Phases of the Moon and Percent Illuminated
From any location on the Earth, the Moon appears to be a circular disk which, at any specific time, is illuminated to some degree by direct sunlight. The geometric shape of the illuminated part and its size, relative to the entire lunar hemisphere that faces the Earth, are continuously changing entities as the Moon orbits the Earth. During each lunar orbit (a lunar month), the Moon's appearance varies from not visibly illuminated to fully illuminated, then to not illuminated again. Although this cycle is a continuous process, there are eight distinct, traditionally recognized stages, called phases, which are ordinarily adequate to designate both the degree to which the Moon is illuminated and the geometric appearance of the illuminated part, to the extent that Moon visibility has relevance to everyday human activities. These phases of the Moon, in the sequence of their occurrence, are:
New Moon -- the Moon is not illuminated by direct sunlight.
Waxing Crescent -- the visible Moon is partly but less than one-half illuminated by direct sunlight while the illuminated part is increasing.
First Quarter -- one-half of the Moon appears illuminated by direct sunlight while the illuminated part is increasing.
Waxing Gibbous -- the Moon is more than one-half but not fully illuminated by direct sunlight while the illuminated part is increasing.
Full Moon -- the visible Moon is fully illuminated by direct sunlight.
Waning Gibbous -- the Moon is less than fully but more than one-half illuminated by direct sunlight while the illuminated part is decreasing.
Last Quarter -- one-half of the Moon appears illuminated by direct sunlight while the illuminated part is decreasing.
Waning Crescent -- the Moon is partly but less than one-half illuminated by direct sunlight while the illuminated part is decreasing.
Following Waning Crescent is a New Moon, beginning a repetition of the complete phase cycle of 29.5 days average duration.
The Crescent and Gibbous phases are descriptive of the appearance of the illuminated part of the Moon during the intervals between the New, First Quarter, Full, and Last Quarter phases. The phases of the Moon are related to the relative positions of the Moon and Sun in the sky. For example, New Moon occurs when the Sun and Moon are quite close together in the sky. Full Moon occurs when the Sun and Moon are at nearly opposite positions in the sky - which is why a Full Moon rises about the time of sunset, and sets about the time of sunrise, for most places on Earth. First and Last Quarters occur when the Sun and Moon are about 90 degrees apart in the sky. The New, First Quarter, Full, and Last Quarter phases of the Moon are instantaneous phenomena, when computed by the method described in the next paragraph, and the dates and times of occurrences are provided by many calendars and almanacs. However, the fraction of the Moon apparently illuminated changes slowly, especially near New and Full Moon, and the times of the phases cannot be determined accurately by observation. Therefore, it is not unusual for a person to state that the Moon was Full, or at First or Last Quarter, on dates that are a few days removed from the instants when these phenomena actually occurred. Generally, such a statement may be regarded as an adequate observation, provided that the Moon was in fact visible at the place and time specified. Technically, the phases New Moon, First Quarter, Full Moon, and Last Quarter are defined to occur when the excess of the apparent ecliptic (celestial) longitude of the Moon over that of the Sun is 0, 90, 180, and 270 degrees, respectively. These definitions are used when the dates and times of the phases are computed for almanacs, calendars, etc. Because the difference between the ecliptic longitudes of the Moon and Sun is a monotonically and rapidly increasing quantity, the dates and times of the phases of the Moon computed this way are instantaneous and well defined.
The percent of the Moon's surface illuminated is a more refined, quantitative description of the Moon's appearance than is the phase. Considering the Moon as a circular disk, the ratio of the area illuminated by direct sunlight to its total area, multiplied by 100, is the percent of the Moon's surface illuminated. At New Moon the part of the Moon illuminated by direct sunlight is zero percent; it is 50 percent at First and Last Quarters, and 100 percent at Full Moon. During Crescent phases the percent illuminated is between 0 and 50 percent and during Gibbous phases it is between 50 and 100 percent.
For practical purposes, phases of the Moon and the percent of the Moon illuminated are independent of the location on the Earth from where the Moon is observed.