There is an interesting article on Oct 2005 issue of Notices of the AMS, titled 'Ground Control to Niels Bohr: Exploring Outer Space with Atomic Physics.' It describes how the study on the atomic scale (esp. the highly excited Rydberg electrons' is applied to design the orbital of Genesis, which was launched on Aug 8th, 2001 to collect the solar wind. Especially interesting is that the transition state theory in chemical dynamics is applied to study the celestial dynamics or the comets and spacecrafts, etc. From electrons to comets, planets and stars, all share the same equations and many-body problems make them hard to grasp. Chaos is an inevitable result. 'Transition state theory' in chemical dynamics explains the reaction rate from reactants to products based on the potential energy surface of chemical reactions.
'Transition states' are surfaces in the many-dimensional phase space (the set of all possible position and momentas that particles can attain) that regulate mass transport through bottlenecks in the that phase space; the transition rates are then computed using a statistical approach developed in chemical dynamics. In such analysis, one assumes that the rate of intramolecular energy distribution is fast relative to the reaction rate, which can then be expressed as the ratio of the flux across the transition state divided by the total volume of phase space associated with the reactants.
Trajectory for the Genesis spacecraft.
Resonance of the Jovian comet Oterma
in heliocentric coordinates
in rotating reference frame
magnified of the bottleneck region.
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