Misplaced Pages

#304695

60-695: The civil lunisolar calendar had years consisting of 12 lunar months , each beginning when a new crescent moon was first sighted low on the western horizon at sunset, plus an intercalary month inserted as needed, at first by decree and then later systematically according to what is now known as the Metonic cycle . Month names from the Babylonian calendar appear in the Hebrew calendar , Assyrian calendar , Syriac calendar , Old Persian calendar , and Turkish calendar . The Babylonian civil calendar, also called

120-654: A contract for 12 months ran for exactly 48 weeks. In the United Kingdom, the lunar month was formally replaced by the calendar month for deeds and other written contracts by section 61(a) of the Law of Property Act 1925 and for post-1850 legislation by the Interpretation Act 1978 (Schedule 1 read with sections 5 and 23 and with Schedule 2 paragraph 4(1)(a)) and its predecessors. There are several types of lunar month. The term lunar month usually refers to

180-593: A final week of eight or nine days inclusive, breaking the continuous seven-day cycle. Among other theories of Shabbat origin, the Universal Jewish Encyclopedia of Isaac Landman advanced a theory of Assyriologists like Friedrich Delitzsch that Shabbat originally arose from the lunar cycle , containing four weeks ending in Sabbath, plus one or two additional unreckoned days per month. The difficulties of this theory include reconciling

240-569: A mythical dragon , said to live in the lunar nodes and eat the Sun or Moon during an eclipse . A solar or lunar eclipse is possible only when the Moon is at or near either of the two points where its orbit crosses the ecliptic plane ; i.e., the satellite is at or near either of its orbital nodes . The orbit of the Moon lies in a plane that is inclined about 5.14° with respect to the ecliptic plane. The line of intersection of these planes passes through

300-484: A predictable lunisolar cycle, so that 19 years comprised 235 months. Although this 19-year cycle is usually called the Metonic cycle after Meton of Athens ( 432 BCE ), the Babylonians used this cycle before Meton, and it may be that Meton learned of the cycle from the Babylonians. After no more than three isolated exceptions, by 380 BCE the months of the calendar were regulated by the cycle without exception. In

360-472: A second calendar system thrived in Babylon during the same time spans, known today as the administrative or schematic calendar. The administrative year consisted of 12 months of exactly 30 days each. In the 4th and 3rd millennia BCE, extra months were occasionally intercalated (in which case the year is 390 days), but by the beginning of the 2nd millenium BCE it did not make any intercalations or modifications to

420-575: A wish", and at least the 28th was known as a "rest-day". On each of them, offerings were made to a different god and goddess, apparently at nightfall to avoid the prohibitions: Marduk and Ishtar on the 7th, Ninlil and Nergal on the 14th, Sin and Shamash on the 21st, and Enki and Mah on the 28th. Tablets from the sixth-century BC reigns of Cyrus the Great and Cambyses II indicate these dates were sometimes approximate. The lunation of 29 or 30 days basically contained three seven-day weeks , and

480-423: Is 29.53059 days with up to seven hours variation about the mean in any given year. (which gives a mean synodic month as 29.53059 days or 29 d 12 h 44 min 3 s) A more precise figure of the average duration may be derived for a specific date using the lunar theory of Chapront-Touzé and Chapront (1988) : 29.5305888531 + 0.00000021621 T − 3.64 × 10 T where T = (JD − 2451545.0)/36525 and JD

540-1445: Is 36,525 days from epoch J2000.0. The angular velocity is the first derivative: d A / d t = A ′ = A 1 + ( 2 × A 2 × T ) {\displaystyle \operatorname {d} \!A/\operatorname {d} \!t=A'=A_{1}+(2\times A_{2}\times T)} . The period ( Q ) is the inverse of the angular velocity: Q = 1 A ′ = 1 A 1 + ( 2 × A 2 × T ) = 1 A 1 × 1 1 + ( 2 × A 2 A 1 × T ) = 1 A 1 × ( 1 − 2 × A 2 A 1 × T ) = 1 A 1 − ( 2 × A 2 ( A 1 × A 1 ) × T ) {\displaystyle Q={1 \over A'}={1 \over A_{1}+(2\times A_{2}\times T)}={1 \over A_{1}}\times {1 \over 1+(2\times {A_{2} \over A_{1}}\times T)}={1 \over A_{1}}\times (1-2\times {A_{2} \over A_{1}}\times T)={1 \over A_{1}}-(2\times {A_{2} \over (A_{1}\times A_{1})}\times T)} , ignoring higher-order terms. A 1 in "/cy ; A 2 in "/cy ; so

