Featured Research

from universities, journals, and other organizations

Math Unites The Celestial And The Atomic

Date:
October 5, 2005
Source:
Georgia Institute of Technology
Summary:
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

Related Articles


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 January 31, 2015 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 January 31, 2015).

Share This


More From ScienceDaily



More Space & Time News

Saturday, January 31, 2015

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Video Shows Stars If They Were as Close to Earth as Sun

Video Shows Stars If They Were as Close to Earth as Sun

Buzz60 (Jan. 30, 2015) Russia&apos;s space agency created a video that shows what our sky would look like with different star if they were as close as our sun. Patrick Jones (@Patrick_E_Jones) walks us through the cool video. Video provided by Buzz60
Powered by NewsLook.com
Dog-Loving Astronaut Wins Best Photo of 2015

Dog-Loving Astronaut Wins Best Photo of 2015

Buzz60 (Jan. 30, 2015) Retired astronaut and television host, Leland Melvin, snuck his dogs into the NASA studio so they could be in his official photo. As Mara Montalbano (@maramontalbano) shows us, the secret is out. Video provided by Buzz60
Powered by NewsLook.com
NASA Holds Memorial to Remember Astronauts

NASA Holds Memorial to Remember Astronauts

AP (Jan. 29, 2015) NASA is remembering 17 astronauts who were killed in the line of duty and dozens more who have died since the agency&apos;s beginning. A remembrance ceremony was held Thursday at NASA&apos;s Marshall Space Flight Center in Alabama. (Jan. 29) Video provided by AP
Powered by NewsLook.com
Asteroid's Moon Spotted During Earth Flyby

Asteroid's Moon Spotted During Earth Flyby

Rumble (Jan. 27, 2015) Scientists working with NASA&apos;s Deep Space Network antenna at Goldstone, California discovered an unexpected moon while observing asteroid 2004 BL86 during its recent flyby past Earth. Credit to &apos;NASA JPL&apos;. Video provided by Rumble
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.

Save/Print:
Share:

Breaking News:

Strange & Offbeat Stories


Space & Time

Matter & Energy

Computers & Math

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:

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