Editing Hour angle

{{Short description|Coordinates used in the equatorial coordinate system}}
{{More citations needed|date=April 2018}}
[[File:HourAngle_Observer_en.png|thumb|right|300px|The hour angle is indicated by an orange arrow on the [[celestial equator]] plane. The arrow ends at the [[hour circle]] of an orange dot indicating the [[apparent place]] of an [[astronomical object]] on the [[celestial sphere]].]]

In [[astronomy]] and [[celestial navigation]], the '''hour angle''' is the [[dihedral angle]] between the ''[[meridian plane]]'' (containing [[axial tilt|Earth's axis]] and the [[zenith]]) and the ''[[hour circle]]'' (containing Earth's axis and a given point of interest).<ref>{{cite book |author=U.S. Naval Observatory Nautical Almanac Office |editor=P. Kenneth Seidelmann |title=Explanatory Supplement to the Astronomical Almanac |publisher=University Science Books |location=[[Mill Valley, California|Mill Valley, CA]] |date=1992 |page=729 |isbn=0-935702-68-7}}</ref> 

It may be given in degrees, time, or rotations depending on the application.
The angle may be expressed as negative east of the 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.
In [[celestial navigation]], the convention is to measure in degrees westward from the [[prime meridian]] ('''Greenwich hour angle''', '''GHA'''), from the local meridian ('''local hour angle''', '''LHA''') or from the [[First Point of Aries|first point of Aries]] ('''sidereal hour angle''', '''SHA''').

The hour angle is paired with the [[declination]] to fully specify the location of a point on the [[celestial sphere]] in the [[equatorial coordinate system]].<ref>''Explanatory Supplement'' (1992), p. 724.</ref>

==Relation with right ascension==
[[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 dot). 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 [[March equinox]] direction.<br>Assuming in this example the day of the year is the March equinox so the sun lies in the direction of the grey arrow then this star will rise about midnight. Just after the observer reaches the green arrow dawn comes and overwhelms with light the visibility of the star about six hours before it sets on the western horizon. The Right Ascension of the star is about 18<sup>h</sup>]]

The local hour angle (LHA) of an object in the observer's sky is
<math display=>\text{LHA}_{\text{object}} = {\text{LST}} - \alpha_{\text{object}}</math>
or
<math display=>\text{LHA}_{\text{object}} = {\text{GST}} + \lambda_{\text{observer}} - \alpha_{\text{object}}</math>
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 east from the [[prime meridian]]).<ref>{{cite book  | last = Meeus | first = Jean | title = Astronomical Algorithms | publisher = Bell, Inc., Richmond, VA | date = 1991 | page = 88 | 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.

Negative hour angles (−180° < LHA<sub>object</sub> < 0°) indicate the object is approaching the meridian, positive hour angles (0° < LHA<sub>object</sub> < 180°) indicate the object is moving away from the meridian; an hour angle of zero means the object is on the meridian.

Right ascension is frequently given in sexagesimal hours-minutes-seconds format (HH:MM:SS) in astronomy, though may be given in decimal hours, sexagesimal degrees (DDD:MM:SS), or, decimal degrees.

==Solar hour angle{{anchor|Solar}}==
{{see also|Sunrise equation}}

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 zero 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 book | last1 = Kreider | first1 = J. F. | chapter = Solar Energy Applications | doi = 10.1002/9780470209738.ch2 | title = Environmentally Conscious Alternative Energy Production | pages = 13–92 | year = 2007 | isbn = 9780470209738 }}</ref>

The [[cosine]] of the hour angle (cos(''h'')) is used to calculate the [[solar zenith angle]]. At solar noon, {{math|1=''h'' = 0.000}} so {{math|1=cos(''h'') = 1}}, and before and after solar noon the cos(±&nbsp;''h'') term = the same value for morning (negative hour angle) or afternoon (positive hour angle), so that the Sun is at the same altitude in the sky at 11:00AM and 1:00PM solar time.<ref>{{Cite book | last1 = Schowengerdt | first1 = R. A. | chapter = Optical radiation models | doi = 10.1016/B978-012369407-2/50005-X | title = Remote Sensing | pages = 45–88 | year = 2007 | isbn = 9780123694072 }}</ref>

==Sidereal hour angle==
The sidereal hour angle (SHA) of a body on the celestial sphere is its angular distance west of the [[Equinox (celestial coordinates)|March equinox]] generally measured in degrees. The SHA of a star varies by less than a minute of arc per year, due to [[precession]], while the SHA of a planet varies significantly from night to night. SHA is often used in [[celestial navigation]] and navigational astronomy, and values are published in nautical [[almanac]]s.{{fact|date=June 2021}}

==See also==
* [[Clock position]]
* [[List of orbits]]

==Notes and references==
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[[Category:Astronomical coordinate systems]]
[[Category:Angle]]