This is an accepted version of this page
92-527: Tierkreis is the German word for the Zodiac . It may also refer to: Suikoden Tierkreis , a Nintendo DS video game Tierkreis (Stockhausen) , a German musical composition Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Tierkreis . If an internal link led you here, you may wish to change
184-515: A Fourier series ) is also discouraged for having an error of up to 0.28°. An additional error of up to 0.5° can occur in all equations around the equinoxes if not using a decimal place when selecting N to adjust for the time after UT midnight for the beginning of that day. So the above equation can have up to 2.0° of error, about four times the Sun's angular width, depending on how it is used. The declination can be more accurately calculated by not making
276-477: A year , which resembles a figure-8. An analemma can be pictured by superimposing photographs taken at the same time of day, a few days apart for a year . An analemma can also be considered as a graph of the Sun's declination , usually plotted vertically, against the equation of time , plotted horizontally. Usually, the scales are chosen so that equal distances on the diagram represent equal angles in both directions on
368-455: A circular path called the ecliptic . Earth's rotation about its axis causes diurnal motion , so that the Sun appears to move across the sky in a Sun path that depends on the observer's geographic latitude . The time when the Sun transits the observer's meridian depends on the geographic longitude . To find the Sun's position for a given location at a given time, one may therefore proceed in three steps as follows: This calculation
460-533: A complete position of the Sun in the ecliptic coordinate system . This can be converted to the equatorial coordinate system by calculating the obliquity of the ecliptic , ϵ {\displaystyle \epsilon } , and continuing: Right ascension , To get RA at the right quadrant on computer programs use double argument Arctan function such as ATAN2(y,x) and declination , Right-handed rectangular equatorial coordinates in astronomical units are: The Sun appears to move northward during
552-408: A constant speed. Thus, the graph of solar declination, as seen from this highly tilted Earth, would resemble a triangle wave rather than a sine wave, zigzagging between plus and minus 90°, with linear segments between the maxima and minima. If the 90° axial tilt is decreased, then the absolute maximum and minimum values of the declination would decrease, to equal the axial tilt. Also, the shapes of
644-433: A digit from 0 to and including 11), degrees from 0 to 29, minutes, and seconds. Mughal king Jahangir issued an attractive series of coins in gold and silver depicting the twelve signs of the zodiac. What follows is a list of the signs of the modern zodiac (with the ecliptic longitudes of their first points), where 0° Aries is understood as the vernal equinox, with their Latin, Greek, Sanskrit, and Babylonian names. But
736-631: A planet were not as important as the astrologically significant dates when the planet crossed from one zodiacal sign to the next. Knowledge of the Babylonian zodiac is said to be reflected in the Hebrew Bible ; E. W. Bullinger interpreted the creatures that appear in the book of Ezekiel ( 1:10 ) as the middle signs of the four quarters of the zodiac, with the Lion as Leo , the Bull as Taurus ,
828-444: A rudimentary stage of evolution. They measured the position of a planet in reference to a set of "normal stars" close to the ecliptic (±9° of latitude). The normal stars were used as observational reference points to help position a planet within this ecliptic coordinate system. In Babylonian astronomical diaries , a planet position was generally given with respect to a zodiacal sign alone, though less often in specific degrees within
920-408: A sign. When the degrees of longitude were given, they were expressed with reference to the 30° of the zodiacal sign, i.e., not with a reference to the continuous 360° ecliptic. In astronomical ephemerides , the positions of significant astronomical phenomena were computed in sexagesimal fractions of a degree (equivalent to minutes and seconds of arc ). For daily ephemerides, the daily positions of
1012-522: A sine wave. Calculating it accurately involves some complexity, as shown below. The declination of the Sun , δ ☉ , is the angle between the rays of the Sun and the plane of the Earth's equator. The Earth's axial tilt (called the obliquity of the ecliptic by astronomers) is the angle between the Earth's axis and a line perpendicular to the Earth's orbit. The Earth's axial tilt changes slowly over thousands of years but its current value of about ε = 23.44°
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#17327828008881104-416: A sundial would be ahead of a clock. The equation of time can be positive or negative. An analemma is a diagram that shows the annual variation of the Sun's position on the celestial sphere , relative to its mean position, as seen from a fixed location on Earth. (The word analemma is also occasionally, but rarely, used in other contexts.) It can be considered as an image of the Sun's apparent motion during
