# Edward Belbruno : Low Energy Trajectories in Celestial Mechanics and Stability Transition Regions With Applications to Astronomy and Space Travel

In the past two decades a new type of chaotic dynamics has been noticed in the three and four body problems which has not been understood. In 1986, using a numerical algorithm, an interesting region supporting chaotic motion was discovered about the moon, under the perturbation of the earth. This region is now termed the weak stability boundary. New types of dynamics were subsequently discovered near this boundary. These dynamics have the property that they give rise to very low energy trajectories with many important applications. In 1991, a new type of low energy trajectory to the moon was discovered which was used to place a Japanese spacecraft, Hiten, in orbit about the moon in October of that year. This was the first application of this type of dynamics to space travel. These low energy trajectories, so called WSB transfers, are now being planned by NASA, Europe and Japan for several new missions to the moon, Europa, Mars. Motion near this boundary also gives rise to an interesting resonance transition dynamics, and work by the speaker with Brian Marsden at Harvard is discussed in its relevance to short period comets, and Kuiper belt objects. An analytic representation for this boundary is also presented and its connections with heteroclinic intersections of hyperbolic invariant manifolds is discussed. If there is time, a new type of periodic motion for Hill's problem is looked at.

**Category**: Applied Math and Analysis**Duration**: 57:45**Date**: April 3, 2000 at 4:00 PM**Views**: 30-
**Tags:**seminar, Applied Math Seminar

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