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In [[celestial mechanics]], the '''longitude of the periapsis''' (symbolized [[Pi (letter)#Variant pi|&piv;]]) of an orbiting body is the [[longitude]] (measured from the point of the vernal equinox) at which the [[periapsis]] (closest approach to the central body) would occur if the body's [[inclination]] were zero. For motion of a planet around the Sun, this position could be called '''longitude of perihelion'''. The longitude of periapsis is a compound angle, with part of it being measured in the [[plane of reference]] and the rest being measured in the plane of the [[orbit]].  Likewise, any angle derived from the longitude of periapsis (e.g. [[mean longitude]] and [[true longitude]]) will also be compound.


Sometimes, the term ''longitude of periapsis'' is used to refer to ω, the angle between the ascending node and the periapsis. That usage of the term is especially common in discussions of binary stars and exoplanets.<ref>See e.g. p. 201, [http://books.google.com/books?id=iCsdAAAAMAAJ ''The Binary Stars''], Robert Grant Aitken, Semicentennial Publications of the University of California, 1918, or [http://ad.usno.navy.mil/wds/orb6/format.html Format, ''Sixth Catalog of Orbits of Visual Binary Stars''], William I. Hartkopf & Brian D. Mason, U. S. Naval Observatory, Washington, D.C.  Accessed on line October 25, 2008</ref> However, the angle ω is less ambiguously known as the [[argument of periapsis]].
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==Calculation from state vectors==
 
<math>\varpi</math> can be calculated from [[longitude of ascending node]] <math>\Omega</math> and [[argument of periapsis]] <math>\omega</math>:
 
<math>\varpi = \Omega + \omega</math>
 
which are derived from [[orbital state vectors]].
 
==References==
{{reflist}}
 
==External links==
* [http://aom.giss.nasa.gov/srorbpar.html Determination of the Earth's Orbital Parameters ] Past and future longitude of perihelion for Earth. [link dead as of 2014-01-14]
 
[[Category:Orbits]]

Latest revision as of 20:05, 1 January 2015

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