1196-399: A takht. First, the astrologer would use an astrolabe to find the position of the sun, align the rule with the persons time of birth and then align the rete to establish the altitude of the sun on that date. Next, the astrologer would use an Ephemeris, a table denoting the mean position of the planets and stars within the sky at any given time. Finally, the astrologer would add the altitude of
1288-611: A very few years of 401 BC. Unlike modern astrologers, who place the beginning of the sign of Aries at the position of the Sun at the vernal equinox in the Northern Hemisphere ( March equinox ), Babylonian astronomers fixed the zodiac in relation to stars, placing the beginning of Cancer at the "Rear Twin Star" ( β Geminorum ) and the beginning of Aquarius at the "Rear Star of the Goat-Fish" ( δ Capricorni ). Due to
1380-432: Is applied, which depends on the observer's distance away from the center of the Earth. This correction is less than 0.0025°. The error in calculating the position of the center of the Sun can be less than 0.00015°. For comparison, the Sun's width is about 0.5°. The declination calculations described above do not include the effects of the refraction of light in the atmosphere, which causes the apparent angle of elevation of
1472-497: Is associated with different attributes. The zodiacal system and its angular measurement in 360 sexagesimal degree (°) originated with Babylonian astronomy during the 1st millennium BC . It was communicated into Greek astronomy by the 2nd century BC, as well as into developing the Hindu zodiac . Due to the precession of the equinoxes , the time of year that the Sun is in a given constellation has changed since Babylonian times, and
1564-550: Is defined as the moment of vernal equinox , and all other dates shift accordingly. The precise Gregorian times and dates vary slightly from year to year as the Gregorian calendar shifts relative to the tropical year . These variations remain within less than two days' difference in the recent past and the near-future, vernal equinox in UT always falling either on 20 or 21 March in the period of 1797 to 2043, falling on 19 March in 1796
1656-433: Is described in the 1st century BC astronomical text of Geminus of Rhodes. Geminus explains that Greek astronomers of his era associate the first degrees of the zodiac signs with the two solstices and the two equinoxes, in contrast to the older Chaldean (Babylonian) system, which placed these points within the zodiac signs. This illustrates that Ptolemy merely clarified the convention of Greek astronomers and did not originate
1748-411: Is nearly constant, so the change in solar declination during one year is nearly the same as during the next year. At the solstices , the angle between the rays of the Sun and the plane of the Earth's equator reaches its maximum value of 23.44°. Therefore, δ ☉ = +23.44° at the northern summer solstice and δ ☉ = −23.44° at the southern summer solstice. At the moment of each equinox , the center of
1840-472: Is the first known depiction of the classical zodiac of twelve signs. The earliest extant Greek text using the Babylonian division of the zodiac into 12 signs of 30 equal degrees each is the Anaphoricus of Hypsicles of Alexandria (fl. 190 BC). Particularly important in the development of Western horoscopic astrology was the astrologer and astronomer Ptolemy , whose work Tetrabiblos laid
1932-557: Is useful in astronomy , navigation , surveying , meteorology , climatology , solar energy , and sundial design. These equations, from the Astronomical Almanac , can be used to calculate the apparent coordinates of the Sun , mean equinox and ecliptic of date , to a precision of about 0°.01 (36″), for dates between 1950 and 2050. Similar equations are coded into a Fortran 90 routine in Ref. and are used to calculate
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#17327828008882024-467: Is usually done even when the analemma is marked on a geographical globe , on which the continents, etc., are shown with west to the left. Some analemmas are marked to show the position of the Sun on the graph on various dates, a few days apart, throughout the year. This enables the analemma to be used to make simple analog computations of quantities such as the times and azimuths of sunrise and sunset . Analemmas without date markings are used to correct
2116-564: The Chaldean period (mid-1st millennium BC), which, in turn, derived from an earlier system of lists of stars along the ecliptic. The construction of the zodiac is described in Ptolemy 's comprehensive 2nd century AD work, the Almagest . Although the zodiac remains the basis of the ecliptic coordinate system in use in astronomy besides the equatorial one, the term and the names of
