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"We now know that chaotic trajectories identical to those that govern the motion of comets, asteroids, and spacecraft are traversed on the atomic scale by highly excited Rydberg electrons," Mason Porter and Predrag Cvitanović remark in the October Notices of the American Mathematical Society.
Indeed, the mathematics describing the motion of gravitationally interacting bodies in space closely parallels the mathematics describing the motion of the smallest particles of atomic and molecular physics. As it happens, the special case of the celestial restricted three-body problem is mathematically analogous to the situation when a hydrogen atom loses its electron (via ionization) in crossed electric and magnetic fields.
So, theory from atomic and molecular physics can be used on a much grander, celestial scale, and celestial mechanics can provide insights into atomic and molecular interactions. "The orbits used to design space missions thus also determine the ionization rates of atoms and chemical-reaction rates of molecules!" Porter and Cvitanović declare.
Originally posted by Off_The_Street
After all, Neils Bohr's depiction of the atom (although it might be flawed in retrospect) astounded everyone in that it looked like a scaled-down solar system!