The zodiac is an area of the sky that extends approximately 8° north or 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. The paths of the Moon and visible planets are also within the belt of the zodiac.
In Western astrology, and formerly astronomy, the zodiac is divided into twelve signs, each occupying 30° of celestial longitude and roughly corresponding to the constellations Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius and Pisces.
The twelve astrological signs form a celestial coordinate system, or even 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.
- 1 Name
- 2 Usage
- 3 History
- 4 Twelve signs
- 5 Constellations
- 6 Table of dates
- 7 Precession of the equinoxes
- 8 In modern astronomy
- 9 Unicode characters
- 10 See also
- 11 References
- 12 External links
The English word zodiac derives from zōdiacus, the Latinized form of the Ancient Greek zōidiakòs kýklos (ζῳδιακός κύκλος), meaning "cycle or circle of little animals". Zōidion (ζῴδιον) is the diminutive of zōion (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 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 vast 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 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 eight 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 five degrees above and below the ecliptic. By extension, the "zodiac of the comets" may refer to the band encompassing most short-period comets.
The division of the ecliptic into the zodiacal signs originates in Babylonian ("Chaldean") 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 of the constellations can be traced even further back, to Bronze Age (First Babylonian dynasty) sources, including Gemini "The Twins", from MAŠ.TAB.BA.GAL.GAL "The Great Twins", and Cancer "The Crab", from AL.LUL "The Crayfish", among others.
Around the end of the 5th century BC, Babylonian astronomers divided the ecliptic into twelve equal "signs", by analogy to twelve schematic months of thirty days each. Each sign contained thirty degrees 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 and probably within a very few years of 401 BC Unlike modern astronomers, who place the beginning of the sign of Aries at the place of the Sun at the vernal 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). The divisions do not correspond exactly to where the constellations started and ended in the sky; this would have resulted in an irregular division. The Sun in fact passed through at least 13, not 12 Babylonian constellations. In order to align with the number of months in a year, designers of the system omitted the major constellation Ophiuchus. Including smaller figures, astronomers have counted up to 21 eligible zodiac constellations. Changes in the orientation of the Earth's axis of rotation also means that the time of year the Sun is in a given constellation has changed since Babylonian times.
Because the division was made into equal arcs, 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 a rudimentary stage of evolution and they measured the position of a planet in reference to a set of "normal stars" close to the ecliptic (±9° of latitude) as observational reference points to help positioning a planet within this ecliptic coordinate system.
In Babylonian astronomical diaries, a planet position was generally given with respect to a zodiacal sign alone, less often in specific degrees within 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 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 also reflected in the Hebrew Bible; E. W. Bullinger interpreted the creatures appearing in the book of Ezekiel as the middle signs of the four quarters of the Zodiac, with the Lion as Leo, the Bull is Taurus, the Man representing Aquarius and the Eagle representing Scorpio. Some authors have linked the twelve tribes of Israel with the twelve signs and/or the lunar Hebrew calendar having 12 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 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.
Hellenistic and Roman era
The Babylonian star catalogs entered Greek astronomy in the 4th century BC, via Eudoxus of Cnidus. Babylonia or Chaldea in 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 ca. 50 BC, 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 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's lost work on precession never circulated very widely until it 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 the same names as the zodiac signs.
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 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, the "archer", and kumbha means "water-pitcher" and corresponds to Aquarius, the "water-carrier".
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 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 glassmaker, André Robin, made the ornate rosettes for the North and South transepts after the fire there in 1451.
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 a digit from 0 to and including 11), degrees from 0 to 29, minutes, and seconds.
The zodiac symbols are Early Modern simplifications of conventional pictorial representations of the signs, attested since Hellenistic times.
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 note that the Sanskrit and the Babylonian name equivalents (after c.500 BC) denote the constellations only, not the tropical zodiac signs). Also, the "English translation" is not usually used by English speakers. The Latin names are standard English usage.
