The Laplace–Runge–Lenz vector is a vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another, such as a planet revolving around a sun. For two bodies interacting by Newtonian gravity, the LRL vector is a constant of motion, meaning that it is the same no matter where it is calculated on the orbit; equivalently, the LRL vector is said to be conserved. More generally, the LRL vector is conserved in all problems in which two bodies interact by a central force that varies as the inverse square of the distance between them; such problems are called Kepler problems. The hydrogen atom is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law of electrostatics, another inverse square central force. The LRL vector was essential in the first quantum mechanical derivation of the spectrum of the hydrogen atom, before the development of the Schrödinger equation. The Laplace–Runge–Lenz vector is named after Pierre-Simon de Laplace, Carle Runge and Wilhelm Lenz. The LRL vector has been re-discovered several times and is also equivalent to the dimensionless eccentricity vector of celestial mechanics. Various generalizations of the LRL vector have been defined, which incorporate the effects of special relativity, electromagnetic fields and even different types of central forces.

Read the rest of this article: http://en.wikipedia.org/wiki/Laplace%E2%80%93Runge%E2%80%93Lenz_vector

_______________________________ Today's selected anniversaries:

1916:

Emperor Charles I of Austria and Empress Zita were coronated as the last King and Queen of Hungary. http://en.wikipedia.org/wiki/Coronation_of_the_Hungarian_monarch

1924:

Astronomer Edwin Hubble announced that Andromeda, previously believed to be a nebula, is actually another galaxy, and that the Milky Way is only one of many such galaxies in the universe. http://en.wikipedia.org/wiki/Edwin_Hubble

1947:

Michael, King of Romania, was forced to abdicate as the Kingdom of Romania became Communist Romania. http://en.wikipedia.org/wiki/Michael_of_Romania

2000:

A series of bombings occurred around Metro Manila in the Philippines within a span of a few hours, killing 22 people and injuring 100 others. http://en.wikipedia.org/wiki/Rizal_Day_bombings

2005:

Tropical Storm Zeta was declared a tropical depression, making it the record-breaking thirtieth tropical cyclone of the 2005 Atlantic hurricane season, the most active in recorded history. http://en.wikipedia.org/wiki/Tropical_Storm_Zeta

_____________________________ Wiktionary's word of the day:

monochrome (n): 1. A black and white image, especially a photograph. 2. A ceramic glaze of a single colour, or an object so glazed. 3. <span class="qualifier-brac">(</span><span class="qualifier-content">dated</span><span class="qualifier-brac">)</span> A painting executed in shades of a single colour http://en.wiktionary.org/wiki/monochrome

___________________________ Wikiquote quote of the day:

Justice has nothing to do with victor nations and vanquished nations, but must be a moral standard that all the world's peoples can agree to. To seek this and to achieve it — that is true civilization. --Hideki Tojo http://en.wikiquote.org/wiki/Hideki_Tojo