Moon phases occur with a period equal to the synodic period of the moon, equal to 29.530589 days, or 29 days, 12 hours, 44 minutes, 3 seconds. However, there is a great deal of variation in the actual time for a given lunation (the time between two successive new moons).

The phase of the moon is determined by its position relative to the Sun (which illuminates the side of the Moon facing it) and the Earth (from where the Moon is observed). Moonrise and moonset times correspond directly to the phase of the moon. For example, when the Sun, Earth, and Moon are in a line (in that order), the near side of the Moon is facing both the Earth and the Sun, and will therefore be completely illuminated, corresponding to a full moon. Since a full moon will be overhead at midnight, it will therefore rise around 6 p.m. and set around 6 a.m. Similarly, if the Sun, Moon, and Earth are in a line (in that order), the illuminated side of the Moon faces the Sun, while the other side faces the Earth, corresponding to a new moon. Since a new moon will be overhead at noon, it will therefore rise around 6 a.m. and set around 6 p.m.

The sequence of names for moon phases (starting at new moon), as illustrated above, is: new moon, crescent waxing, half-moon waxing, gibbous waxing, full moon, gibbous waning,half-moon waning, and crescent waning. A calendar of Moon phases for a given year can be generated using MoonCalendar[year] in the Mathematica application package Scientific Astronomer.

The age of the moon on the Dth day of the Mth month of the th year of the Gregorian calendar with is roughly

(1)

where

(2)

, and

(3)

Full Moon, Lunation, Moon, Moonrise, Moonset, New Moon, Old Moon in the New Moon's Arms, Sunrise, Sunset, Synodic Month