# True longitude

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In [celestial mechanics](/source/celestial_mechanics), '''true longitude''' is the [ecliptic longitude](/source/Ecliptic_coordinate_system) at which an orbiting body could actually be found if its [inclination](/source/inclination) were zero.  Together with the inclination and the [ascending node](/source/ascending_node), the true longitude can tell us the precise direction from the central object at which the body would be located at a particular time.

==Calculation==
The true longitude {{math|''l''}} can be calculated as follows:<ref name=Moulton_1970>{{cite book|last=Multon|first=F. R.|date=1970|title=An Introduction to Celestial Mechanics|edition=2nd|pages=182–183|location=New York, NY|publisher=Dover}}</ref><ref name=Roy_1978>{{cite book|last=Roy|first=A. E.|date=1978|title=Orbital Motion|page=174|ISBN=0-470-99251-4|location=New York, NY|publisher=[John Wiley & Sons](/source/John_Wiley_%26_Sons)}}</ref><ref name=Brouwer_Clemence_1961>{{cite book|last1=Brouwer|first1=D.|last2=Clemence|first2=G. M.|date=1961|title=Methods of Celestial Mechanics|url=https://archive.org/details/methodsofcelesti00brou|url-access=registration|page=[https://archive.org/details/methodsofcelesti00brou/page/45 45]|location=New York, NY|publisher=[Academic Press](/source/Academic_Press)}}</ref>

:{{math|1=''l'' = ''ν'' + ''ϖ''}}

where:
*{{math|''ν''}} is the orbit's [true anomaly](/source/true_anomaly),
*{{math|''ϖ'' ≡ ''ω'' + ''Ω''}} is the [longitude of orbit's periapsis](/source/longitude_of_the_periapsis),
**{{math|''ω''}} is the [argument of periapsis](/source/argument_of_periapsis), and
**{{math|''Ω''}} is the [longitude of the orbit's ascending node](/source/longitude_of_the_ascending_node),

==References==
{{Reflist}}

{{Orbits}}

{{DEFAULTSORT:True Longitude}}
Category:Orbits
Category:Equations of astronomy

{{Astrophysics-stub}}

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Adapted from the Wikipedia article [True longitude](https://en.wikipedia.org/wiki/True_longitude) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/True_longitude?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.