Spirograph: Difference between revisions

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{{Confusing|date=July 2009}}
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]].
 
==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]]

Revision as of 07:48, 9 January 2014

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My web site - http://www.hostgator1centcoupon.info/ In celestial mechanics, the longitude of the periapsis (symbolized ϖ) 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.[1] However, the angle ω is less ambiguously known as the argument of periapsis.

Calculation from state vectors

can be calculated from longitude of ascending node and argument of periapsis :

which are derived from orbital state vectors.

References

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External links

  1. ↑ See e.g. p. 201, The Binary Stars, Robert Grant Aitken, Semicentennial Publications of the University of California, 1918, or 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
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