the limited computational assets. Clearly, the next generation lunar missions will require more robust capabilities than the Apollo missions. These increased capabilities coupled with farther reaching objectives will result in a much more complex mission profile. The complexity of the mission profile causes abort planning to be a much more intricate undertaking. Fortunately, this challenge is alleviated in part because new vehicles will have orders of magnitude more computational power than was available in the past. However, the complexity of the problem is such that simplifying assumptions still must be made for the problem to be solvable on-board a spacecraft in a timely fashion.