2208-612: The Latinized form of the Ancient Greek zōdiakòs kýklos ( ζῳδιακός κύκλος ), meaning "cycle or circle of little animals". Zōdion ( ζῴδιον ) is the diminutive of zōon ( ζῷον , "animal"). The name reflects the prominence of animals (and mythological hybrids ) among the twelve signs. The zodiac was in use by the Roman era , based on concepts inherited by Hellenistic astronomy from Babylonian astronomy of
2300-419: The astronomical constellations with the following modern names: Aries , Taurus , Gemini , Cancer , Leo , Virgo , Libra , Scorpio , Sagittarius , Capricorn , Aquarius , and Pisces . The signs have been used to determine the time of the year by identifying each sign with the days of the year the Sun is in the respective sign. In Western astrology , and formerly astronomy , the time of each sign
2392-593: The ecliptic and equator , which shifts in relation to the backdrop of fixed stars at a rate of 1° every 72 years, creating the phenomenon known as precession of the equinoxes. The Hindu zodiac, being sidereal, does not maintain this seasonal alignment, but there are still similarities between the two systems. The Hindu zodiac signs and corresponding Greek signs sound very different, being in Sanskrit and Greek respectively, but their symbols are nearly identical. For example, dhanu means "bow" and corresponds to Sagittarius,
2484-513: The ecliptic longitude of the Sun is: The ecliptic latitude of the Sun is nearly: as the ecliptic latitude of the Sun never exceeds 0.00033° (a little over 1″), and the distance of the Sun from the Earth, in astronomical units , is: Where the obliquity of the ecliptic is not obtained elsewhere, it can be approximated: λ {\displaystyle \lambda } , β {\displaystyle \beta } and R {\displaystyle R} form
2576-421: The precession of the equinoxes , the time of year the Sun is in a given constellation has changed since Babylonian times, as the point of March equinox has moved from Aries into Pisces . Because the divisions were made into equal arcs of 30° each, they constituted an ideal system of reference for making predictions about a planet's longitude. However, Babylonian techniques of observational measurements were in
2668-474: The solar zenith angle and solar azimuth angle as observed from the surface of the Earth. Start by calculating n , the number of days (positive or negative, including fractional days) since Greenwich noon, Terrestrial Time, on 1 January 2000 ( J2000.0 ). If the Julian date for the desired time is known, then The mean longitude of the Sun, corrected for the aberration of light , is: The mean anomaly of
2760-492: The "archer", and kumbha means "water-pitcher" and corresponds to Aquarius, the "water-carrier". During the Abbasid era , Greek reference books were translated into Arabic , and Islamic astronomers then did their own observations, correcting Ptolemy's Almagest. One such book was Al-Sufi 's Book of Fixed Stars , which has pictorial depictions of 48 constellations. The book was divided into three sections: constellations of
2852-420: The Earth's perihelion . The number 0.0167 is the current value of the eccentricity of the Earth's orbit. The eccentricity varies very slowly over time, but for dates fairly close to the present, it can be considered to be constant. The largest errors in this equation are less than ± 0.2°, but are less than ± 0.03° for a given year if the number 10 is adjusted up or down in fractional days as determined by how far
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2944-426: The Earth's axis is at an angle, some signs take longer to rise than others, and the farther away from the equator the observer is situated, the greater the difference. Thus, signs are spoken of as "long" or "short" ascension . In tropical astrology , the zodiacal signs are distinct from the constellations associated with them, not only because of their drifting apart due to the precession of equinoxes but because
3036-463: The Earth's axis of rotation, rather than the plane of the planet's orbit around the Sun. Position of the Sun The position of the Sun in the sky is a function of both the time and the geographic location of observation on Earth 's surface. As Earth orbits the Sun over the course of a year , the Sun appears to move with respect to the fixed stars on the celestial sphere , along
3128-527: The Hellenistic world came to be so identified with astrology that "Chaldean wisdom" became among Greeks and Romans the synonym of divination through the planets and stars . Hellenistic astrology derived in part from Babylonian and Egyptian astrology . Horoscopic astrology first appeared in Ptolemaic Egypt (305 BC–30 BC). The Dendera zodiac , a relief dating to c. 50 BC ,
3220-870: The IAU, NASA , or the Royal Astronomical Society . This happened in a 1995 report of the BBC Nine O'Clock News and various reports in 2011 and 2016. Some "parazodiacal" constellations are touched by the paths of the planets, leading to counts of up to 25 "constellations of the zodiac". The ancient Babylonian MUL.APIN catalog lists Orion , Perseus , Auriga , and Andromeda . Modern astronomers have noted that planets pass through Crater , Sextans , Cetus , Pegasus , Corvus , Hydra , Orion , and Scutum , with Venus very rarely passing through Aquila , Canis Minor , Auriga , and Serpens . Some other constellations are mythologically associated with
