Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 303604, 12 pages
Research Article

Alternative Transfers to the NEOs 99942 Apophis, 1994 WR12, and 2007 UW1 via Derived Trajectories from Periodic Orbits of Family G

1UFABC, Universidade Federal do ABC, Santo André, 09210-170, SP, Brazil
2INPE, Instituto Nacional de Pesquisas Espaciais, São José dos Campos, 12227-010, SP, Brazil
3UNESP, Universidade Estadual Paulista, Guaratinguetá, 12516-410, SP, Brazil

Received 30 July 2009; Accepted 11 December 2009

Academic Editor: Maria F. P. S. Zanardi

Copyright © 2009 C. F. de Melo 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.


Swing-by techniques are extensively used in interplanetary missions to minimize fuel consumption and to raise payloads of spacecrafts. The effectiveness of this type of maneuver has been proven since the beginning of space exploration. According to this premise, we have explored the existence of a natural and direct link between low Earth orbits and the lunar sphere of influence to get low-energy transfer trajectories to the Near Earth Objects (NEOs) 99942 Apophis, 1994 WR12, and 2007 UW1 through swing-bys with the Moon. The existence of this link is related to a family of retrograde periodic orbits around the Lagrangian equilibrium point L1 predicted for the circular, planar, restricted three-body Earth-Moon-particle problem. The trajectories in this link are sensitive to small disturbances. This enables them to be conveniently diverted reducing so the cost of the swing-by maneuver. These maneuvers allow a gain in energy sufficient for the trajectories to escape from the Earth-Moon system and to stabilize in heliocentric orbits between the Earth and Venus or Earth and Mars. Therefore, the trajectories have sufficient reach to intercept the NEOs' orbits.