Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Math Unites The Celestial And The Atomic

29.09.2005


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:
http://www.icpa.gatech.edu

More articles from Physics and Astronomy:

nachricht Breakthrough with a chain of gold atoms
17.02.2017 | Universität Konstanz

nachricht New functional principle to generate the „third harmonic“
16.02.2017 | Laser Zentrum Hannover e.V.

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: Breakthrough with a chain of gold atoms

In the field of nanoscience, an international team of physicists with participants from Konstanz has achieved a breakthrough in understanding heat transport

In the field of nanoscience, an international team of physicists with participants from Konstanz has achieved a breakthrough in understanding heat transport

Im Focus: DNA repair: a new letter in the cell alphabet

Results reveal how discoveries may be hidden in scientific “blind spots”

Cells need to repair damaged DNA in our genes to prevent the development of cancer and other diseases. Our cells therefore activate and send “repair-proteins”...

Im Focus: Dresdner scientists print tomorrow’s world

The Fraunhofer IWS Dresden and Technische Universität Dresden inaugurated their jointly operated Center for Additive Manufacturing Dresden (AMCD) with a festive ceremony on February 7, 2017. Scientists from various disciplines perform research on materials, additive manufacturing processes and innovative technologies, which build up components in a layer by layer process. This technology opens up new horizons for component design and combinations of functions. For example during fabrication, electrical conductors and sensors are already able to be additively manufactured into components. They provide information about stress conditions of a product during operation.

The 3D-printing technology, or additive manufacturing as it is often called, has long made the step out of scientific research laboratories into industrial...

Im Focus: Mimicking nature's cellular architectures via 3-D printing

Research offers new level of control over the structure of 3-D printed materials

Nature does amazing things with limited design materials. Grass, for example, can support its own weight, resist strong wind loads, and recover after being...

Im Focus: Three Magnetic States for Each Hole

Nanometer-scale magnetic perforated grids could create new possibilities for computing. Together with international colleagues, scientists from the Helmholtz Zentrum Dresden-Rossendorf (HZDR) have shown how a cobalt grid can be reliably programmed at room temperature. In addition they discovered that for every hole ("antidot") three magnetic states can be configured. The results have been published in the journal "Scientific Reports".

Physicist Dr. Rantej Bali from the HZDR, together with scientists from Singapore and Australia, designed a special grid structure in a thin layer of cobalt in...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Booth and panel discussion – The Lindau Nobel Laureate Meetings at the AAAS 2017 Annual Meeting

13.02.2017 | Event News

Complex Loading versus Hidden Reserves

10.02.2017 | Event News

International Conference on Crystal Growth in Freiburg

09.02.2017 | Event News

 
Latest News

Switched-on DNA

20.02.2017 | Materials Sciences

Second cause of hidden hearing loss identified

20.02.2017 | Health and Medicine

Prospect for more effective treatment of nerve pain

20.02.2017 | Health and Medicine

VideoLinks
B2B-VideoLinks
More VideoLinks >>>