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45-598: A marble inscription plaque found at the entrance of the castle records the date of its construction as 967 AD (357 AH ), during the reign of the caliph Al-Hakam II , who is also named in the inscription. The marble plaque is now kept at the National Archaeological Museum in Madrid. The castle was built as a military base and garrison to defend the valley of the Guadalquivir River and the roads to and from

90-487: 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 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

135-447: 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 ), 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

180-444: A large walled enclosure, of elongated but irregular shape, measuring roughly 100 meters long and 50 meters wide. Fifteen towers stand at close intervals around the perimeter. All the towers have a square or rectangular base, which was typical of caliphal fortresses in the 10th century, except for the northernmost tower, the 15th-century Torre del Homenaje , which is larger and has a semi-round profile. There are two entrance gates: one in

225-537: 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 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

270-1445: 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

315-415: 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 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

360-529: 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 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

405-740: Is the era used in the Islamic lunar calendar . It begins its count from the Islamic New Year in which Muhammad and his followers migrated from Mecca to Yathrib (now Medina ) in 622 CE. This event, known as the Hijrah , is commemorated in Islam for its role in the founding of the first Muslim community ( ummah ). In the West, this era is most commonly denoted as AH ( Latin : Anno Hegirae , / ˈ æ n oʊ ˈ h ɛ dʒ ɪ r iː / , lit.   ' in

450-507: 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 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

495-498: The Islamic New Year does not begin January 1 and that a Hijri calendar year is about 11 days shorter than a Gregorian calendar year, there is no direct correspondence between years of the two eras. A given Hijri year will usually fall in two successive Gregorian years. A CE year will always overlap two or occasionally three successive Hijri years. For example, the year 2008 CE maps to the last week of AH 1428, all of 1429, and

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540-480: The Islamic lunar calendar , whose epoch (first year) is the year of Muhammad's Hijrah , and begins on the first day of the month of Muharram (equivalent to the Julian calendar date of July 16, 622 CE). The date of the Hijrah itself did not form the Islamic New Year . Instead, the system continues the earlier ordering of the months, with the Hijrah occurring around the 8th day of Rabi al-Awwal , 66 days into

585-578: The Kingdom of Castile in 1212, shortly before the Battle of Las Navas de Tolosa , but returned to Almohad control three days after the battle. The castle was definitively conquered by Castile in 1225, when it conquered the surrounding region. The Castilians later added a keep tower called the Torre del Homenaje ("Tower of Homage") in 1466. It was designated a National Monument of Spain in 1931. The castle consists of

630-518: 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 the synodic month because it is the cycle of the visible phases of the Moon . Most of the following types of lunar month, except

675-407: 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 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

720-554: 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 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

765-441: 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 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

810-606: The Elephant ". The first year of the Hijra (622-23 CE) was named the "Permission to Travel" in this calendar. 17 years after the Hijra , a complaint from Abu Musa Ashaari prompted the caliph Umar to abolish the practice of named years and to establish a new calendar era . Umar chose as epoch for the new Muslim calendar the hijrah , the emigration of Muhammad and 70 Muslims from Mecca to Medina . Tradition credits Othman with

855-565: The Islamic lunar calendar consists of twelve lunar months and has only 354 or 355 days in its year. Consequently, its New Year's Day occurs ten days earlier each year relative to the Gregorian calendar . The year 2024 CE corresponds to the Islamic years AH   1445 – 1446; AH   1446 corresponds to 2024 – 2025 in the Common Era. The Hijri era is calculated according to

900-417: 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 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

945-511: 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 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

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990-438: 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 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

1035-545: 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 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

1080-613: 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, 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

1125-403: 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 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

1170-465: 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 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

1215-797: 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 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)

1260-409: The calendar year is entirely determined by solar observation or calculation. Each year begins on the northward equinox . By the age of Muhammad, there was already an Arabian lunar calendar , with named months. Likewise, the years of its calendar used conventional names rather than numbers: for example, the year of the birth of Muhammad and of Ammar ibn Yasir (570 CE) was known as the " Year of

1305-560: The capital city of Córdoba. In the 12th and 13th centuries, during the Reconquista , the castle changed hands multiple times between the Muslim rulers of Al-Andalus and the Christian kingdoms to the north. Alfonso VII captured it in 1147 but it returned to Muslim control after his death in 1157. Alfonso VIII and Alfonso IX together captured it again for a time in 1189. It was captured by

1350-484: 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 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

1395-509: 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 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

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1440-476: The end of the previous lunar cycle and hence the previous month, thereby beginning the new month. Consequently, each month can have 29 or 30 days depending on the visibility of the moon, astronomical positioning of the earth and weather conditions. However, certain sects and groups, most notably Bohras Muslims namely Alavis , Dawoodis and Sulaymanis and Shia Ismaili Muslims, use a tabular Islamic calendar in which odd-numbered months have thirty days (and also

1485-414: 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 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

1530-416: The first few days of 1430. Similarly, the year 1976 CE corresponded with the last few days of AH 1395, all of 1396, and the first week of 1397. The Hijri year has twelve months, whose precise lengths vary by sect of Islam. Each month of the Islamic calendar commences on the birth of the new lunar cycle. Traditionally this is based on actual observation of the moon's crescent ( hilal ) marking

1575-546: The first year. Unlike Sunnis, Twelver Shias start the Hijri year with the month of the Hijra, Rabi' al-Awwal, rejecting that Muharram is the start of a new year. As a result of this, the dates of some events are described differently by one year. For example, Shias state that the Muharram-transpiring battle of Karbala occurred 60 years after the Hijra, while Sunnis state it to have occurred 61 years after. In Shia Islam,

1620-415: 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 the Sun, the Moon does not yet finish a synodic cycle until it has reached the point in its orbit where

1665-641: 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 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

1710-736: The north and one in the south/southeast. The more important southern gate consists of a straight passage (instead of the bent entrance common in later fortifications) with horseshoe arches, set between two towers. Chambers were located above the passage with slots in the floor where missiles could be thrown down onto attackers. Inside the castle today are the remains of a cistern and the foundations of later buildings. 38°10′12.6″N 3°46′31.8″W  /  38.170167°N 3.775500°W  / 38.170167; -3.775500 Hijri year The Hijri year ( Arabic : سنة هجرية , romanized :  sanat hijriyya ) or era ( Arabic : التقويم الهجري , romanized :  at-taqwīm al-hijrī )

1755-572: 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})}

1800-405: The same star. A draconic month or draconitic month is also known as a nodal month or nodical month . The name draconic refers to 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

1845-463: 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 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

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1890-486: The successful proposal, simply continuing the order of the months that had already been established by Muhammad , beginning with Muharram , as there was no set order of months during the pre-Islamic era (Age of Ignorance - Jahiliya ). Adoption of this calendar was then enforced by Umar. Different approximate conversion formulas between the Gregorian (AD or CE) and Islamic calendars (AH) are possible: or Given that

1935-477: 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 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,

1980-462: The twelfth month in a leap year) and even months have twenty nine. 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 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

2025-465: The year of the Hijra ' ) in parallel with the Christian / Common (AD/CE) and Jewish eras (AM) and can similarly be placed before (preferably) or after the date. In predominantly Muslim countries , it is also commonly abbreviated H ("Hijra") from its Arabic abbreviation hāʾ ( هـ ). Years prior to AH 1 are reckoned in English as BH ("Before the Hijra"), which should follow the date. A year in

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