arcsecond

An arcsecond is a unit of angular measurement equal to 1/3600 of a degree. It is part of the sexagesimal system used in astronomy to express small angles. One arcsecond is commonly abbreviated arcsec and is often written with a double prime symbol (″) in print. There are 60 arcseconds in an arcminute and 60 arcminutes in a degree.

In radians, one arcsecond equals pi/648000 radians, approximately 4.8481 x 10^-6 radians. Equivalently, 1 degree is about 57.2958 degrees, so a single arcsecond is a very small portion of a degree, about 1/3600 of a degree.

In astronomy, arcseconds are used to express angular sizes, separations between objects, and parallaxes. They quantify the apparent size of stars and galaxies as seen from Earth, as well as the apparent separation of close binary stars. The concept of resolving power is often stated in arcseconds; for example, the Rayleigh criterion gives a telescope’s theoretical resolution approximately theta ≈ 1.22 lambda/D, which translates to sub-arcsecond scales for large apertures under ideal conditions, though atmospheric seeing commonly limits practical measurements to around an arcsecond on many nights.

The milliarcsecond (mas), equal to one thousandth of an arcsecond, is widely used in modern astrometry to describe extremely small angles. Missions such as Gaia measure stellar positions with accuracies in the microarcsecond to milliarcsecond range, enabling precise parallax and proper motion determinations.

History and usage note: the arcsecond arises from repeatedly dividing a degree into 60 arcminutes and each arcminute into 60 arcseconds, following the historical sexagesimal system.