Routine RISET (3100) calculates the local sidereal times and azimuths of a celestial body given its right ascension and declination as input parameters. We may combine this routine with SUN (3400) and EQECL (2000) to calculate the right ascension and declination of the Sun on any given date, and hence the circumstances of sunrise and sunset. The procedure is complicated, however, by the fact that the Sun is not stationary in the sky with respect to the background of stars but moves by about 1 degree of ecliptic longitude per day. The calculated circumstances of rising and setting would be correct for an object at the Sun's position at the given instant, but would not correspond exactly with the observed circumstances of sunrise or sunset unless we had chosen the correct time already. We therefore have to adopt an iterative procedure, refining an initial crude estimate to achieve the required accuracy.

Routine SUNRS first calculates the Sun's right ascension and declination at local midday of the date in question, and hence the local sidereal times of rising and setting corresponding to the Sun's position at midday. The times are then corrected for the observer's longitude to find the Greenwich sidereal times, and converted to universal times using routine TIME. These times are already fair approximations to the actual times of rising and setting.