Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Optimal Time-fixed Earth-Moon trajectories
Submission Author:
Luiz Arthur Gagg Filho , SP
Co-Authors:
Luiz Arthur Gagg Filho, Sandro da Silva Fernandes
Presenter: Administrador ABCM
doi://10.26678/ABCM.COBEM2021.COB2021-0158
Abstract
This work analyses the time-fixed Earth-Moon trajectories to transfer a space vehicle from a circular Low Earth Orbit to a circular Low Moon Orbit by an application of two impulses at these terminal orbits. The majority of previous works deals with minimum fuel consumption trajectories without any constraint in the time of flight. However, the time of flight for crewed missions is of paramount importance. Based on this argument, this work analyses and formulates problems to solve trajectories by prescribing this parameter. At first, the classic lunar patched-conic approximation and the circular restricted three-body model are considered to study the possibilities of time fixed Earth-Moon trajectories. It is observed that if one prescribes a feasible total time of flight, there is only one Earth-Moon direct ascent trajectory solution which is obtained by a formulation of a two-point boundary value problem. Due to the existence of only one solution, the total fuel consumption, which is represented by the the sum of the two velocity increments, can not be optimized. However, if the eccentricity of the Moon's orbit around the Earth is considered, an extra parameter, related to the position of the Moon on its eccentric orbit, is add to the models. In this case, an one-degree optimization problem is formulated to determine the minimum fuel consumption trajectory given a prescribed total time of flight. Each optimal time-fixed solution corresponds to an optimal value of the Moon position on its eccentric orbit at the initial time. A curve of time of flight versus optimal Moon's position is built, in which a minimum fuel consumption point is observed.
Keywords
Earth-Moon trajectories, Optimal trajectories, time-fixed trajectories
