Same Math Explains Movement of Spaceships and Atoms
The physics of spaceflight and the motion of atoms in a chemical reaction are explained in certain cases by the same math, scientists have found.
The discovery emerged gradually over years and has been written about in various technical publications in recent weeks.
Let's start with the cosmic side of things. All objects with mass generate gravity. The gravitational relationship between the Sun, Earth and a spacecraft, and the movement of each in that system, can all be described using a complex mathematical theory called dynamical systems.
The gravitational forces create "tubular highways" that allow cheap spaceflight. A spacecraft -- whose mass is insignificant insofar as the other two objects are concerned -- can travel along one of these routes at a given speed with less force and therefore less fuel. This knowledge was employed by NASA to choose a more efficient trajectory for its Genesis mission, which studied emanations from the Sun.
In what scientists call "a surprising twist," almost identical formulas work to explain reactions at the much smaller atomic scale, where gravity is not a factor.
In chemical reactions, scientists describe "transition states," which are like barriers that must be crossed before chemical reactants can turn into products. Specifically, the energy levels of electrons in some of those reactions share a "hidden unity" with the paths of spaceships in the three-body cosmic setup.
"The orbits used to design space missions thus also determine the ionization rates of atoms and chemical-reaction rates of molecules," write Mason Porter and Predrag Cvitanovic in an article in the October 2005 issue of the Notices of the American Mathematical Society.
The article describes work by, among other scientists, mathematician Jerrold Marsden of the California Institute of Technology, engineer Shane Ross of the University of Southern California, and physicist Turgay Uzer of the Georgia Institute of Technology.
Scientists expect the cosmic knowledge to aid in understanding the subatomic world, and vice-versa.
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