Math unites the celestial and the atomic
These insights have led to new ways to design space missions, as described in the article, "Ground Control to Niels Bohr: Exploring Outer Space with Atomic Physics" by Mason Porter and Predrag Cvitanovic, which appears in the October 2005 issue of the Notices of the American Mathematical Society.
The article describes work by, among other scientists, physicist Turgay Uzer of the Georgia Institute of Technology, mathematician Jerrold Marsden of the California Institute of Technology and engineer Shane Ross of the University of Southern California.
Imagine a group of celestial bodies—say, the Sun, the Earth, and a Spacecraft—moving along paths determined by their mutual gravitational attraction. The mathematical theory of dynamical systems describes how the bodies move in relation to one another. In such a celestial system, the tangle of gravitational forces creates tubular "highways" in the space between the bodies. If the spacecraft enters one of the highways, it is whisked along without the need to use very much energy. With help from mathematicians, engineers and physicists, the designers of the Genesis spacecraft mission used such highways to propel the craft to its destinations with minimal use of fuel.
In a surprising twist, it turns out that some of the same phenomena occur on the smaller, atomic scale. This can be quantified in the study of what are known as "transition states", which were first employed in the field of chemical dynamics. One can imagine transition states as barriers that need to be crossed in order for chemical reactions to occur (for "reactants" to be turned into "products"). Understanding the geometry of these barriers provides insights not only into the nature of chemical reactions but also into the shape of the "highways" in celestial systems.
|There is an almost perfect parallel between math describing the motion of celestial objects, like the sun (shown here in an ultraviolet image), and atomic objects. (Photo: NASA)|
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