3312-674: The Man as Aquarius and the Eagle as a higher aspect of Scorpio. Some authors have linked the signs of the zodiac with the twelve tribes of Israel , and with the lunar Hebrew calendar , which has twelve lunar months in a lunar year . Martin and others have argued that the arrangement of the tribes around the Tabernacle (reported in the Book of Numbers ) corresponded to the order of the zodiac, with Judah , Reuben , Ephraim , and Dan representing
3404-424: The Sanskrit and the name equivalents (after c.500 BC) denote the constellations only, not the tropical zodiac signs. The "English translation" is not usually used by English speakers. The Latin names are standard English usage (except that "Capricorn" is used rather than "Capricornus"). These twelve signs have been arranged into a nursery rhyme as a mnemonic device: The ram, the bull, the heavenly twins, And next
3496-536: The Sun (actually, of the Earth in its orbit around the Sun, but it is convenient to pretend the Sun orbits the Earth), is: Put L {\displaystyle L} and g {\displaystyle g} in the range 0° to 360° by adding or subtracting multiples of 360° as needed — which is to say, L {\displaystyle L} and g {\displaystyle g} are really to be evaluated ( mod 360). Finally,
3588-458: The Sun appears to pass through the celestial equator , and δ ☉ is 0°. The Sun's declination at any given moment is calculated by: where EL is the ecliptic longitude (essentially, the Earth's position in its orbit). Since the Earth's orbital eccentricity is small, its orbit can be approximated as a circle which causes up to 1° of error. The circle approximation means the EL would be 90° ahead of
3680-412: The Sun as seen by an observer to be higher than the actual angle of elevation, especially at low Sun elevations. For example, when the Sun is at an elevation of 10°, it appears to be at 10.1°. The Sun's declination can be used, along with its right ascension , to calculate its azimuth and also its true elevation, which can then be corrected for refraction to give its apparent position. In addition to
3772-410: The Sun's declination during a year resembles a sine wave with an amplitude of 23.44°, but one lobe of the wave is several days longer than the other, among other differences. The following phenomena would occur if Earth were a perfect sphere , in a circular orbit around the Sun, and if its axis were tilted 90°, so that the axis itself is on the orbital plane (similar to Uranus ). At one date in
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3864-492: The Sun's planets have orbits that have only a slight inclination to the orbital plane of the Earth. Stars within the zodiac are subject to occultations by the Moon and other solar system bodies. These events can be useful, for example, to estimate the cross-sectional dimensions of a minor planet , or check a star for a close companion. The Sun's placement upon the vernal equinox, which occurs annually around 21 March, defines
3956-450: The annual north–south oscillation of the Sun's apparent position, corresponding to the variation of its declination described above, there is also a smaller but more complex oscillation in the east–west direction. This is caused by the tilt of the Earth's axis, and also by changes in the speed of its orbital motion around the Sun produced by the elliptical shape of the orbit. The principal effects of this east–west oscillation are variations in
4048-400: The apparent position of the Sun, compared with its mean position. A westward shift causes the sundial to be ahead of the clock. Since the main effect of this oscillation concerns time, it is called the equation of time , using the word "equation" in a somewhat archaic sense meaning "correction". The oscillation is measured in units of time, minutes and seconds, corresponding to the amount that
4140-563: The basis of the Western astrological tradition . Under the Greeks, and Ptolemy in particular, the planets, Houses, and signs of the zodiac were rationalized and their function set down in a way that has changed little to the present day. Ptolemy lived in the 2nd century AD, three centuries after the discovery of the precession of the equinoxes by Hipparchus around 130 BC. Hipparchus' lost work on precession never circulated very widely until it
4232-511: The best date for founding the new capital of Baghdad. Whilst horoscopes were generally widely accepted by society, many scholars condemned the use of astrology and divination, linking it to occult influences. Many theologians and scholars thought that it went against the tenets of Islam; as only God should be able to determine events rather than astrologers looking at the positions of the planets. In order to calculate someone's horoscope, an astrologer would use 3 tools: an astrolabe, ephemeris and
