Cutchi Language Tutorial, Kerala

Although this cycle is a continuous process, there are eight distinct, traditionally recognized stages, called phases. The phases designate both the degree to which the Moon is illuminated and the geometric appearance of the illuminated part. These phases of the Moon, in the sequence of their occurrence (starting from New Moon), are listed below.

New Moon - The Moon's unilluminated side is facing the Earth. The Moon is not visible (except during a solar eclipse. See the last figure, absolutely dark).

Waxing Crescent -The Moon appears to be partly but less than one-half illuminated by direct sunlight. The fraction of the Moon's disk that is illuminated is increasing.

First Quarter - One-half of the Moon appears to be illuminated by direct sunlight. The fraction of the Moon's disk that is illumina-ted is increasing.

Waxing Gibbous - The Moon appears to be more than one-half but not fully illuminated by direct sunlight. The fraction of the Moon's disk that is illuminated is increasing.

Full Moon - The Moon's illuminated side is facing the Earth. The Moon appears to be completely illuminated by direct sunlight.

Waning Gibbous - The Moon appears to be more than one-half but not fully illuminated by direct sunlight. The fraction of the Moon's disk that is illuminated is decreasing.

Last Quarter - One-half of the Moon appears to be illuminated by direct sunlight. The fraction of the Moon's disk that is illuminated starts decreasing.

Waning Crescent - The Moon appears to be partly but less than one-half illuminated by direct sunlight. The fraction of the Moon's disk that is illuminated is decreasing.

Following waning crescent is New Moon, beginning a repetition of the complete phase cycle of 29.53 days average duration. The time in days counted from the time of New Moon is called the Moon's "age". Each complete cycle of phases is called a "lunation".

Because the cycle of the phases is shorter than most calendar months, the phase of the Moon at the very beginning of the month usually repeats at the very end of the month. When there are two Full Moons in a month (which occurs, on average, every 2.7 years), the second one is called a "Blue Moon". The first time that the thin waxing crescent Moon is visible after New Moon (low in the evening sky just after sunset) marks the beginning of a month in the Islamic Calendar. Although Full Moon occurs each month at a specific date and time, the Moon's disk may appear to be full for several nights in a row if it is clear. This is because the percentage of the Moon's disk that appears illuminated changes very slowly around the time of Full Moon (also around New Moon, but the Moon is not visible at all then). The Moon may appear 100% illuminated only on the night closest to the time of exact Full Moon, but on the night before and night after will appear 97-99% illuminated; most people would not notice the difference. Even two days from Full Moon the Moon's disk is 93-97% illuminated.

New Moon, First Quarter, Full Moon, and Last Quarter phases are considered to be primary phases and their dates and times are published in almanacs and on calendars. The two crescent and two gibbous phases are intermediate phases, each of which lasts for about a week between the primary phases, during which time the exact fraction of the Moon's disk that is illuminated gradually changes.

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.

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 is the fraction of the Moon's surface illuminated; multiplied by 100, it is the percent illuminated. At New Moon the percent illuminated is 0; at First and Last Quarters it is 50%; and at Full Moon it is 100%. During the crescent phases the percent illuminated is between 0 and 50% and during gibbous phases it is between 50% and 100%.

Summary

A lunation is a lunar month, during which time the Moon completely circles the Earth in its orbit. The complete cycle of phases is obvious. Two other effects can be easily seen. First, due to the elliptical shape of the Moon's orbit, the apparent size of the Moon's disk changes as its distance from Earth varies. The closest and farthest points do not always occur at the same phases, however. Second, although the Moon’s near side directly faces the Earth on an average, we get to view the Moon from slightly different angles as it orbits us. This effect, called libration, is caused partly by the tilt of the Moon's rotation axis with respect to its orbital plane and partly by the fact that the Moon's speed in its orbit varies but its rotation rate does not.

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. That is, all the phases occur at the same time regardless of the observer's position.

