Low-thrust trajectories to the moon

Author(s)

Prado, Antonio F. B. A. ; Benra, FK ; Mastorakis, N ; Lache, S ; Kadioglu, N ; Hassanen, MAH

• Document type: Journal article
• Source: PROCEEDINGS OF THE 3RD WSEAS INTERNATIONAL CONFERENCE ON APPLIED AND THEORETICAL MECHANICS (MECHANICS '07); v. N/A, p. 2-pg., 2007-01-01.

Abstract

In this paper the problem of sending a spacecraft from Low Earth Orbit (LEO) to the Moon with minimum fuel consumption is considered. It is assumed that the "Two-Body model" approximation is valid in all phases of the mission and that the final orbit around the Moon is polar. The first part deals with impulsive maneuvers, and obtain a set of values for fuel expenditure and trip time for several trajectories. Two possible scenarios are considered: a single mission (only one spacecraft in orbit around the Moon) and a double mission (one main spacecraft and a sub-satellite around the Moon). The second part considers the use of low-thrust trajectories. The Euler-Lagrange equations are used to generate a set of differential equations that are numerically integrated to obtain the final orbit. The difficulty caused by a lack of initial values for all variables in the same point (Two Point Boundary Value Problem) is treated by making iterations in the initial values of the Lagrange multipliers. The results showed that large savings in fuel consumption can be obtained by using low thrust trajectories for the Earth-Moon part of the mission. The contribution of the present paper related to previous ones written by the same author is the use of the Powell's Quadratically Convergent method to solve the problem, that showed to have a better numerical behaviour regarding convergence. (AU)