4324-401: The celestial sphere. Thus 4 minutes (more precisely 3 minutes, 56 seconds), in the equation of time, are represented by the same distance as 1° in the declination , since Earth rotates at a mean speed of 1° every 4 minutes, relative to the Sun. An analemma is drawn as it would be seen in the sky by an observer looking upward. If north is shown at the top, then west is to the right . This
4416-479: The crab, the lion shines, The virgin and the scales, The scorpion, archer, and the goat, The man who holds the watering-pot, And fish with glittering scales. The following table compares the Gregorian dates on which the Sun enters a sign in the Ptolemaic tropical zodiac, and a sign in the sidereal system proposed by Cyril Fagan . The beginning of Aries
4508-522: The days part of the ordinal date −1). The number 10, in (N+10), is the approximate number of days after the December solstice to January 1. This equation overestimates the declination near the September equinox by up to +1.5°. The sine function approximation by itself leads to an error of up to 0.26° and has been discouraged for use in solar energy applications. The 1971 Spencer formula (based on
4600-461: The eccentricity of the Earth's orbit . Sidereal astrology remedies this by assigning the zodiac sign approximately to the corresponding constellation. This alignment needs re calibrating every so often to keep the alignment in place. The ecliptic intersects with 13 constellations of Ptolemy 's Almagest , as well as of the more precisely delineated IAU designated constellations . In addition to
4692-716: The ecliptic into the zodiacal signs originates in Babylonian astronomy during the first half of the 1st millennium BC . The zodiac draws on stars in earlier Babylonian star catalogues , such as the MUL.APIN catalogue, which was compiled around 1000 BC. Some constellations can be traced even further back, to Bronze Age ( Old Babylonian Empire ) sources, including Gemini "The Twins", from Sumerian : 𒀯𒈦𒋰𒁀𒃲𒃲 , romanized: MAŠ.TAB.BA.GAL.GAL "The Great Twins"; Cancer "The Crab", from Sumerian : 𒀯𒀠𒇻 , romanized: AL.LUL "The Crayfish", among others. Around
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#17327828008884784-420: The ecliptic longitude by using terms in addition to the 1st-order eccentricity correction above. They also correct the 23.44° obliquity which changes very slightly with time. Corrections may also include the effects of the moon in offsetting the Earth's position from the center of the pair's orbit around the Sun. After obtaining the declination relative to the center of the Earth, a further correction for parallax
4876-483: The ecliptic. By extension, the "zodiac of the comets" may refer to the band encompassing most short-period comets . As early as the 14th century BC a complete list of the 36 Egyptian decans was placed among the hieroglyphs adorning the tomb of Seti I ; they figured again in the temple of Ramesses II , and characterize every Egyptian astrological monument. Both the famous zodiacs of Dendera display their symbols, identified by Karl Richard Lepsius . The division of
4968-416: The end of the constellation Pisces, having been within that constellation since the 2nd century AD. The subsequent 30° of the ecliptic is nominally designated the zodiac sign Taurus, and so on through the twelve signs of the zodiac so that each occupies 1 ⁄ 12 th (30°) of the zodiac's great circle. Zodiac signs have never been used to determine the boundaries of astronomical constellations that lie in
5060-405: The end of the fifth century BC, Babylonian astronomers divided the ecliptic into 12 equal "signs", by analogy to 12 schematic months of 30 days each. Each sign contained 30° of celestial longitude , thus creating the first known celestial coordinate system. According to calculations by modern astrophysics, the zodiac was introduced between 409 and 398 BC, during Persian rule , and probably within
5152-550: The equation of Munjaala. The discovery of precession is attributed to Hipparchus around 130 BC. Ptolemy quotes from Hipparchus' now-lost work entitled "On the Displacement of the Solstitial and Equinoctial Points" in the seventh book of his 2nd century astronomical text, Almagest , where he describes the phenomenon of precession and estimates its value. Ptolemy clarified that the convention of Greek mathematical astronomy
5244-593: The influence that the stars have on events on the earth was important in Islamic civilization. As a rule, it was believed that the signs of the zodiac and the planets control the destiny not only of people but also of nations, and that the zodiac has the ability to determine a person's physical characteristics as well as intelligence and personal traits. The practice of astrology at this time could be divided into 4 broader categories: Genethlialogy, Catarchic Astrology, Interrogational Astrology and General Astrology. However
