Pareto Frontier for the time-energy cost vector to an Earth-Moon transfer orbit using the patched-conic approximation

Abstract

In this work, we present a study about the determination of the optimal time-energy cost vector, i.e., flight time and total (velocity change) spent in an orbital transfer of a spacecraft from an Earth circular parking orbit to a circular orbit around the Moon. The method used to determine the flight time and total is based on the well-known approach of patched conic in which the three-body problem that involves Earth, Moon and spacecraft is decomposed into two 'two bodies'problems, i.e., Earth-spacecraft and Moon-spacecraft. Thus, the trajectory followed by the spacecraft is a composition of two parts: The first one, when the spacecraft is within the Earth's sphere of influence; The second one, when the spacecraft enters into the Moon's sphere of influence. Therefore, the flight time and total to inject the spacecraft into the lunar trajectory and place it around the Moon can be determined using the expressions for the two-body problem. In this study, we use the concept of Pareto Frontier to find a set of parameters in the geometry of patched-conic solution that minimizes simultaneously the flight time and total of the mission. These results present different possibilities for performing an Earth-Moon transfer where two conflicting objectives are optimized.