The lunar phase or Moon phase is the shape of the Moon's directly sunlit portion as viewed from Earth. The lunar phases gradually change over a synodic month (about 29.53 days or 29 days 12 hours 44 minutes 3 seconds); because of perturbations in the Moon's orbit, the lengths of all astronomical months vary slightly....) as the Moon's orbital positions around Earth and Earth around the Sun shift. The visible side of the moon is variously sunlit, depending on the position of the Moon in its orbit. Thus, this face's sunlit portion can vary from 0% (at new moon) to 100% (at full moon). Each of the four "intermediate" lunar phases is approximately 7.4 days, with +/- 19 hours in variation (6.58-8.24 days) due to the Moon's orbit's elliptical shape.
There are four principal lunar phases: the new moon, first quarter, full moon, and last quarter (also known as third or final quarter), when the Moon's ecliptic longitude is at an angle to the Sun (as viewed from the centre of the Earth) of 0°, 90°, 180°, and 270°, respectively. Each of these phases appears at slightly different times at different locations on Earth. During the intervals between principal phases are intermediate phases, during which the Moon's apparent shape is either crescent or gibbous. On average, the intermediate phases last one-quarter of a synodic month, or 7.38 days. The descriptor waxing is used for an intermediate phase when the Moon's apparent shape is thickening, from new to a full moon, and waning when the shape is thinning. The longest duration between full moon to new moon (or new moon to full moon) lasts about 15 days and 14+1⁄2 hours, while the shortest duration between full moon to new moon (or new moon to full moon) lasts only about 13 days and 22+1⁄2 hours.
The Gregorian calendar month, which is 1⁄12 of a tropical year, is about 30.44 days, while the cycle of lunar phases (the Moon's synodic period) repeats every 29.53 days on average. The shortest cycle was on 20 July 1978 and it only took 29.27 days to complete the cycle. The longest cycle will take place on 19 January 2049 and it will take 29.83 days. Therefore, the timing of the lunar phases shifts by an average of almost one day for each successive month. (A lunar year lasts about 354 or 355 days.)
Photographing the Moon's phase every day for a month (starting in the evening after sunset, and repeating roughly 24 hours and 50 minutes later, and ending in the morning before sunrise) and arranging the series of photos on a calendar would create a composite image.
Similarly, on a calendar listing moonrise or moonset times, some days will appear to be skipped. When moonrise precedes midnight one night, the next moonrise will follow midnight on the next night (so too with moonset). The "skipped day" is just a feature of the Moon's eastward movement in relation to the Sun, which at most latitudes, causes the Moon to rise later each day. The Moon follows a predictable orbit every month.
Each of the four intermediate phases lasts approximately seven days (7.38 days on average), but varies ±11.25% due to lunar apogee and perigee.
The approximate age of the Moon, and hence the approximate phase, can be calculated for any date by calculating the number of days since a known new moon (such as January 1, 1900 or August 11, 1999) and reducing this modulo 29.53059 days (the mean length of a synodic month). The difference between two dates can be calculated by subtracting the Julian day number of one from that of the other, or there are simpler formulae giving (for instance) the number of days since December 31, 1899. However, this calculation assumes a perfectly circular orbit and makes no allowance for the time of day at which the new moon occurred and therefore may be incorrect by several hours. (It also becomes less accurate the larger the difference between the required date and the reference date). It is accurate enough to use in a novelty clock application showing lunar phase, but specialist usage taking account of lunar apogee and perigee requires a more elaborate calculation.
The Earth subtends an angle of about two degrees when seen from the Moon. This means that an observer on Earth who sees the Moon when it is close to the eastern horizon sees it from an angle that is about 2 degrees different from the line of sight of an observer who sees the Moon on the western horizon. The Moon moves about 12 degrees around its orbit per day, so, if these observers were stationary, they would see the phases of the Moon at times that differ by about one-sixth of a day, or 4 hours. But in reality, the observers are on the surface of the rotating Earth, so someone who sees the Moon on the eastern horizon at one moment sees it on the western horizon about 12 hours later. This adds an oscillation to the apparent progression of the lunar phases. They appear to occur more slowly when the Moon is high in the sky than when it is below the horizon. The Moon appears to move jerkily, and the phases do the same. The amplitude of this oscillation is never more than about four hours, which is a small fraction of a month. It does not have any obvious effect on the appearance of the Moon. It does however affect accurate calculations of the times of lunar phases.
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