5336-517: The last time and in 2044 the next. The vernal equinox has fallen on 20 March UT since 2008, and will continue to do so until 2043. As each sign takes up exactly 30 degrees of the zodiac, the average duration of the solar stay in each sign is one twelfth of a sidereal year , or 30.43 standard days . Due to Earth's slight orbital eccentricity , the duration of each sign varies appreciably, between about 29.4 days for Capricorn and about 31.4 days for Cancer (see Equation of time ). In addition, because
5428-399: The link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Tierkreis&oldid=933209660 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Zodiac The zodiac is a belt-shaped region of
5520-444: The maxima and minima on the graph would become less acute, being curved to resemble the maxima and minima of a sine wave. However, even when the axial tilt equals that of the actual Earth, the maxima and minima remain more acute than those of a sine wave. In reality, Earth's orbit is elliptical . Earth moves more rapidly around the Sun near perihelion , in early January, than near aphelion , in early July. This makes processes like
5612-463: The middle signs of Leo, Aquarius, Taurus, and Scorpio, respectively. Such connections were taken up by Thomas Mann , who in his novel Joseph and His Brothers , attributes characteristics of a sign of the zodiac to each tribe, in his rendition of the Blessing of Jacob . The Babylonian star catalogs entered Greek astronomy in the 4th century BC, via Eudoxus of Cnidus . Babylonia or Chaldea in
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#17327828008885704-500: The most common type of astrology was Genethlialogy, which examined all aspects of a person's life in relation to the planetary positions at their birth; more commonly known as our horoscope. Astrology services were offered widely across the empire, mainly in bazaars, where people could pay for a reading. Astrology was valued in the royal courts, for example, the Abbasid Caliph Al-Mansur used astrology to determine
5796-408: The natures of the signs from the theory of prognostication, or impossible to avoid error in then retaining and making use of them; as the regularity of their spaces and distances, upon which their influence depends, would then be invaded and broken in upon. Astronomically, the zodiac defines a belt of space extending 8° or 9° in celestial latitude to the north and south of the ecliptic , within which
5888-560: The northern spring , crossing the celestial equator on the March equinox . Its declination reaches a maximum equal to the angle of Earth's axial tilt (23.44° or 23°26') on the June solstice , then decreases until reaching its minimum (−23.44° or -23°26') on the December solstice , when its value is the negative of the axial tilt. This variation produces the seasons . A line graph of
5980-424: The orbits of the Moon and the principal planets remain. It is a feature of the ecliptic coordinate system – a celestial coordinate system centered upon the ecliptic (the plane of the Earth's orbit and the Sun's apparent path), by which celestial longitude is measured in degrees east of the vernal equinox (the ascending intersection of the ecliptic and equator). The zodiac is narrow in angular terms because most of
6072-417: The physical constellations take up varying widths of the ecliptic, so the Sun is not in each constellation for the same amount of time. Thus, Virgo takes up 5 times as much ecliptic longitude as Scorpius . The zodiacal signs are an abstraction from the physical constellations, and each represent exactly 1 ⁄ 12 th of the full circle, but the time spent by the Sun in each sign varies slightly due to
6164-458: The point of March equinox has moved from Aries into Pisces . The zodiac forms a celestial coordinate system , or more specifically an ecliptic coordinate system , which takes the ecliptic as the origin of latitude and the Sun's position at vernal equinox as the origin of longitude. In modern astronomy, the ecliptic coordinate system is still used for tracking Solar System objects. The English word zodiac derives from zōdiacus ,
6256-477: The previous year's December solstice occurred before or after noon on December 22. These accuracies are compared to NOAA's advanced calculations which are based on the 1999 Jean Meeus algorithm that is accurate to within 0.01°. (The above formula is related to a reasonably simple and accurate calculation of the Equation of Time , which is described here .) More complicated algorithms correct for changes to
6348-468: The principle of the tropical zodiac, as is sometimes assumed. Ptolemy demonstrates that the principle of the tropical zodiac was well known to his predecessors within his astrological text, the Tetrabiblos , where he explains why it would be an error to associate the regularly spaced signs of the seasonally aligned zodiac with the irregular boundaries of the visible constellations: The beginnings of
