Finding the optimal spatial geometry in an earth-moon mission

Abstract

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.This work deals with a preliminary mission analysis to find the best geometrical parameters of the terminal orbits – Low Earth Orbit (LEO) and Low Moon Orbit (LMO) – of an Earth-Moon mission by means of a spatial lunar patched-conic approximation formulated in the present paper. The Earth-Moon transfer problem considers that the terminal orbits are circular, and that all the Keplerian elements of the LEO and of the LMO are prescribed, but the true latitude of the point of the application of the impulses. The transfer problem based on the spatial patched-conic approximation involves the solution of a two-point boundary value problem obtained by means of Newton-Raphson algorithm. After that, a one degree of freedom optimization problem is formulated which minimizes the fuel consumption represented by the total velocity increment. The transfer problem is also formulated considering the dynamics of the Spatial Circular Restricted Three-Body Problem (SCR3BP). A two-point boundary value problem and a one degree of freedom optimization problem are also enunciated for this model. The optimization problems based on the two dynamical models are solved by means of the Sequential Gradient Restoration Algorithm (SGRA). In the present study, only direct ascent maneuvers with a time of flight of 2. 5 to 4. 0 days are considered. The altitude of the LEO and the altitude of the LMO are set equal to 167 km and 100 km, respectively. Numerical results show that the trajectories provided by the patched-conic approximation and the SCR3BP are too close to each one, which enhances the possibility to utilize this patched-conic approximation in a preliminary mission analysis. According to the results, a great amount of fuel consumption can be saved if the longitude of the ascending node of the LMO is chosen properly. By taking advantage of the numerical performance associated to the processing speed of the spatial patched-conic approximation, this model is applied to determine several optimal trajectories by parameterization of the terminal orbital elements to find the best combination of them that minimizes the fuel consumption.