During the course of one day, the stars and other celestial objects appear to move in circles about a single point in the sky. This point is the north celestial pole for observers in the northern hemisphere or the south celestial pole in the southern hemisphere, and it marks the intersection of the Earth's spin axis with the celestial sphere. Stars which are close enough to the pole remain above the horizon all day and are called circumpolar stars. Stars which are far enough away from the pole spend part of the day below the horizon. As they cross the horizon on the way down they set, and as they cross on the way up they rise. Stars further still from the pole spend all day below the horizon and are never seen in that location.

Routine RISET finds the circumstances of rising and setting for a celestial object whose right ascension and declination are known. The local sidereal times are calculated for a given geographical latitude, GP, and are returned via the variables LU (rising) and LD (setting). The azimuths are also given by AU and AD. the local sidereal times may be converted to Greenwich sidereal times, Universal Times, and local civil times using routine TIME (1300).

The coordinates input to the routine by X and Y are usually the true geocentric coordinates.