Hour angle

In astronomy and celestial navigation, the hour angle is the dihedral angle between the meridian plane (containing Earth's axis and the zenith) and the hour circle (containing Earth's axis and a given point of interest).

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.

Relation with right ascension

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

LHA

object

=

LST

−

α

object

{\text{LHA}}_{\text{object}}={\text{LST}}-\alpha _{\text{object}}

or

LHA

object

=

GST

+

λ

observer

−

α

object

{\text{LHA}}_{\text{object}}={\text{GST}}+\lambda _{\text{observer}}-\alpha _{\text{object}}

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

α

object

{\displaystyle \alpha _{\text{object}}}

is the object's right ascension, GST is Greenwich sidereal time and

λ

observer

{\displaystyle \lambda _{\text{observer}}}

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.

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.