Abstract
ABSTRACT: An interesting process is described where a particle can very rapidly jump between different resonance orbits about the Earth, where the resonances are with respect to the Moon. This was discovered numerically in 1988, and until recently there was no way to prove its validity. Recent results with Brian Marsden and the author have proven that comets are performing this dynamics about the Sun in resonances with Jupiter. The fast resonance shift, termed the hop, occurs in a region of sensitive dynamics where weak capture occurs. The hop provides an interesting mechanism for instability of motion in the n‐body problem, n > 2. Although most of this paper is survey in nature, some new results are presented on special capture‐hop‐escape trajectories, CHEs, which may have relevance to the Birkhoff conjecture. The significance of the weak capture region about the Moon was demonstrated in 1991 when a Japanese spacecraft arrived there on a new low‐energy transfer.
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