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Mathematical Problems in Engineering
Volume 2018, Article ID 7489120, 10 pages
Research Article

Numerical Study of the Zero Velocity Surface and Transfer Trajectory of a Circular Restricted Five-Body Problem

School of Mathematical Science, Yangzhou University, Yangzhou 225002, China

Correspondence should be addressed to F. B. Gao; moc.anis@oabafoag

Received 14 May 2018; Revised 26 July 2018; Accepted 5 September 2018; Published 15 October 2018

Academic Editor: Chris Goodrich

Copyright © 2018 R. F. Wang and F. B. Gao. 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.


We focus on a type of circular restricted five-body problem in which four primaries with equal masses form a regular tetrahedron configuration and circulate uniformly around the center of mass of the system. The fifth particle, which can be regarded as a small celestial body or probe, obeys the law of gravity determined by the four primaries. The geometric configuration of zero-velocity surfaces of the fifth particle in the three-dimensional space is numerically simulated and addressed. Furthermore, a transfer trajectory of the fifth particle skimming over four primaries then is designed.