Routine RISET (3100) calculates the times and azimuths of rising and setting of a celestial body given its right ascension and declination as input parameters. We may therefore combine it with the routines MOON (6000) and EQECL (2000) to find the circumstances of moonrise and moonset at any place on the Earth's surface for any given calendar date. There is a snag, however, as the Moon's position is constantly changing by about half a degree of ecliptic longitude per hour and, unless we already know the times of rising and setting, we cannot find the correct position of the Moon in advance. If we use the position calculated for a set time, say midnight, we may be as much as one hour out in the calculation of moonrise and moonset. We must therefore adopt an iterative procedure, refining an initial crude estimate to achieve the required accuracy, just as in SUNRS (3600).

Routine MOONRS first calculates the right ascension and declination of the Moon at local midday of the given date, making allowance for nutation (NUTAT, 1800). Then the universal times (UTs) and azimuths of the corresponding moonrise and moonset are found via RISET (3100) and TIME (1300) with the corrections for parallax, refraction and the angular size of the Moon's disk incorporated in the parameter DI. The Moon's position is now recalculated at each of these approximations to moonrise or moonset and the whole procedure repeated twice more to find times of rising and setting accurate to within one minute, and azimuths to within about 1 arcminute.