Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 351759, 22 pages
Research Article

Application of Periapse Maps for the Design of Trajectories Near the Smaller Primary in Multi-Body Regimes

School of Aeronautics and Astronautics, Purdue University, Armstrong Hall, West Lafayette, IN 47907, USA

Received 15 July 2011; Accepted 4 September 2011

Academic Editor: Antonio F. Bertachini A. Prado

Copyright © 2012 Kathleen C. Howell et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The success of the Genesis spacecraft, as well as the current Artemis mission, continue to generate interest in expanding the trajectory options for future science and exploration goals throughout the solar system. Incorporating multi-body dynamics into the preliminary design can potentially offer flexibility and influence the maneuver costs to achieve certain objectives. In the current analysis, attention is focused on the development and application of design tools to facilitate preliminary trajectory design in a multi-body environment. Within the context of the circular restricted three-body problem, the evolution of a trajectory in the vicinity of the smaller primary is investigated. Introduced previously, periapse Poincaré maps have emerged as a valuable resource to predict both short- and long-term trajectory behaviors. By characterizing the trajectories in terms of radius and periapse orientation relative to the 𝑃 1 - 𝑃 2 line, useful trajectories with a particular set of desired characteristics can be identified and computed.