Featured Research

from universities, journals, and other organizations

Math Unites The Celestial And The Atomic

October 5, 2005
Georgia Institute of Technology
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.

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.
Credit: Image courtesy of NASA

Thearticle describes work by, among other scientists, physicist TurgayUzer of the Georgia Institute of Technology, mathematician JerroldMarsden of the California Institute of Technology and engineer ShaneRoss of the University of Southern California.

Imagine a group ofcelestial bodies—say, the Sun, the Earth, and a Spacecraft—moving alongpaths determined by their mutual gravitational attraction. Themathematical theory of dynamical systems describes how the bodies movein relation to one another. In such a celestial system, the tangle ofgravitational forces creates tubular “highways” in the space betweenthe bodies. If the spacecraft enters one of the highways, it is whiskedalong without the need to use very much energy. With help frommathematicians, engineers and physicists, the designers of the Genesisspacecraft mission used such highways to propel the craft to itsdestinations with minimal use of fuel.

In a surprising twist, itturns out that some of the same phenomena occur on the smaller, atomicscale. This can be quantified in the study of what are known as“transition states", which were first
employed in the field ofchemical dynamics. One can imagine transition states as barriers thatneed to be crossed in order for chemical reactions to occur (for“reactants” to be turned into “products"). Understanding the geometryof these barriers provides insights not only into the nature ofchemical reactions but also into the shape of the “highways” incelestial systems.

The connection between atomic and celestialdynamics arises because the same equations govern the movement ofbodies in celestial systems and the energy levels of electrons insimple systems—and these equations are believed to apply to morecomplex molecular systems as well. This similarity carries over to theproblems’ transition states; the difference is that which constitutes a“reactant” and a “product” is interpreted differently in the twoapplications. The presence of the same underlying mathematicaldescription is what unifies these concepts. Because of this unifyingdescription, the article states, “The orbits used to design spacemissions thus also determine the ionization rates of atoms andchemical-reaction rates of molecules!” The mathematics that unitesthese two very different kinds of problems is not only of greattheoretical interest for mathematicians, physicists, and chemists, butalso has practical engineering value in space mission design andchemistry.
Founded in 1888 to further mathematical research andscholarship, the 30,000-member American Mathematical Society fulfillsits mission through programs and services that promote mathematicalresearch and its uses, strengthen mathematical education, and fosterawareness and appreciation of mathematics and its connections to otherdisciplines and to everyday life.

Story Source:

The above story is based on materials provided by Georgia Institute of Technology. Note: Materials may be edited for content and length.

Cite This Page:

Georgia Institute of Technology. "Math Unites The Celestial And The Atomic." ScienceDaily. ScienceDaily, 5 October 2005. <www.sciencedaily.com/releases/2005/10/051005074603.htm>.
Georgia Institute of Technology. (2005, October 5). Math Unites The Celestial And The Atomic. ScienceDaily. Retrieved July 29, 2014 from www.sciencedaily.com/releases/2005/10/051005074603.htm
Georgia Institute of Technology. "Math Unites The Celestial And The Atomic." ScienceDaily. www.sciencedaily.com/releases/2005/10/051005074603.htm (accessed July 29, 2014).

Share This

More Space & Time News

Tuesday, July 29, 2014

Featured Research

from universities, journals, and other organizations

Featured Videos

from AP, Reuters, AFP, and other news services

Russia Saves Gecko Sex Satellite, Media Has Some Fun With It

Russia Saves Gecko Sex Satellite, Media Has Some Fun With It

Newsy (July 27, 2014) The satellite is back under ground control after a tense few days, but with a gecko sex experiment on board, the media just couldn't help themselves. Video provided by Newsy
Powered by NewsLook.com


NASA (July 25, 2014) NASA EDGE webcasts live from Vandenberg AFB for the launch of the Oribiting Carbon Observatory-2 (OCO) launch. Video provided by NASA
Powered by NewsLook.com
This Week @ NASA, July 25, 2014

This Week @ NASA, July 25, 2014

NASA (July 25, 2014) Apollo 11 celebration, Next Giant Leap anticipation, ISS astronauts appear in the House and more... Video provided by NASA
Powered by NewsLook.com
Space to Ground: Coming and Going

Space to Ground: Coming and Going

NASA (July 25, 2014) One station cargo ship leaves, another arrives, aquatic research and commercial spinoffs. Questions or comments? Use #spacetoground to talk to us. Video provided by NASA
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.


Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News


Free Subscriptions

Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile

Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?

Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile: iPhone Android Web
Follow: Facebook Twitter Google+
Subscribe: RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins