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.
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Today's selected anniversaries:
Emperor Charles I of Austria and Empress Zita were coronated as the
last King and Queen of Hungary.
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.
Michael, King of Romania, was forced to abdicate as the Kingdom of
Romania became Communist Romania.
A series of bombings occurred around Metro Manila in the Philippines
within a span of a few hours, killing 22 people and injuring 100
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.
Wiktionary's word of the day:
1. A black and white image, especially a photograph.
2. A ceramic glaze of a single colour, or an object so glazed.
class="qualifier-brac">)</span> A painting executed in shades of a
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.
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