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Concept
Hour angle
Summary
In astronomy and celestial navigation, the hour angle is the angle between two planes: one containing Earth's axis and the zenith (the meridian plane), and the other containing Earth's axis and a given point of interest (the hour circle).
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 24h = 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 (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.
The local hour angle (LHA) of an object in the observer's sky is
or
where LHAobject is the local hour angle of the object, LST is the local sidereal time, is the object's right ascension, GST is Greenwich sidereal time and is the observer's longitude (positive east from the prime meridian). 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° < LHAobject < 0°) indicate the object is approaching the meridian, positive hour angles (0° < LHAobject < 180°) indicate the object is moving away from the meridian; an hour angle of zero means the object is on the meridian.
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).
Official source
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