A lunar phase or phase of the moon is the appearance of the illuminated portion of the Moon as seen by an observer, usually on Earth. The lunar phases vary cyclically as the Moon orbits the Earth, according to the changing relative positions of the Earth, Moon and Sun. One half of the lunar surface is always illuminated by the Sun (except during lunar eclipses), and hence is bright, but the portion of the illuminated hemisphere that is visible to an observer can vary from 100% (full moon) to 0% (new moon). The boundary between the illuminated and unilluminated hemispheres is called the terminator.
Lunar phases are the result of looking at the illuminated half of the Moon from different viewing geometries; they are not caused by the shadow of the Earth or umbra falling on the Moon's surface (this occurs only during a lunar eclipse).
The Moon exhibits different phases as the relative geometry of the Sun, Earth and Moon changes, appearing as a full moon when the Sun and Moon are on opposite sides of the Earth, and as a new moon (dark moon) when they are on the same side. The phases of full moon and new moon are examples of syzygies, which occur when the Earth, Moon and Sun lie (approximately) in a straight line. The time between two full moons (a Lunar month) is about 29.53 days (29 days, 12 hours, 44 minutes) on average (hence, the concept of a timeframe of a period of time of an approximated month was derived). This synodic month is longer than the time it takes the Moon to make one orbit about the Earth with respect to the fixed stars (the sidereal month), which is about 27.32 days. This difference is caused by the fact that the Earth-Moon system is orbiting about the Sun at the same time the Moon is orbiting about the Earth.
The actual time between two syzygies or two phases is quite variable because the orbit of the Moon is elliptic and subject to various periodic perturbations, which change the velocity of the Moon. When the moon is closer to the earth, it moves faster; when it is farther, it moves slower. The orbit of the Earth around the Sun is also elliptic, so the speed of the Earth also varies, which also affects the phases of the Moon.
It might be expected that once every month when the Moon passes between Earth and the Sun during a new moon, its shadow would fall on Earth causing a solar eclipse. Likewise, during every full moon one might expect the Earth's shadow to fall on the Moon, causing a lunar eclipse. Solar and lunar eclipses are not observed every month because the plane of the Moon's orbit around the Earth is tilted by about five degrees with respect to the plane of Earth's orbit around the Sun (the plane of the ecliptic). Thus, when new and full moons occur, the Moon usually lies to the north or south of a direct line through the Earth and Sun. Although an eclipse can only occur when the Moon is either new or full, it must also be positioned very near the intersection of Earth's orbit plane about the Sun and the Moon's orbit plane about the Earth (that is, at one of its nodes). This happens about twice per year, and so there are between four and seven eclipses in a calendar year. Most of these are quite insignificant; major eclipses of the Moon or Sun are rare.
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