arcsecond

An arcsecond (arcsec or second of arc, or in context, second or sec) is a unit of angle or arc, commonly used in astronomy for celestial coordinate systems and distances across the celestial sphere. A degree (angular degree, unit of angle corresponding to 1/360 of a full circle which is 1/90 of a right angle) is divided into 60 arcminutes (arcmin, minute of arc, or in context, minute or min), which, in turn, is divided into 60 arcseconds, making an arcsecond 1/3600 of a degree or 1/1296000 of a full circle, or 2π/1296000 of a radian. A milli-arcsecond (or mas) and micro-arcsecond are 1/1000 and 1/1000000 of this unit.

Right ascension is traditionally indicated by a different set of units, hours (aka angular hours), 1/24 (15 angular degrees) of the circle around the sky at the given declination, which corresponds to the shift in the sky over the course of an hour (1/24 of a day). Fractions of an (angular) hour are also expressed as (angular) minutes (1/60 angular hour) and (seconds (1/60 minute). These minutes and seconds are not the same angular size as arcminutes and arcseconds, creating the possibility of ambiguity. The only terms I've been able to find to avoid the ambiguity are minute of right ascension, second of right ascension, and hour of right ascension. It is significant that the angle measured in hours is between planes through Earth's axis, or equivalently, an angular distance along the celestial equator: two objects with coordinates differing by an hour are generally separated by less than an angular distance of 15 degrees; for example, a pair of stars within a degree of the celestial north pole are within two degrees of each other regardless of their hour-difference.

When describing patches of the sky (e.g., survey fields) astronomers often avoid units of right ascension: radians (1/2π of a full circle, the length of the circle's radius) may be used, or angular measures such as degrees, arcminutes, and arcseconds may be used. The same is true of small angles, such as the yearly proper motion of a star. Also, degrees are sometimes expressed in decimal fashion rather than using arcminutes and arcseconds, and arcminutes (and perhaps minutes of right ascension) are also sometimes expressed in decimal fashion. Equivalences:

(These are hours, minutes, and seconds of right ascension, the table referring to their implied angles between the planes associated with meridians with that difference in right ascension, or equivalently, the angular distance at the equator.)