600-452: Is between 19 and 26 hours long. The date is named after the tithi ruling at sunrise. When the tithi is shorter than the day, the tithi may jump. This case is called kṣaya or lopa . Conversely a tithi may 'stall' as well, that is – the same tithi is associated with two consecutive days. This is known as vriddhi . In English common law , a "lunar month" traditionally meant exactly 28 days or four weeks, thus

660-686: Is characterized by having an almost exactly equal amount of daylight and night across most latitudes on Earth. The Babylonian calendar began with the first new moon after the March equinox, the day after the return of the Sumerian goddess Inanna (later known as Ishtar ) from the underworld, in the Akitu ceremony, with parades through the Ishtar Gate to the Eanna temple and the ritual re-enactment of

SECTION 10

#1732780540305

720-613: Is the Julian day number (and JD = 2451545 corresponds to 1 January AD 2000). The duration of synodic months in ancient and medieval history is itself a topic of scholarly study. The period of the Moon's orbit as defined with respect to the celestial sphere of apparently fixed stars (the International Celestial Reference Frame ; ICRF) is known as a sidereal month because it is the time it takes

780-483: Is the draconic month. D is the elongation of the Moon from the Sun: its period is the synodic month. Derivation of a period from a polynomial for an argument A (angle): A = A 0 + ( A 1 × T ) + ( A 2 × T 2 ) {\displaystyle A=A_{0}+(A_{1}\times T)+(A_{2}\times T^{2})} ; T in centuries (cy)

840-731: Is the equinox on the Earth when the subsolar point appears to leave the Southern Hemisphere and cross the celestial equator , heading northward as seen from Earth. The March equinox is known as the vernal equinox (spring equinox) in the Northern Hemisphere and as the autumnal equinox (autumn equinox or fall equinox) in the Southern Hemisphere. On the Gregorian calendar at 0° longitude ,

900-506: Is the ecliptic longitude of the Moon w.r.t. the fixed ICRS equinox: its period is the sidereal month. If we add the rate of precession to the sidereal angular velocity, we get the angular velocity w.r.t. the Equinox of the Date: its period is the tropical month (which is rarely used). l is the mean anomaly: its period is the anomalistic month. F is the argument of latitude: its period

960-494: The Hebrew calendar or the ecclesiastical lunar calendar . Calendars count integer days, so months may be 29 or 30 days in length, in some regular or irregular sequence. Lunar cycles are prominent, and calculated with great precision in the ancient Hindu Panchangam calendar, widely used in the Indian subcontinent. In India, the month from conjunction to conjunction is divided into thirty parts known as tithi . A tithi

1020-693: The Levant , the solar Gregorian calendar system is used, with Classical Arabic names replacing the Roman ones , and the month names in the Assyrian calendar descend directly from Aramaic, which descended from Akkadian. Similarly, while Turkey uses the Gregorian calendar in the present day, the names of Turkish months were inspired by the 1839 Rumi calendar of the Ottoman Empire , itself derived from

1080-403: The apsides : perigee and apogee ), rotates once ( apsidal precession ) in about 3,233 days (8.85 years). It takes the Moon longer to return to the same apsis because it has moved ahead during one revolution. This longer period is called the anomalistic month and has an average length of 27.554 551  days (27 d 13 h 18 min 33.2 s). The apparent diameter of

1140-463: The epoch J2000.0 (1 January 2000 12:00 TT ): Note: In this table, time is expressed in Ephemeris Time (more precisely Terrestrial Time ) with days of 86,400 SI seconds . T is centuries since the epoch (2000), expressed in Julian centuries of 36,525 days. For calendrical calculations, one would probably use days measured in the time scale of Universal Time , which follows