A tabular Islamic calendar has been established by the Kingdom of Saudi Arabia in which the lengths of the months alternate between 29, 29 and 30 days. This calendar consists of a 30-year cycle in which 11 of the 30 years are leap years

The Islamic dates, traditionally, begin at sunset on the previous evening and end at sunset on the succeeding day. These dates may or may not correspond to the evenings on which the crescent Moon is first visible, and it is generally conceived that it is the visibility of the crescent Moon that determines when the religious observance begins.The Moon's visibility at these times varies with location; generally, the visibility increases to the west, and locations in the tropics are favored over those in middle or high latitudes.

The visibility of the lunar crescent as a function of the Moon's "age" - the time counted from New Moon - is obviously of great importance to Muslims. The date and time of each New Moon can be computed exactly, but the time that the oon first becomes visible after the New Moon depends on many factors and cannot be predicted with certainty. In the first two days after New Moon, the young crescent Moon appears very low in the western sky after sunset, and must be viewed through bright twilight. It sets shortly after sunset. The sighting of the lunar crescent within one day of New Moon is usually difficult. The crescent at this time is quite thin, has a low surface brightness, and can easily be lost in the twilight. Generally, the lunar crescent will become visible to suitably-located, experienced observers with good sky conditions about one day after New Moon. However, the time that the crescent actually becomes visible varies quite a bit from one month to another. The record for an early sighting of a lunar crescent, with a telescope, is 12.1 hours after New Moon; for naked-eye sightings, the record is 15.5 hours from New Moon. These are exceptional observations and crescent sightings this early in the lunar month should not be expected as the norm.

Obviously, the visibility of the young lunar crescent depends on sky conditions and the location, experience, and preparation of the observer. Generally, low latitude and high altitude observers who know exactly where and when to look will be favored. For observers at mid-northern latitudes, months near the spring equinox are also favored, because the ecliptic makes a relatively steep angle to the western horizon at sunset during these months (tending to make the Moon'saltitude greater).

If we ignore local conditions for the moment, and visualize the problem from outside the Earth's atmosphere, the size and brightness of the lunar crescent depend on only one astro-nomical quantity - the elongation of the Moon from the Sun, which is the apparent angular dis-tance between their centers. For this reason the elongation has also been called the arc of light. If we know the value of the elongation at any instant, we can immediately compute the width of the crescent.

What is the value of the elongation when the Moon's age is one day? It varies, depending on several factors:

(1) The elongation at New Moon. The Moon can pass directly in front of the Sun at New Moon (when a solar eclipse will occur) or can pass as far as five degrees away. That is, the Moon can start the month with an elongation ranging from zero to five degrees. A minor com-plicating factor involves the definition of New Moon in the almanacs. Astronomical New Moon is defined to occur when the Sun and Moon have the same geocentric ecliptic longitude, which may not occur precisely when the Sun and Moon are closest together.

(2) The speed of the Moon in its orbit. The Moon's orbit is elliptical, and its speed is great-est when it is near perigee, least near apogee. If perigee occurs near New Moon, the Moon will appear to be moving away from the Sun in the sky at a greater than average rate.

(3) The distance of the Moon. Again, because of its elliptical orbit, the distance of the Moon varies, so even if the Moon moved with a con-stant speed, its angular motion as viewed from the Earth would be greater when the Moon is near perigee.

(4) The location of the observer. If the observ-er is located in the tropics such that the one-day-old-Moon is observed just before it sets, its elongation as seen by the observer will be about a degree less than that seen by a fictitious ob-server at the center of the Earth, which is the ba-sis for most almanac calculations. This decrease in observed elongation is less for observers at middle or high latitudes (although other geo-metric factors are less favorable for these observers).

Factors (2) and (3) are linked by Kepler's second law, which predicts that the angular speed of the Moon as seen from the Earth will vary by about 22%. If we combine all these factors we find that geocentric elongation of the Moon from the Sun at an age of one day can vary between about 10 and 15 degrees.