|No.||Symbol||Long.||Latin name||English translation||Greek name (with Romanization of Greek)||Sanskrit name||Sumero-Babylonian name|
|1||♈||0°||Aries||The Ram||Κριός (Krios)||Meṣa (मेष)||MUL LU.ḪUŊ.GA "The Agrarian Worker", Dumuzi|
|2||♉||30°||Taurus||The Bull||Ταῦρος (Tauros)||Vṛṣabha (वृषभ)||MULGU4.AN.NA "The Steer of Heaven"|
|3||♊||60°||Gemini||The Twins||Δίδυμοι (Didymoi)||Mithuna (मिथुन)||MULMAŠ.TAB.BA.GAL.GAL "The Great Twins" (Castor and Pollux)|
|4||♋||90°||Cancer||The Crab||Καρκίνος (Karkinos)||Karkaṭa (कर्क)||MULAL.LUL "The Crayfish"|
|5||♌||120°||Leo||The Lion||Λέων (Leōn)||Siṃha (सिंह)||MULUR.GU.LA "The Lion"|
|6||♍||150°||Virgo||The Maiden||Παρθένος (Parthenos)||Kanyā (कन्या)||MULAB.SIN "The Furrow"; "The Furrow, the goddess Shala's ear of grain"|
|7||♎||180°||Libra||The Scales||Ζυγός (Zygos)||Tulā (तूळ)||MULZIB.BA.AN.NA "The Scales"|
|8||♏||210°||Scorpio||The Scorpion||Σκoρπίος (Skorpios)||Vṛścika (वृश्चिक)||MULGIR.TAB "The Scorpion"|
|9||♐||240°||Sagittarius||The (Centaur) Archer||Τοξότης (Toxotēs)||Dhanuṣa (धनु)||MULPA.BIL.SAG, Nedu "soldier"|
|10||♑||270°||Capricorn||"Goat Mountain" or "Goat-horned" (The Sea-Goat)||Αἰγόκερως (Aigokerōs)||Makara (मकर)||MULSUḪUR.MAŠ "The Goat-Fish" of Enki|
|11||♒||300°||Aquarius||The Water-Bearer||Ὑδροχόος (Hydrokhoos)||Kumbha (कुंभ)||MULGU.LA "The Great One", later qâ "pitcher"|
|12||♓||330°||Pisces||The Fish||Ἰχθύες (Ikhthyes)||Mīna (मीन)||MULSIM.MAḪ "The Tail of the Swallow", later DU.NU.NU "fish-cord"|
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 also because the physical constellations take up varying widths of the ecliptic, so the Sun is not in each constellation for the same amount of time.:25 Thus, Virgo takes up five times as much ecliptic longitude as Scorpius. The zodiacal signs are an abstraction from the physical constellations, and each represent exactly one twelfth of the full circle, or the longitude traversed by the Sun in about 30.4 days.
The path of the Sun passes through thirteen constellations recognized by ancient Babylonian, Greek, and Roman astronomers (including in Ptolemy's Almagest) and the modern International Astronomical Union. Because the Babylonians had a 12-month lunar calendar, they chose twelve and divided the year up evenly. The thirteenth was left out: 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 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. Professional astronomers generally consider astrology a pseudoscience which has been disproven by scientific experimentation. For example, in drawing a distinction between astrology and scientific astronomy, NASA notes that "No one has shown that astrology can be used to predict the future or describe what people are like based on their birth dates."
Some "parazodiacal" constellations are also 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 also pass through Crater, Sextans, Cetus, Pegasus, Corvus, Hydra, and Scutum; with Venus very rarely passing through Aquila, Canis Minor, Auriga, and Serpens.
Some other constellations are also mythologically associated with 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 the serpent on the Dendera zodiac. Corvus is the Crow or Raven mysteriously perched on the tail of Hydra.
Table of dates
The following table compares the Gregorian dates on which the Sun enters
- a sign in the Ptolemaic tropical zodiac
- a sign in the Hindu sidereal system (date given below may change by one or two days each year)
- the astronomical constellation of the same name as the sign, with constellation boundaries as defined in 1930 by the International Astronomical Union.
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 the last time and in 2044 the next. Except for 2003 and 2007, the vernal equinox has started on 20 March since 1980, and is projected to until 2043.
||Name||IAU boundaries||Solar stay||Brightest star|
|Aries||21 March –
|15 April –
|Aries||19 April – 13 May||25 days||Hamal|
|Taurus||21 April –
|16 May –
|Taurus||14 May – 19 June||37 days||Aldebaran|
|Gemini||22 May –
|16 June –
|Gemini||20 June – 20 July||31 days||Pollux|
|Cancer||22 June –
|16 July –
|Cancer||21 July – 9 August||20 days||Al Tarf|
|Leo||23 July –
|16 August –
|Leo||10 August – 15 September||37 days||Regulus|
|Virgo||23 August –
|16 September –
|Virgo||16 September – 30 October||45 days||Spica|
|Libra||24 September –
|16 October –
|Libra||31 October – 22 November||23 days||Zubeneschamali|
|Scorpio||24 October –
|16 November –
|Scorpius||23 November – 29 November||7 days||Antares|
|Ophiuchus||N/A||Ophiuchus||30 November – 17 December||18 days||Rasalhague|
|Sagittarius||23 November –
|16 December –
|Sagittarius||18 December – 18 January||32 days||Kaus Australis|
|Capricorn||22 December –
|15 January –
|Capricornus||19 January – 15 February||28 days||Deneb Algedi|
|Aquarius||21 January –
|15 February –
|Aquarius||16 February – 11 March||24 days||Sadalsuud|
|Pisces||20 February –
|15 March –
|Pisces||12 March – 18 April||38 days||Eta Piscium|
|Cetus||N/A||Cetus||14 March||<1 day||Diphda|
Because 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.
Precession of the equinoxes
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 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 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 Bhaskara 2'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 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 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 is also 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 the principle of the tropical zodiac, as is sometimes assumed.
Ptolemy also 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 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 also 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 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.