1200-588: The opposite direction to that in which the Moon is orbiting Earth, one rotation every 18.6 years. Therefore, the Moon returns to the same node slightly earlier than it returns to meet the same reference star. Regardless of the culture, all lunar calendar months approximate the mean length of the synodic month, the average period the Moon takes to cycle through its phases ( new , first quarter, full , last quarter) and back again: 29–30 days . The Moon completes one orbit around Earth every 27.3 days (a sidereal month), but due to Earth's orbital motion around

1260-610: The precession of the equinoxes , this point is no longer in the constellation Aries , but rather in Pisces . By the year 2600 it will be in Aquarius . The Earth's axis causes the First Point of Aries to travel westwards across the sky at a rate of roughly one degree every 72 years. Based on the modern constellation boundaries , the northward equinox passed from Taurus into Aries in the year −1865 (1866 BC), passed into Pisces in

SECTION 20

#1732780540305

1320-483: The synodic month and calendar years in sync with the tropical year . Since new months of the civil calendar were declared by observing the crescent moon, the calendar months could not drift from the synodic month. On the other hand, since the length of a calendar year was handled by the Metonic cycle starting after 499 BCE, there is some inherent drift present in the formulaic computation of the new year when compared to

1380-466: The synodic month because it is the cycle of the visible phases of the Moon . Most of the following types of lunar month, except the distinction between the sidereal and tropical months, were first recognized in Babylonian lunar astronomy . The synodic month ( Greek : συνοδικός , romanized :  synodikós , meaning "pertaining to a synod, i.e., a meeting"; in this case, of the Sun and

1440-454: The 360-day year. This calendar saw use in areas requiring precision in dates or long-term planning; there is tablet evidence demonstrating it was used to date business transactions and astronomical observations , and that mathematics problems , wage calculations, and tax calculations all assumed the administrative calendar instead of the civil calendar. Babylonian astronomers in particular made all astral calculations and predictions in terms of

1500-540: The Babylonian Shabattu , the festival of the full moon, but, all trace of any such origin having been lost, the Hebrews ascribed it to Biblical legend." This conclusion is a contextual restoration of the damaged Enûma Eliš creation account, which is read as: "[Sa]bbath shalt thou then encounter, mid[month]ly." The Akkadian names for months surface in a number of calendars still used today. In Iraq and

1560-469: The Moon to return to a similar position among the stars ( Latin : sidera ): 27.321 661 days (27 d 7 h 43 min 11.6 s). This type of month has been observed among cultures in the Middle East, India, and China in the following way: they divided the sky into 27 or 28 lunar mansions , one for each day of the month, identified by the prominent star(s) in them. Just as the tropical year is based on

1620-403: The Moon varies with this period, so this type has some relevance for the prediction of eclipses (see Saros ), whose extent, duration, and appearance (whether total or annular) depend on the exact apparent diameter of the Moon. The apparent diameter of the full moon varies with the full moon cycle , which is the beat period of the synodic and anomalistic month, as well as the period after which

1680-520: The Moon), also lunation , is the average period of the Moon's orbit with respect to the line joining the Sun and Earth: 29 (Earth) days, 12 hours, 44 minutes and 2.9 seconds. This is the period of the lunar phases , because the Moon's appearance depends on the position of the Moon with respect to the Sun as seen from Earth. Due to tidal locking , the same hemisphere of the Moon always faces the Earth and thus

1740-635: The North Pole once every tropical month, and likewise at the South Pole. It is customary to specify positions of celestial bodies with respect to the First Point of Aries (Sun's location at the March equinox ). Because of Earth's precession of the equinoxes , this point moves back slowly along the ecliptic . Therefore, it takes the Moon less time to return to an ecliptic longitude of 0° than to

1800-478: The Ottoman fiscal calendar of 1677 based on the Julian calendar . This last calendar month names of both Syriac and Islamic origin, and in the modern calendar four of these names descend from the original Akkadian names. Lunar month In lunar calendars , a lunar month is the time between two successive syzygies of the same type: new moons or full moons . The precise definition varies, especially for

