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| In [[astronomy]] and [[celestial navigation]], the '''hour angle''' is one of the coordinates used in the [[equatorial coordinate system]] to give the direction of a point on the [[celestial sphere]].
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| The hour angle of a point is the angle between two planes: one containing the [[Axial tilt|Earth's axis]] and the [[zenith]] (the [[Meridian_(astronomy)|meridian]] plane), and the other containing the [[Axial tilt|Earth's axis]] and the given point (the [[hour circle]] passing through the point).
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| [[File:Hour angle still1.png|thumb|right|300px|As seen from above the [[Earth]]'s [[geographic pole|north pole]], a star's local hour angle (LHA) for an observer near New York (red). Also depicted are the star's [[right ascension]] and Greenwich hour angle (GHA), the [[Sidereal_time|local mean sidereal time]] (LMST) and [[Sidereal_time|Greenwich mean sidereal time]] (GMST). The symbol ʏ identifies the [[equinox|vernal equinox]] direction.]]
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| The angle may be expressed as negative east of the [[Meridian (astronomy) | meridian plane]] and positive west of the meridian plane, or as positive westward from 0° to 360°. The angle may be measured in degrees or in time, with 24<sup>h</sup> = 360° exactly.
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| In [[astronomy]], hour angle is defined as the [[angle|angular distance]] on the [[celestial sphere]] measured westward along the [[celestial equator]] from the [[Meridian (astronomy) | meridian]] to the [[hour circle]] passing through a point.<ref>
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| {{cite book
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| | author = U.S. Naval Observatory Nautical Almanac Office
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| | editor = P. Kenneth Seidelmann
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| | title = Explanatory Supplement to the Astronomical Almanac
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| | publisher = University Science Books, Mill Valley, CA
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| | year = 1992
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| |page=729
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| | isbn = 0-935702-68-7}}</ref> It may be given in degrees, time, or rotations depending on the application.
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| In [[celestial navigation]], the convention is to measure in degrees westward from the [[prime meridian]] (Greenwich hour angle, GHA), the [[Meridian_(astronomy)|local meridian]] (local hour angle, LHA) or the [[Vernal_equinox#Celestial_coordinate_systems|first point of Aries]] (sidereal hour angle, SHA).
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| The hour angle is paired with the [[declination]] to fully specify the direction of a point on the [[celestial sphere]] in the [[equatorial coordinate system]].<ref>
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| ''Explanatory Supplement'' (1992), p. 724.</ref>
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| ==Relation with the right ascension==
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| The local hour angle (LHA) of an object in the observer's sky is
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| :<math>\text{LHA}_{\text{object}} = {\text{LST}} - \alpha_{\text{object}}</math>
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| :or
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| :<math>\text{LHA}_{\text{object}} = {\text{GST}} - \lambda_{\text{observer}} - \alpha_{\text{object}}</math>
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| where LHA<sub>object</sub> is the local hour angle of the object, LST is the [[Sidereal_time|local sidereal time]], <math>\alpha_{\text{object}}</math> is the object's [[right ascension]], GST is [[Sidereal_time|Greenwich sidereal time]] and <math>\lambda_{\text{observer}}</math> is the observer's [[longitude]] (positive west from the [[Prime_Meridian|prime meridian]]).<ref>
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| {{cite book
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| | last = Meeus
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| | first = Jean
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| | title = Astronomical Algorithms
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| | publisher = Willmann-Bell, Inc., Richmond, VA
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| | year = 1991
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| |page=88
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| |ISBN=0-943396-35-2 }}</ref> These angles can be measured in time (24 hours to a circle) or in degrees (360 degrees to a circle)— one or the other, not both.
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| Negative hour angles indicate the time until the next transit across the meridian; an hour angle of zero means the object is on the meridian.
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| ==Solar hour angle==
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| Observing the sun from earth, the '''solar hour angle''' is an expression of time, expressed in angular measurement, usually degrees, from [[solar noon]]. At solar noon the hour angle is 0.000 degrees, with the time before solar noon expressed as negative degrees, and the local time after solar noon expressed as positive degrees. For example, at 10:30 AM local apparent time the hour angle is -22.5° (15° per hour times 1.5 hours before noon).<ref>{{cite doi|10.1002/9780470209738.ch2}}</ref>
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| The [[cosine]] of the hour angle (cos(''h'')) is used to calculate the [[solar zenith angle]]. At solar noon, ''h'' = 0.000 so cos(''h'')=1, and before and after solar noon the cos(± ''h'') term = the same value for morning (negative hour angle) or afternoon (positive hour angle), i.e. the sun is at the same altitude in the sky at 11:00AM and 1:00PM solar time, etc.<ref>{{cite doi|10.1016/B978-012369407-2/50005-X}}</ref>
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| ==Sidereal hour angle==
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| The sidereal hour angle of a body on the celestial sphere is its angular distance west of the [[Vernal_equinox#Celestial_coordinate_systems|vernal equinox]] generally measured in degrees. The SHA of a star changes slowly, and the SHA of a planet doesn't change very quickly, so SHA is a convenient way to list their positions in an almanac. SHA is often used in [[celestial navigation]] and navigational astronomy.
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| ==Notes and references==
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| {{reflist}}
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| {{DEFAULTSORT:Hour Angle}}
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| [[Category:Celestial coordinate system]]
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