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The phases of the Moon are related to (actually, caused by) 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. In fact, the two "half Moon" phases are called First Quarter and Last
Quarter because they occur when the Moon is, respectively, one- and three-quarters of the way around the sky
(i.e., along its orbit) from New Moon. The relationship of the Moon's phase to its angular distance in the sky
from the Sun allows us to establish very exact definitions of when the primary phases occur, independent of how
they appear. 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.
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