A study of the influence of the sun on optimal two-impulse Earth-to-Moon trajectories with moderate time of flight in the three-body and four-body models. (May 2017)

• Record Type: Journal Article
• Authors: Filho, Luiz Arthur Gagg; da Silva Fernandes, Sandro
• Is Part Of: Acta astronautica. Volume 134(2017)
• Page Start: 197
• Page End: 220
• Publication Date: 2017-05
• Subjects: Earth-to-Moon trajectories -- Optimal two-impulse trajectories -- Bi-circular restricted four-body problem -- Circular restricted three-body problem; Astronautics -- Periodicals; Outer space -- Exploration -- Periodicals; Astronautics; Periodicals; 629.405
• DOI: 10.1016/j.actaastro.2017.02.006
• Languages: English
• ISSNs: 0094-5765

Abstract

Abstract: In this work, a study about the influence of the Sun on optimal two-impulse Earth-to-Moon trajectories for interior transfers with moderate time of flight is presented considering the three-body and the four-body models. The optimization criterion is the total characteristic velocity which represents the fuel consumption of an infinite thrust propulsion system. The optimization problem has been formulated using the classic planar circular restricted three-body problem (PCR3BP) and the planar bi-circular restricted four-body problem (PBR4BP), and, it consists of transferring a spacecraft from a circular low Earth orbit (LEO) to a circular low Moon orbit (LMO) with minimum fuel consumption. The Sequential Gradient Restoration Algorithm (SGRA) is applied to determine the optimal solutions. Numerical results are presented for several final altitudes of a clockwise or a counterclockwise circular low Moon orbit considering a specified altitude of a counterclockwise circular low Earth orbit. Two types of analysis are performed: in the first one, the initial position of the Sun is taken as a parameter and the major parameters describing the optimal trajectories are obtained by solving an optimization problem of one degree of freedom. In the second analysis, an optimization problem with two degrees of freedom is considered and the initial position of the Sun is taken as an additional unknown. Highlights: A study about the influence of the Sun on Earth-to-Moon trajectories is presented. Optimization problems with one and two-degrees of freedom are enunciated. Optimal trajectories are compared considering the three-body and four-body models. The Sun has small effect on the fuel consumption for direct ascent maneuvers. Close encounters with the Moon and the Sun attraction can help in fuel saving.