6440-556: The same names as the zodiac signs. According to mathematician-historian Montucla , the Hindu zodiac was adopted from the Greek zodiac through communications between ancient India and the Greek empire of Bactria . The Hindu zodiac uses the sidereal coordinate system , which makes reference to the fixed stars. The tropical zodiac (of Mesopotamian origin) is divided by the intersections of
6532-515: The serpent on the Dendera zodiac . The zodiac system was developed in Babylonia , some 2,500 years ago, during the " Age of Aries ". At the time, it is assumed, the precession of the equinoxes was unknown. Contemporary use of the coordinate system is presented with the choice of interpreting the system either as sidereal , with the signs fixed to the stellar background , or as tropical , with
6624-522: The signs fixed to the point ( vector of the Sun) at the March equinox . Western astrology takes the tropical approach, whereas Hindu astrology takes the sidereal one. This results in the originally unified zodiacal coordinate system drifting apart gradually, with a clockwise (westward) precession of 1.4 degrees per century. For the tropical zodiac used in Western astronomy and astrology, this means that
6716-454: The signs, and likewise those of the terms, are to be taken from the equinoctial and tropical points. This rule is not only clearly stated by writers on the subject, but is especially evident by the demonstration constantly afforded, that their natures, influences and familiarities have no other origin than from the tropics and equinoxes, as has been already plainly shown. And, if other beginnings were allowed, it would either be necessary to exclude
6808-510: The sky that extends approximately 8° north and south (as measured in celestial latitude ) of the ecliptic , the apparent path of the Sun across the celestial sphere over the course of the year. Also within this zodiac belt appear the Moon and the brightest planets , along their orbital planes. The zodiac is divided along the ecliptic into 12 equal parts ("signs") , each occupying 30° of celestial longitude . These signs roughly correspond to
6900-414: The solstices in Earth's orbit (at the equinoxes), so that sin(EL) can be written as sin(90+NDS)=cos(NDS) where NDS is the number of days after the December solstice. By also using the approximation that arcsin[sin(d)·cos(NDS)] is close to d·cos(NDS), the following frequently used formula is obtained: where N is the day of the year beginning with N=0 at midnight Universal Time (UT) as January 1 begins (i.e.
6992-405: The starting point for measurement, the first degree of which is historically known as the " first point of Aries ". The first 30° along the ecliptic is nominally designated as the zodiac sign Aries, which no longer falls within the proximity of the constellation Aries since the effect of precession is to move the vernal point through the backdrop of visible constellations. It is currently located near
7084-408: The sun taken from the astrolabe, with the mean position of the planets on the person's birthday, and add them together on the takht (also known as the dustboard). The dust board was merely a tablet covered in sand; on which the calculations could be made and erased easily. Once this had been calculated, the astrologer was then able to interpret the horoscope. Most of these interpretations were based on
7176-422: The timing of events such as sunrise and sunset, and in the reading of a sundial compared with a clock showing local mean time . As the graph shows, a sundial can be up to about 16 minutes fast or slow, compared with a clock. Since the Earth rotates at a mean speed of one degree every four minutes, relative to the Sun, this 16-minute displacement corresponds to a shift eastward or westward of about four degrees in
7268-577: The tropical sign of Aries currently lies somewhere within the constellation Pisces (" Age of Pisces "). The sidereal coordinate system takes into account the ayanamsa , ayan meaning "transit' or 'movement', and amsa meaning 'small part', i.e. movement of equinoxes in small parts. It is unclear when Indians became aware of the precession of the equinoxes, but Bhāskara II 's 12th-century treatise Siddhanta Shiromani gives equations for measurement of precession of equinoxes, and says his equations are based on some lost equations of Suryasiddhanta plus
7360-399: The twelve constellations after which the twelve zodiac signs are named, the ecliptic intersects Ophiuchus , the bottom part of which interjects between Scorpio and Sagittarius. Occasionally this difference between the astronomical constellations and the astrological signs is mistakenly reported in the popular press as a "change" to the list of traditional signs by some astronomical body like
7452-418: The twelve signs are today mostly associated with horoscopic astrology . The term "zodiac" may also refer to the region of the celestial sphere encompassing the paths of the planets corresponding to the band of about 8 arc degrees above and below the ecliptic. The zodiac of a given planet is the band that contains the path of that particular body; e.g., the "zodiac of the Moon" is the band of 5° above and below
