hour angle

In astronomy, the hour angle is one of the coordinates used in the equatorial coordinate system for describing the position of a point on the celestial sphere. The hour angle of a point is the angle between the half plane determined by the Earth axis and the zenith (half of the meridian plane) and the half plane determined by the Earth axis and the given point. The angle is taken with minus sign if the point is eastward of the meridian plane and with the plus sign if the point is westward of the meridian plane.

The hour angle is usually expressed in time units, with 24 hours corresponding to 360 degrees.

The hour angle must be paired with the declination in order to fully specify the position of a point on the celestial sphere as seen by the observer at a given time.

Relation with the right ascension

The hour angle (HA) of an object is equal to the difference between the current local sidereal time (LST) and the right ascension (α) of that object:

HA_object = LST - α_object

Thus, the object's hour angle indicates how much sidereal time has passed since the object was on the local meridian. It is also the angular distance between the object and the meridian, measured in hours (1 hour = 15 degrees). For example, if an object has an hour angle of 2.5 hours, it transited across the local meridian 2.5 sidereal hours ago (i.e., hours measured using sidereal time), and is currently 37.5 degrees west of the meridian. Negative hour angles indicate the time until the next transit across the local meridian. Of course, an hour angle of zero means the object is currently on the local meridian.

Solar hour angle

The hour angle (h or ha) of a point on the earth's surface is the angle through which the earth would turn to bring the meridian of the point directly under the sun. The earth is rotating, so this angular displacement represents time.

So in observing the sun from earth, the solar hour angle is an expression of time, expressed in angular measurement, most usually degrees, from the solar noon.

At solar noon, at that observer's longitude on earth, the hour angle is 0.000 degrees with the time before solar noon expressed as negative degrees, and the local time after solar noon expressed as positive degrees.

The hour angle is the angular displacement of the sun east or west of the local meridian due to rotation of the earth on its axis at 15^o per hour with morning being negative and afternoon being positive. For example, at 10:30 am, the hour angle is -22.5^o (15^o per hour times 1.5 hours before noon).

The cosine of the hour angle (cosh) becomes an easy computation tool in determining the cosine term for the computation of the angle of the sun's altitude (or the complementary zenith angle) at any time during the day. At solar noon, h=0.000 so of course, cosh=1, and before and after solar noon the cos(± h) term = the same value for morning (negative hour angle) or afternoon (positive hour angle), i.e. the sun is at the same altitude in the sky at both 11:00AM and 1:00PM solar time, etc.