Hour angle

Relation with right ascension

The local hour angle (LHA) of an object in the observer's sky is \text{LHA}{\text{object}} = {\text{LST}} - \alpha{\text{object}} or \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, \alpha_{\text{object}} is the object's right ascension, GST is Greenwich sidereal time and \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° object object

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.

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 (about 1.0027) 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{{anchor|Solar}}

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).

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 (cos(h)) is used to calculate the solar zenith angle. 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 March equinox generally measured in degrees. The SHA of a star varies by less than a minute of arc per year, due to precession, 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 nautical almanacs.

References

1. U.S. Naval Observatory Nautical Almanac Office. (1992). "Explanatory Supplement to the Astronomical Almanac". University Science Books.
2. ''Explanatory Supplement'' (1992), p. 724.
3. Meeus, Jean. (1991). "Astronomical Algorithms". Bell, Inc., Richmond, VA.
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