Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:


Math Unites The Celestial And The Atomic


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. Image courtesy of NASA.

In recent years, researchers have developed astonishing new insights into a hidden unity between the motion of objects in space and that of the smallest particles. It turns out there is an almost perfect parallel between the mathematics describing celestial mechanics and the mathematics governing some aspects of atomic physics. 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.

The connection between atomic and celestial dynamics arises because the same equations govern the movement of bodies in celestial systems and the energy levels of electrons in simple systems—and these equations are believed to apply to more complex molecular systems as well. This similarity carries over to the problems’ transition states; the difference is that which constitutes a “reactant” and a “product” is interpreted differently in the two applications. The presence of the same underlying mathematical description is what unifies these concepts. Because of this unifying description, the article states, “The orbits used to design space missions thus also determine the ionization rates of atoms and chemical-reaction rates of molecules!” The mathematics that unites these two very different kinds of problems is not only of great theoretical interest for mathematicians, physicists, and chemists, but also has practical engineering value in space mission design and chemistry.

Founded in 1888 to further mathematical research and scholarship, the 30,000-member American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.

The Georgia Institute of Technology is one of the nation’s premiere research universities. Ranked among U.S. News & World Report’s top 10 public universities, Georgia Tech educates more than 16,000 students every year through its Colleges of Architecture, Computing, Engineering, Liberal Arts, Management and Sciences. Tech maintains a diverse campus and is among the nation’s top producers of women and African-American engineers. The Institute offers research opportunities to both undergraduate and graduate students and is home to more than 100 interdisciplinary units plus the Georgia Tech Research Institute. During the 2003-2004 academic year, Georgia Tech reached $341.9 million in new research award funding.

David Terraso | EurekAlert!
Further information:

More articles from Physics and Astronomy:

nachricht First results of NSTX-U research operations
26.10.2016 | DOE/Princeton Plasma Physics Laboratory

nachricht Scientists discover particles similar to Majorana fermions
25.10.2016 | Chinese Academy of Sciences Headquarters

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Etching Microstructures with Lasers

Ultrafast lasers have introduced new possibilities in engraving ultrafine structures, and scientists are now also investigating how to use them to etch microstructures into thin glass. There are possible applications in analytics (lab on a chip) and especially in electronics and the consumer sector, where great interest has been shown.

This new method was born of a surprising phenomenon: irradiating glass in a particular way with an ultrafast laser has the effect of making the glass up to a...

Im Focus: Light-driven atomic rotations excite magnetic waves

Terahertz excitation of selected crystal vibrations leads to an effective magnetic field that drives coherent spin motion

Controlling functional properties by light is one of the grand goals in modern condensed matter physics and materials science. A new study now demonstrates how...

Im Focus: New 3-D wiring technique brings scalable quantum computers closer to reality

Researchers from the Institute for Quantum Computing (IQC) at the University of Waterloo led the development of a new extensible wiring technique capable of controlling superconducting quantum bits, representing a significant step towards to the realization of a scalable quantum computer.

"The quantum socket is a wiring method that uses three-dimensional wires based on spring-loaded pins to address individual qubits," said Jeremy Béjanin, a PhD...

Im Focus: Scientists develop a semiconductor nanocomposite material that moves in response to light

In a paper in Scientific Reports, a research team at Worcester Polytechnic Institute describes a novel light-activated phenomenon that could become the basis for applications as diverse as microscopic robotic grippers and more efficient solar cells.

A research team at Worcester Polytechnic Institute (WPI) has developed a revolutionary, light-activated semiconductor nanocomposite material that can be used...

Im Focus: Diamonds aren't forever: Sandia, Harvard team create first quantum computer bridge

By forcefully embedding two silicon atoms in a diamond matrix, Sandia researchers have demonstrated for the first time on a single chip all the components needed to create a quantum bridge to link quantum computers together.

"People have already built small quantum computers," says Sandia researcher Ryan Camacho. "Maybe the first useful one won't be a single giant quantum computer...

All Focus news of the innovation-report >>>



Event News

#IC2S2: When Social Science meets Computer Science - GESIS will host the IC2S2 conference 2017

14.10.2016 | Event News

Agricultural Trade Developments and Potentials in Central Asia and the South Caucasus

14.10.2016 | Event News

World Health Summit – Day Three: A Call to Action

12.10.2016 | Event News

Latest News

Greater Range and Longer Lifetime

26.10.2016 | Power and Electrical Engineering

VDI presents International Bionic Award of the Schauenburg Foundation

26.10.2016 | Awards Funding

3-D-printed magnets

26.10.2016 | Power and Electrical Engineering

More VideoLinks >>>