1860-420: The Sun varies during the year. Thus, the angular velocity is faster nearer periapsis and slower near apoapsis . The same is true (to an even larger extent) for the Moon's orbit around Earth. Because of these two variations in angular rate, the actual time between lunations may vary from about 29.274 days (or 29 d 6 h 35 min ) to about 29.829 days (or 29 d 19 h 54 min ). The average duration in modern times

Babylonian calendar - Misplaced Pages Continue

1920-425: The Sun, appearing to move with respect to the stars since the previous month. Consequently, at 27 days, 7 hours, 43 minutes and 11.5 seconds, the sidereal month is about 2.2 days shorter than the synodic month. Thus, about 13.37 sidereal months, but about 12.37 synodic months, occur in a Gregorian year . Since Earth's orbit around the Sun is elliptical and not circular , the speed of Earth's progression around

1980-405: The Sun, the Moon does not yet finish a synodic cycle until it has reached the point in its orbit where the Sun is in the same relative position . This table lists the average lengths of five types of astronomical lunar month, derived from Chapront, Chapront-Touzé & Francou 2002 . These are not constant, so a first-order (linear) approximation of the secular change is provided. Valid for

2040-453: The administrative calendar. Discrepancies were accounted for in different ways according to the heavenly measurements being taken. When predicting the phase of the moon , it was treated as if each ideal month began with a new moon , even though this could not be true. In fact, this guideline appears in the MUL.APIN, which goes on further to specify that months that began "too early" (on the 30th of

2100-494: The amount of time between perceived rotations of the sun around the earth (based on the Greek word τροπή meaning "turn"), the tropical month is the average time between corresponding equinoxes . It is also the average time between successive moments when the moon crosses from the southern celestial hemisphere to the northern (or vice versa), or successive crossing of a given right ascension or ecliptic longitude . The moon rises at

2160-559: The appearance of the new moon was predictable with some accuracy into the short-term future. Still, during the Neo-Assyrian period (c. 700 BCE) the calendar was sometimes retroactively "shifted back" a day to account for the fact that the king should have declared a new month, but only did so the following day because of obstructive weather . נִיסָן ࡍࡉࡎࡀࡍ אִיָּיר ࡀࡉࡀࡓ סִיוָן ࡎࡉࡅࡀࡍ 'Month of Tammuz ' תַּמּוּז ࡕࡀࡌࡅࡆ אָב ࡀࡁ אֱלוּל ࡀࡉࡋࡅࡋ 'Month of Beginning' (i.e.

2220-437: The apsides point to the Sun again. An anomalistic month is longer than a sidereal month because the perigee moves in the same direction as the Moon is orbiting the Earth, one revolution in about 8.85 years. Therefore, the Moon takes a little longer to return to perigee than to return to the same star. A draconic month or draconitic month is also known as a nodal month or nodical month . The name draconic refers to

2280-570: The beginning of the month. In Shona , Middle Eastern , and European traditions, the month starts when the young crescent moon first becomes visible, at evening, after conjunction with the Sun one or two days before that evening (e.g., in the Islamic calendar ). In ancient Egypt , the lunar month began on the day when the waning moon could no longer be seen just before sunrise. Others run from full moon to full moon. Yet others use calculation, of varying degrees of sophistication, for example,

2340-457: The cultic calendar, was a lunisolar calendar descended from the Nippur calendar, which has evidence of use as early as 2600 BCE and descended from the even older Third Dynasty of Ur (Ur III) calendar. The original Sumerian names of the months are seen in the orthography for the next couple millennia, albeit in more and more shortened forms. When the calendar came into use in Babylon circa 1780 BCE,

2400-416: The cycle of 19 years, the month Addaru 2 was intercalated, except in the year that was number 17 in the cycle, when the month Ulūlu 2 was inserted instead. During this period, the first day of each month (beginning at sunset) continued to be the day when a new crescent moon was first sighted—the calendar never used a specified number of days in any month. However, as astronomical science grew in Babylon,

2460-543: The differences between an unbroken week and a lunar week, and explaining the absence of texts naming the lunar week as Shabbat in any language. The rarely attested Sapattu or Sabattu as the full moon is cognate or merged with Hebrew Shabbat , but is monthly rather than weekly; it is regarded as a form of Sumerian sa-bat ("mid-rest"), attested in Akkadian as um nuh libbi ("day of mid-repose"). According to Marcello Craveri , Sabbath "was almost certainly derived from

