# American Institute of Mathematical Sciences

December  2008, 1(4): 519-540. doi: 10.3934/dcdss.2008.1.519

## Random walk in the three-body problem and applications

 1 Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, United States

Received  April 2008 Revised  July 2008 Published  September 2008

The process of random walk is described, in general, and how it can be applied in the three-body problem in a systematic manner. Several applications are considered. The main one which is a focus of this paper is on the evolution of horseshoe orbits and their transition to breakout motion in the restricted three-body problem. This connection is related to their use for an Earth-impactor in a theory on the formation of the Moon. We briefly discuss another application on the instability of asteroid orbits.
Citation: Edward Belbruno. Random walk in the three-body problem and applications. Discrete & Continuous Dynamical Systems - S, 2008, 1 (4) : 519-540. doi: 10.3934/dcdss.2008.1.519
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