Low Energy Transfer to the Moon, Chaos, and Random Walk
Edward Belbruno, Princeton University and Innovative Orbital Design, Inc.


 In 1991 the Japanese spacecraft Hiten was rescued by the speaker and successfully brought to the Moon demonstrating a new type of transfer trajectory. This transfer is low energy and chaotic in nature, using weak stability boundaries.  The existence of this transfer solved a conjecture of Charles Conley.  Its dynamics can be described by using invariant manifolds in the four-body problem together with weak capture. This transfer is being planned to be used by NASA.s upcoming GRAIL mission in 2011, among other missions. The nature of weak stability boundaries and their associated dynamics have been elusive in nature, but are now being better understood. New results are presented showing their interesting relationship to special invariant sets. The same methods together with the random walk process can be applied to a new theory on the origin of the Moon by the speaker and R. Gott.  This demonstrates random walk in the three-body problem.