Babylonian calendar - Misplaced Pages Continue

2520-417: The end of astronomical summer in the Southern Hemisphere. In astronomy , the March equinox is the zero point of sidereal time and, consequently, the right ascension and ecliptic longitude . It also serves as a reference for calendars and celebrations in many cultures and religions. The point where the Sun crosses the celestial equator northwards is called the First Point of Aries . However, due to

2580-469: The intercalary month with an intercalary day to be added every four years to February. It was based on a length for the year of 365 days and 6 hours (365.25 d), while the mean tropical year is about 11 minutes and 15 seconds less than that. This had the effect of adding about three quarters of an hour every four years. The effect accumulated from inception in 45 BC until the 16th century, when the northern vernal equinox fell on 10 or 11 March. The date in 1452

2640-403: The length of a lunar day (sunrise to sunrise on the Moon) equals the time that the Moon takes to complete one orbit around Earth , returning to the same lunar phase . While the Moon is orbiting Earth, Earth is progressing in its orbit around the Sun. After completing its § Sidereal month , the Moon must move a little further to reach the new position having the same angular distance from

2700-458: The marriage to Tammuz , or Sumerian Dummuzi . The Persian calendar begins each year at the northward equinox, observationally determined at Tehran . The Indian national calendar starts the year on the day next to the vernal equinox on 22 March (21 March in leap years) with a 30-day month (31 days in leap years), then has 5 months of 31 days followed by 6 months of 30 days. The Julian calendar reform lengthened seven months and replaced

2760-487: The month of barley harvesting, and it aligned with the vernal equinox . However, during the intervening Nippur period, it was the twelfth month instead. Until the 5th century BCE , the calendar was fully observational, and the intercalary month was inserted approximately every two to three years, at first by guidelines which survive in the MUL.APIN tablet. Beginning in around 499 BCE , the intercalation began to be regulated by

2820-400: The nodes gradually rotate around Earth. As a result, the time it takes the Moon to return to the same node is shorter than a sidereal month, lasting 27.212 220  days (27 d 5 h 5 min 35.8 s). The line of nodes of the Moon's orbit precesses 360° in about 6,793 days (18.6 years). A draconic month is shorter than a sidereal month because the nodes precess in

2880-400: The northward equinox can occur as early as 19 March (which happened most recently in 1796, and will happen next in 2044). And it can occur as late as 21 March (which happened most recently in 2007, and will happen next in 2102). For a common year the computed time slippage is about 5 hours 49 minutes later than the previous year, and for a leap year about 18 hours 11 minutes earlier than

2940-921: The numerical conversion factor then becomes 2 × B1 × B1 ÷ B2 = 2 × 1,296,000. This would give a linear term in days change (of the period) per day, which is also an inconvenient unit: for change per year multiply by a factor 365.25, and for change per century multiply by a factor 36,525. C 2 = 2 × 1,296,000 × 36,525 × A 2 ÷ (A 1 × A 1 ). Then period P in days: P = C 1 − C 2 × T {\displaystyle P=C_{1}-C_{2}\times T} . Example for synodic month, from Delaunay's argument D : D′ = 1602961601.0312 − 2 × 6.8498 × T "/cy; A 1 = 1602961601.0312 "/cy; A 2 = −6.8498"/cy ; C 1 = 47,336,400,000 ÷ 1,602,961,601.0312 = 29.530588860986 days; C 2 = 94,672,800,000 × −6.8498 ÷ (1,602,961,601.0312 × 1,602,961,601.0312) = −0.00000025238 days/cy. March equinox The March equinox or northward equinox

3000-447: The previous month) were considered unlucky, and months that began "on time" (the day after the 30th of the previous month) were considered auspicious. When discussing the dates of equinoxes and solstices , the events were assigned fixed days of the administrative calendar, with shortening or lengthening of intervening days taking place to ensure that the celestial phenomena would fall on the "correct" day. Which fixed day each phenomenon

