Edward Belbruno

Program in Applied and Computational Mathematics

Princeton University

**Low Energy Routes Using Chaos in Space Travel and Astronomy**

Over the past two decades, a new type of chaotic motion was noticed in celestial mechanics that was little understood. In 1987, the speaker was able to find a numerical way to estimate this chaos and to apply it to finding very low energy pathways that spacecraft can follow, for example from the earth to the moon. This approach, now called WSB (weak stability boundary) theory, was validated by being operationally demonstrated in 1991 when it produced a new low energy route to the moon, used to enable the Japanese spacecraft Hiten to reach the moon in October of that year. Since then this approach has evolved considerably, and is being used for a number of new missions including Japan's Lunar-A and PLANET B, and ESA's SMART-1. It is also being used in the Europa mission study at JPL. An interesting application of WSB theory involves the subject of resonance jumping comets, with Brian Marsden at Harvard, and Edgeworth-Kuiper belt objects. Some new work by Jerrold Marsden and his colleagues at Caltech/JPL is discussed in relevance to WSB motions. Also discussed is the 'invariant manifold' approach to halo orbit station keeping as another way of using chaos. A new analytic approach to estimating the WSB is presented which is very interesting. If there is time, some new theoretical work of Hill's problem will be mentioned.

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