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1 The months 2 A month is a unit of time, used with calendars, which was first

1 The months 2 A month is a unit of time, used with calendars, which was first used and invented in Sumer, Mesopotamia, as a natural period related to the motion of the moon; In English "month" and "moon" are cognates. In many languages the same word is used for month and moon. [Hebrew " ירחyerah/ yareah"] The traditional concept arose with the cycle of moon phases; such months (lunations) are synodic months and last approximately 29.53 days. From excavated tally sticks, researchers have deduced that people counted days in relation to the moon's phases as early as the paleolithic age. Synodic months, based on the moon's orbital period, are still the basis of many calendars today, and are used to divide the year. Types of months Sidereal month The period of the Moon's orbit as defined with respect to the celestial sphere (of the fixed stars, nowadays the International Celestial Reference Frame (ICRF)) is known as a sidereal month because it is the time it takes the Moon to return to a given position among the stars (Latin: sidera): 27.321661 days (27 d 7 h 43 min 11.5 s). Tropical month It is customary to specify positions of celestial bodies with respect to the vernal equinox. Because of precession, this point moves back slowly along the ecliptic. Therefore it takes the Moon less time to return to an ecliptic longitude of zero than to the same point amidst the fixed stars: 27.321582 days (27 d 7 h 43 min 4.7 s). This slightly shorter period is known as tropical month; cf. the analogous tropical year of the Sun. Anomalistic month The Moon's orbit approximates an ellipse rather than a circle. However, the orientation (as well as the shape) of this orbit is not fixed. In particular, the position of the extreme points (the line of the apsides: perigee and apogee), makes a full circle (lunar precession) in about nine years. It takes the Moon longer to return to the same apsis because it moved ahead during one revolution. This longer period is called the anomalistic month, and has an average length of 27.554551 days (27 d 13 h 18 min 33.2 s). Draconic month Sometimes written 'draconitic' month,[1] and also called the nodical month. The orbit of the moon lies in a plane that is tilted with respect to the plane of the ecliptic: it has an inclination of about five degrees. The line of intersection of these planes defines two points on the celestial sphere: the ascending node, when the moon's path crosses the ecliptic as the moon moves into the northern hemisphere, and descending node when the moon's path crosses the ecliptic as the moon moves into the southern hemisphere. The draconic or nodical month is the average interval between two successive transits of the moon through its ascending node. Because of the sun's 3 gravitational pull on the moon, the moon's orbit gradually rotates westward on its axis, which means the nodes gradually rotate around the earth. As a result, the time it takes the moon to return to the same node is shorter than a sidereal month. It lasts 27.212220 days (27 d 5 h 5 min 35.8 s). The plane of the moon's orbit precesses over a full circle in about 18.6 years. Because the moon's orbit is inclined with respect to the ecliptic, the sun, moon, and earth are in line only when the moon is at one of the nodes. Whenever this happens a solar or lunar eclipse is possible. The name "draconic" refers to a mythical dragon, said to live in the nodes and eat the sun or moon during an eclipse. Synodic month This is the average period of the Moon's revolution with respect to the line joining the Sun and Earth. The synodic month is the period of the Moon's phases, because the Moon's appearance depends on the position of the Moon with respect to the Sun as seen from the Earth. While the moon is orbiting the Earth, the Earth is progressing in its orbit around the Sun. After completing a sidereal month the Moon must move a little further to reach the new position having the same angular distance from the Sun. This longer period is called the synodic month (Greek: σὺν ὁδῴ, sun hodō, meaning "with the way [of the Sun]"). Because of perturbations in the orbits of the Earth and Moon, the actual time between lunations may range from about 29.18 to about 29.93 days. The long-term average duration is 29.530589 days (29 d 12 h 44 min 2.9 s). The synodic month is used to calculate eclipse cycles. Month lengths Here is a list of the average length of the various astronomical lunar months. These are not constant, so a first-order (linear) approximation of the secular change is provided: Valid for the epoch J2000.0 (1 January 2000 12:00 Terrestial Time): Month type Length in days anomalistic 27.554549878 − 0.000000010390 × Y sidereal 27.321661547 + 0.000000001857 × Y tropical 27.321582241 + 0.000000001506 × Y draconic 27.212220817 + 0.000000003833 × Y synodic 29.530588853 + 0.000000002162 × Y Note: In this table, time is expressed in Ephemeris Time (more precisely Terrestrial Time) with days of 86,400 SI seconds. Y is years since the epoch (2000), expressed in Julian years of 365.25 days. For calendrical calculations, one would probably use days measured in the time scale of Universal Time, which follows the somewhat unpredictable rotation of the Earth, and progressively accumulates a difference with ephemeris time called ∆T. Calendrical consequences At the simplest level, all lunar calendars are based on the approximation that 2 lunations last 59 days: a 30 day full month followed by a 29 day hollow month — but this is only marginally accurate and quickly needs correction by using larger cycles, or the equivalent of leap days. One exception is the Hebrew calendar, which was calculated very precisely over a thousand years ago, based on a lunation of 29 days, 12 hours, 44 minutes and 3⅓ seconds, which differs from modern calculations by only one day in 15000 years. 4 Second, the synodic month does not fit easily into the year, which makes constructing accurate, rule-based lunisolar calendars difficult. The most common solution to this problem is the Metonic cycle, which takes advantage of the fact that 235 lunations are approximately 19 tropical years (which add up to not quite 6940 days). However, a Metonic calendar (such as the Hebrew calendar) will drift against the seasons by about 1 day every 200 years. The problems of creating reliable lunar calendars may explain why solar calendars, having months which no longer relate to the phase of the Moon, and being based only on the motion of the Sun against the sky, have generally replaced lunar calendars for civil use in most societies. Months in various calendars Beginning of the lunar month The Hellenic calendars, the Hebrew Lunisolar calendar and the Islamic Lunar calendar started the month with the first appearance of the thin crescent of the new moon. However, the motion of the Moon in its orbit is very complicated and its period is not constant. The date and time of this actual observation depends on the exact geographical longitude as well as latitude, atmospheric conditions, the visual acuity of the observers, etc. Therefore the beginning and lengths of months in these calendars can not be accurately predicted. While some like the Jewish Karaites still rely on actual moon observations, most people use the Gregorian solar calendar. Julian and Gregorian calendars The Julian calendar was introduced by Julius Caesar in 45 B.C.E. Before the Julian calendar was introduced, priests in the Roman Empire exploited the calendar for political ends, inserting days and even months into the calendar to keep the politicians they favored in office. Tired of the chaos that this undependable system eventually gave rise to, Julius Caesar finally set out to put the long-abused calendar back on track. The Gregorian calendar is the one commonly used today. It was proposed by Aloysius Lilius, a physician from Naples, and adopted by Pope Gregory XIII in accordance with instructions from the Council of Trent (1545-1563) to correct for errors in the older Julian Calendar. It was decreed by Pope Gregory XIII in a papal bull, Inter Gravissimas, on February 24, 1582 . http://webexhibits.org/calendars/i/InterGravissimas2.gifIn the Gregorian calendar, the tropical year is approximated as 365 97/400 days = 365.2425 days. Thus it takes approximately 3300 years for the tropical year to shift one day with respect to the Gregorian calendar. The Gregorian calendar, like the Julian calendar before it, has twelve months: 5 January is the first month of the Roman Calendar year. January is named after the god Janus in Roman mythology. Janus was a god of portals and beginnings, and had two faces to see opposite directions. February is the second month of the Roman Calendar year. Translated from the Latin Februarius Mensis, the month of purification is aptly described. A Roman purificatory festival was uploads/Litterature/ the-months.pdf