In modern astronomy
Astronomically, the zodiac defines a belt of space extending 9° either side of the ecliptic, within which the orbits of the Moon and the principal planets remain. It is a feature of 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). 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 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 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 1/12th (30°) of the zodiac's great circle. Zodiac signs have never been used to determine the boundaries of astronomical constellations that lie in 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 from 0° to 360°, rather than 0° to 30° within each sign.
The use of 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.
In Unicode, the symbols of zodiac signs are encoded in block "Miscellaneous Symbols":
- U+2648 ♈ ARIES (HTML
- U+2649 ♉ TAURUS (HTML
- U+264A ♊ GEMINI (HTML
- U+264B ♋ CANCER (HTML
- U+264C ♌ LEO (HTML
- U+264D ♍ VIRGO (HTML
- U+264E ♎ LIBRA (HTML
- U+264F ♏ SCORPIUS (HTML
- U+2650 ♐ SAGITTARIUS (HTML
- U+2651 ♑ CAPRICORN (HTML
- U+2652 ♒ AQUARIUS (HTML
- U+2653 ♓ PISCES (HTML
In Unicode 6.0 the sign for Ophiuchus has been added, too:
- U+26CE ⛎ OPHIUCHUS (HTML
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- Because the signs are each 30° in longitude but constellations have irregular shapes, and because of precession, they do not correspond exactly to the boundaries of the constellations after which they are named.
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- Leadbetter, Charles (1742), A Compleat System of Astronomy, J. Wilcox, London, p. 94; numerous examples of this notation appear throughout the book.
- See MUL.APIN. See also Lankford, John; Rothenberg, Marc (1997). History of Astronomy: An Encyclopedia. Taylor & Francis. p. 43. ISBN 978-0-8153-0322-0.
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[T]he zodiac was introduced between −408 and −397 and probably within a very few years of −400.
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- MUL.APIN; Peter Whitfield, History of Astrology (2001); W. Muss-Arnolt, The Names of the Assyro-Babylonian Months and Their Regents, Journal of Biblical Literature (1892).
- Alternative form: Σκορπίων Skorpiōn. Later form (with synizesis): Σκορπιός.
- American Heritage Dictionary of the English Language 3rd ed., s.v. "Pisces."
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- 30.4368 SI days or 2629743 seconds in tropical astrology and 30.4380 SI days or 2629846 seconds in sidereal astrology on average (the time spent by the Sun in each sign varies slightly due to the eccentricity of the Earth's orbit).
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- Kollerstrom, N. (October 1995). "Ophiuchus and the media". The Observatory. KNUDSEN; OBS. 115: 261–262. Bibcode:1995Obs...115..261K.
- The notion received further international media attention in January 2011, when it was reported that astronomer Parke Kunkle, a board-member of the Minnesota Planetarium Society, had suggested that Ophiuchus was the zodiac's "13th sign". He later issued a statement to say he had not reported that the zodiac ought to include 13 signs instead of 12, but was only mentioning that there were 13 constellations; reported in Mad Astronomy: Why did your zodiac sign change? 13 January 2011.
- Plait, Phil (26 September 2016). "No, NASA Didn't Change Your Astrological Sign".
- NASA (20 September 2016). "Constellations and the Calendar".
- Mosley, John (2011). "The Real, Real Constellations of the Zodiac". International Planetarium Society. Retrieved 21 March 2017.
- The Gregorian calendar is built to satisfy the First Council of Nicaea, which placed vernal equinox is on 21 March, but it is not possible to keep it on a single day within a reasonable system of leap days.
- See Jean Meeus, Astronomical Tables of the Sun, Moon, and Planets, 1983 published by Willmann-Bell, Inc., Richmond, Virginia Archived 9 April 2009 at the Wayback Machine. The date in other time zones may vary.
- Swift, Jackson (2015). "Astrology: Tropical Zodiac and Sidereal Zodiac". goarticles.com. Archived from the original on 18 November 2015. Retrieved 24 March 2016.[unreliable source?]
- "Zodiacal symbols in Unicode block Miscellaneous Symbols" (PDF). The Unicode Standard. 2010.
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- Julia Parker "The Astrologer's Handbook", pp 10, Alva Press, NJ, 2010
- Sachs, Abraham (1948), "A Classification of the Babylonian Astronomical Tablets of the Seleucid Period", Journal of Cuneiform Studies, Vol. 2, No. 4, pp. 271–290
- Rochberg, Francesca (1998), "Babylonian Horoscopes", American Philosophical Society, New Series, Vol. 88, No. 1, pp i-164
- Evans, James; Berggren, J. Lennart (2006). Geminos's Introduction to the Phenomena. Princeton University Press. p. 115. ISBN 069112339X.
- "tropo-". Dictionary.com. Random House, Inc. Retrieved 21 May 2015.
- Encyclopædia Britannica. "Zodiac". Encyclopædia Britannica Online. Retrieved 7 May 2015.
- Encyclopædia Britannica. "Ecliptic". Encyclopædia Britannica Online. Retrieved 7 May 2015.
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