Hour angle
In astronomy and celestial navigation, the hour angle is the dihedral angle between the meridian plane and 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, from the local meridian or from the first point of Aries.
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.
Relation with right ascension
The local hour angle of an object in the observer's sky isor
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. These angles can be measured in time or in degrees —one or the other, not both.
Negative hour angles indicate the object is approaching the meridian, positive hour angles 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 in astronomy, though may be given in decimal hours, sexagesimal degrees, or, decimal degrees.
Because the earth rotates 365.2564 times in a sidereal year whereas fixed stars appear to go around one time more, the hour angle of a fixed star increases by 366.2564/365.2564 per hour, or in other words it takes 59 minutes and 50.17 seconds for the hour angle to increase by one hour.
Solar hour angle
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°.The solar hour angle increases on average by one hour per hour, but because of the equation of time this varies with time of year. In mid-September a solar day is about 22 seconds less than 24 hours, meaning that the solar hour angle increases by 1.00025 hours per hour, whereas in late December a solar day is about 28 seconds more than 24 hours, so the solar hour angle increases by 0.99968 hours per hour.
The cosine of the hour angle is used to calculate the solar zenith angle. At solar noon, so, and before and after solar noon the cos term = the same value for morning or afternoon, so that the Sun is at the same altitude in the sky at 11:00AM and 1:00PM solar time.