astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...

and celestial navigation, the hour angle is the

angle In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the '' vertex'' of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles a ...

between two planes: one containing Earth's axis and the

zenith The zenith (, ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction ( plumb line) opposite to the gravity direction at that location ( nadir). The zenith is the "high ...

(the '' meridian plane''), and the other containing Earth's axis and a given point of interest (the ''

hour circle In astronomy, the hour circle, which together with declination and distance (from the planet's centre of mass) determines the location of any celestial object, is the great circle through the object and the two celestial poles. As such, it is a ...

''). 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^h = 360° exactly. In celestial navigation, the convention is to measure in degrees westward from the

prime meridian A prime meridian is an arbitrary meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°. Together, a prime meridian and its anti-meridian (the 180th meridian in a 360°-system) form a great ...

(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 equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fu ...

Relation with right ascension

The local hour angle (LHA) of an object in the observer's sky is

\text_ =  - \alpha_

\text_ =  + \lambda_ - \alpha_

where LHA_object is the local hour angle of the object, LST is the local sidereal time,

\alpha_

is the object's right ascension, GST is

Greenwich sidereal time Sidereal time (as a unit also sidereal day or sidereal rotation period) (sidereal ) is a timekeeping system that astronomers use to locate celestial objects. Using sidereal time, it is possible to easily point a telescope to the proper coord ...

and

\lambda_

is the observer's

longitude Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lette ...

(positive east from the

). 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_object < 0°) indicate the object is approaching the meridian, positive hour angles (0° < LHA_object < 180°) indicate the object is moving away from the meridian; an hour angle of zero means the object is on the meridian.

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 Noon (or midday) is 12 o'clock in the daytime. It is written as 12 noon, 12:00 m. (for meridiem, literally 12:00 noon), 12 p.m. (for post meridiem, literally "after noon"), 12 pm, or 12:00 (using a 24-hour clock) or 1200 ( military time). Sola ...

. 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). The cosine of the hour angle (cos(''h'')) is used to calculate the

solar zenith angle The solar zenith angle is the zenith angle of the sun, i.e., the angle between the sun’s rays and the vertical direction. It is the complement to the solar altitude or solar elevation, which is the altitude angle or elevation angle between the ...

. At solar noon, so , and before and after solar noon the cos(± ''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.

Sidereal hour angle

The sidereal hour angle (SHA) of a body on the celestial sphere is its angular distance west of the vernal equinox generally measured in degrees. The SHA of a star varies by less than a minute of arc per year, due to

precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In oth ...

, 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 astronomical

almanac An almanac (also spelled ''almanack'' and ''almanach'') is an annual publication listing a set of current information about one or multiple subjects. It includes information like weather forecasts, farmers' planting dates, tide tables, and othe ...

Notes and references

{{DEFAULTSORT:Hour Angle Astronomical coordinate systems

Relation with right ascension

Solar hour angle

Sidereal hour angle

See also

Notes and references