7544-420: The two approximations, using the parameters of the Earth's orbit to more accurately estimate EL: which can be simplified by evaluating constants to: N is the number of days since midnight UT as January 1 begins (i.e. the days part of the ordinal date −1) and can include decimals to adjust for local times later or earlier in the day. The number 2, in (N-2), is the approximate number of days after January 1 to
7636-527: The variation of the solar declination happen faster in January than in July. On the graph, this makes the minima more acute than the maxima. Also, since perihelion and aphelion do not happen on the exact dates as the solstices, the maxima and minima are slightly asymmetrical. The rates of change before and after are not quite equal. The graph of apparent solar declination is therefore different in several ways from
7728-463: The vicinity of the zodiac, which are, and always have been, irregular in their size and shape. The convention of measuring celestial longitude within individual signs was still being used in the mid-19th century, but modern astronomy now numbers degrees of celestial longitude continuously from 0° to 360°, rather than 0° to 30° within each sign. This coordinate system is primary used by astronomers for observations of solar system objects. The use of
7820-627: The year, the Sun would be directly overhead at the North Pole , so its declination would be +90°. For the next few months, the subsolar point would move toward the South Pole at constant speed, crossing the circles of latitude at a constant rate, so that the solar declination would decrease linearly with time. Eventually, the Sun would be directly above the South Pole, with a declination of −90°; then it would start to move northward at
7912-519: The zodiac as a means to determine astronomical measurement remained the main method for defining celestial positions by Western astronomers until the Renaissance, at which time preference moved to the equatorial coordinate system, which measures astronomical positions by right ascension and declination rather than the ecliptic-based definitions of celestial longitude and celestial latitude . The orientation of equatorial coordinates are aligned with
8004-479: The zodiac in literature. For example, there were several manuals on how to interpret each zodiac sign, the treatise relating to each individual sign and what the characteristics of these zodiacs were. An example of the use of signs as astronomical coordinates may be found in the Nautical Almanac and Astronomical Ephemeris for the year 1767 . The "Longitude of the Sun" columns show the sign (represented as
8096-720: The zodiac, as found, e.g., in the Sefer Raziel HaMalakh . The zodiac is found in medieval stained glass as at Angers Cathedral , where the master glass maker, André Robin, made the ornate rosettes for the North and South transepts after the fire there in 1451. Astrology emerged in the 8th century AD as a distinct discipline in Islam, with a mix of Indian, Hellenistic Iranian and other traditions blended with Greek and Islamic astronomical knowledge, for example Ptolemy's work and Al-Sufi's Book of Fixed Stars. A knowledge of
8188-700: The zodiac, constellations north of the zodiac, and southern constellations. When Al-Sufi's book, and other works, were translated in the 11th century, there were mistakes made in the translations. As a result, some stars ended up with the names of the constellation they belong to (e.g. Hamal in Aries). The High Middle Ages saw a revival of interest in Greco-Roman magic , first in Kabbalism and later continued in Renaissance magic . This included magical uses of
8280-483: The zodiacal ones: Piscis Austrinus , The Southern Fish, is attached to Aquarius. In classical maps, it swallows the stream poured out of Aquarius' pitcher, but perhaps it formerly just swam in it. Aquila , The Eagle, was possibly associated with the zodiac by virtue of its main star, Altair . Hydra in the Early Bronze Age marked the celestial equator and was associated with Leo, which is shown standing on
8372-415: Was brought to prominence by Ptolemy, and there are few explanations of precession outside the work of Ptolemy until late Antiquity, by which time Ptolemy's influence was widely established. Ptolemy clearly explained the theoretical basis of the western zodiac as being a tropical coordinate system , by which the zodiac is aligned to the equinoxes and solstices, rather than the visible constellations that bear
8464-399: Was to commence the zodiac from the point of the vernal equinox and to always refer to this point as "the first degree" of Aries. This is known as the "tropical zodiac" (from the Greek word trópos, turn) because its starting point revolves through the circle of background constellations over time. The principle of the vernal point acting as the first degree of the zodiac for Greek astronomers
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