3060-471: The previous year. Balancing the increases of the common years against the losses of the leap years keeps the calendar date of the March equinox from drifting more than one day from 20 March each year. The March equinox may be taken to mark the beginning of astronomical spring and the end of astronomical winter in the Northern Hemisphere but marks the beginning of astronomical autumn and

SECTION 50

#1732780540305

3120-572: The result Q is expressed in cy/" which is a very inconvenient unit. 1 revolution (rev) is 360 × 60 × 60" = 1,296,000"; to convert the unit of the velocity to revolutions/day, divide A 1 by B 1 = 1,296,000 × 36,525 = 47,336,400,000; C 1 = B 1 ÷ A 1 is then the period (in days/revolution) at the epoch J2000.0. For rev/day divide A 2 by B 2 = 1,296,000 × 36,525 = 1,728,962,010,000,000. For A 2 ÷ ( A 1 × A 1 ) {\displaystyle A_{2}\div (A_{1}\times A_{1})}

3180-406: The same point amid the fixed stars . This slightly shorter period, 27.321 582 days (27 d 7 h 43 min 4.7 s), is commonly known as the tropical month by analogy with Earth's tropical year . 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

3240-579: The somewhat unpredictable rotation of the Earth, and progressively accumulates a difference with ephemeris time called ΔT ("delta-T"). Apart from the long term (millennial) drift in these values, all these periods vary continually around their mean values because of the complex orbital effects of the Sun and planets affecting its motion. The periods are derived from polynomial expressions for Delaunay's arguments used in lunar theory , as listed in Table 4 of Chapront, Chapront-Touzé & Francou 2002 W1

3300-532: The spoken month names became a mix from the calendars of the local subjugated cities, which were Akkadian. Historians agree that it was probably Samsu-iluna who effected this change. During the sixth century BCE Babylonian captivity of the Jews , these month names were adopted into the Hebrew calendar . The first month of the civil calendar during the Ur III and Old Babylonian periods was Šekinku (Akk. Addaru ), or

3360-481: The start of the second half-year) תִּשְׁרֵי ࡕࡉࡔࡓࡉࡍ 'Month the Eighth' מַרְחֶשְׁוָן/חֶשְׁוָן ࡌࡀࡔࡓࡅࡀࡍ כִּסְלֵו ࡊࡀࡍࡅࡍ 'Muddy Month' טֵבֵת ࡈࡀࡁࡉࡕ שְׁבָט ࡔࡀࡁࡀࡈ אֲדָר (אֲדָר א׳/אֲדָר רִאשׁון if there is an intercalary month that year) ࡀࡃࡀࡓ Araḫ Addaru Arku – 𒌚𒋛𒀀𒊺 אֲדָר ב׳/אֲדָר שֵׁנִי As a lunisolar calendar, the civil calendar aimed to keep calendar months in sync with

3420-400: The true new year. While on any given year the first day of the first month could be up to 20 days off from the vernal equinox , on average the length of a year was very well approximated by the Metonic cycle; the computed average length is within 30 minutes of the true solar year length. Since the civil calendar was not standardized and predictable for at least the first millennium of its use,

3480-484: The two points at which the Moon's orbit crosses the ecliptic plane: the ascending node and the descending node . The draconic or nodical month is the average interval between two successive transits of the Moon through the same node . Because of the torque exerted by the Sun's gravity on the angular momentum of the Earth–;Moon system, the plane of the Moon's orbit gradually rotates westward, which means

3540-435: The year −67 (68 BC), will pass into Aquarius in the year 2597, and will pass into Capricornus in the year 4312. It passed by (but not into) a 'corner' of Cetus at 0°10′ distance in the year 1489. In its apparent motion on the day of an equinox, the Sun's disk crosses the Earth's horizon directly to the east at sunrise ; and again, some 12 hours later, directly to the west at sunset . The March equinox, like all equinoxes,

3600-463: Was assigned varied throughout time, for one because which month was designated first varied throughout history. In general, they were assigned to the 15th day of four equally spaced months. Counting from the new moon , the Babylonians celebrated every seventh day as a "holy-day", also called an "evil-day" (meaning "unsuitable" for prohibited activities). On these days officials were prohibited from various activities and common men were forbidden to "make

#304695