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122-428: One of the 48 constellations described by the 2nd-century astronomer Ptolemy , Boötes is now one of the 88 modern constellations . It contains the fourth-brightest star in the night sky, the orange giant Arcturus . Epsilon Boötis, or Izar, is a colourful multiple star popular with amateur astronomers . Boötes is home to many other bright stars , including eight above the fourth magnitude and an additional 21 above

244-536: A Roman citizen . Gerald Toomer, the translator of Ptolemy's Almagest into English, suggests that citizenship was probably granted to one of Ptolemy's ancestors by either the emperor Claudius or the emperor Nero . The 9th century Persian astronomer Abu Ma'shar al-Balkhi mistakenly presents Ptolemy as a member of Ptolemaic Egypt's royal lineage , stating that the descendants of the Alexandrine general and Pharaoh Ptolemy I Soter were wise "and included Ptolemy

366-503: A giant star with a stellar classification of G8 IIIa. The star is radiating around 188 times as much luminosity as the Sun from its outer envelope at an effective temperature of 5,000 K. This heat gives it the yellow-hued glow of a G-type star . It has an estimated rotation period of about 200 days and the pole is inclined 28° ± 6° to the line of sight from the Earth. In 1993,

488-417: A perfect fourth ) and octaves . Ptolemy reviewed standard (and ancient, disused ) musical tuning practice of his day, which he then compared to his own subdivisions of the tetrachord and the octave , which he derived experimentally using a monochord / harmonic canon. The volume ends with a more speculative exposition of the relationships between harmony, the soul ( psyche ), and the planets ( harmony of

610-479: A recurrent nova . Extrasolar planets have been discovered encircling ten stars in Boötes as of 2012. Tau Boötis is orbited by a large planet, discovered in 1999. The host star itself is a magnitude 4.5 star of type F7V, 15.6 parsecs from Earth. It has a mass of 1.3  M ☉ and a radius of 1.331 solar radii ( R ☉ ); a companion, GJ527B , orbits at a distance of 240 AU. Tau Boötis b ,

732-601: A Roman citizen, but was ethnically either a Greek or at least a Hellenized Egyptian. Astronomy was the subject to which Ptolemy devoted the most time and effort; about half of all the works that survived deal with astronomical matters, and even others such as the Geography and the Tetrabiblos have significant references to astronomy. Ptolemy's Mathēmatikē Syntaxis ( Greek : Μαθηματικὴ Σύνταξις , lit.   ' Mathematical Systematic Treatise ' ), better known as

854-470: A coherent mathematical description, which persists to the present as just intonation – the standard for comparison of consonance in the many other, less-than exact but more facile compromise tuning systems. During the Renaissance , Ptolemy's ideas inspired Kepler in his own musings on the harmony of the world ( Harmonice Mundi , Appendix to Book V). The Optica ( Koine Greek : Ὀπτικά ), known as

976-402: A handful of places. Ptolemy's real innovation, however, occurs in the second part of the book, where he provides a catalogue of 8,000 localities he collected from Marinus and others, the biggest such database from antiquity. About 6 300 of these places and geographic features have assigned coordinates so that they can be placed in a grid that spanned the globe. Latitude was measured from

1098-492: A long exposition on the relationship between reason and sense perception in corroborating theoretical assumptions. After criticizing the approaches of his predecessors, Ptolemy argues for basing musical intervals on mathematical ratios (as opposed to the ideas advocated by followers of Aristoxenus ), backed up by empirical observation (in contrast to the excessively theoretical approach of the Pythagoreans ). Ptolemy introduces

1220-406: A mass of 1.09  M ☉ and a radius of 1  R ☉ . The star is orbited by a gas giant, HD 132406 b , discovered in 2007. HD 132406 orbits 1.98 AU from its host star with a period of 974 days and has a mass of 5.61   M J . The planet was discovered by the radial velocity method. WASP-23 is a star with one orbiting planet, WASP-23 b . The planet, discovered by

1342-520: A meal. To verify that the guest was really the king of the gods, Lycaon killed his grandson and prepared a meal made from his flesh. Zeus noticed and became very angry, transforming Lycaon into a wolf and giving life back to his son. In the meantime Callisto had been transformed into a she- bear by Zeus's wife Hera , who was angry at Zeus's infidelity . This is corroborated by the Greek name for Boötes, Arctophylax , which means "Bear Watcher". Callisto, in

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1464-541: A method for specifying the location of the Sun in three pairs of locally oriented coordinate arcs as a function of the declination of the Sun, the terrestrial latitude, and the hour. The key to the approach is to represent the solid configuration in a plane diagram that Ptolemy calls the analemma . In another work, the Phaseis ( Risings of the Fixed Stars ), Ptolemy gave a parapegma , a star calendar or almanac , based on

1586-461: A much later pseudepigraphical composition. The identity and date of the actual author of the work, referred to now as Pseudo-Ptolemy , remains the subject of conjecture. Ptolemy wrote a work entitled Harmonikon ( Greek : Ἁρμονικόν ), known as the Harmonics , on music theory and the mathematics behind musical scales in three books. Harmonics begins with a definition of harmonic theory, with

1708-419: A period of 1544 days. Its orbit is somewhat elliptical, with an eccentricity of 0.22. HD 132563B b is one of very few planets found in triple star systems; it orbits the isolated member of the system, which is separated from the other components, a spectroscopic binary , by 400 AU. Also discovered through the radial velocity method, albeit a year earlier, is HD 136418 b , a two-Jupiter-mass planet that orbits

1830-417: A period of 258 days, and magnitude 4.7 to 5.4 over 450 days, respectively. BL Boötis is the prototype of its class of pulsating variable stars, the anomalous Cepheids . These stars are somewhat similar to Cepheid variables , but they do not have the same relationship between their period and luminosity. Their periods are similar to RRAB variables ; however, they are far brighter than these stars. BL Boötis

1952-489: A period of 883 days. Another single planetary system in Boötes is the HD 132563 system, a triple star system. The parent star, technically HD 132563B , is a star of magnitude 9.47, 96 parsecs from Earth. It is almost exactly the size of the Sun, with the same radius and a mass only 1% greater. Its planet, HD 132563B b , was discovered in 2011 by the radial velocity method. 1.49   M J , it orbits 2.62 AU from its star with

2074-495: A radius of 1.27   R J . It orbits every 3.05 days at a distance of 0.04 AU. HAT-P-4 , the host star, is an F-type star of magnitude 11.2, 310 parsecs from Earth. It is larger than the Sun, with a mass of 1.26  M ☉ and a radius of 1.59  R ☉ . Boötes is also home to multiple-planet systems. HD 128311 is the host star for a two-planet system, consisting of HD 128311 b and HD 128311 c , discovered in 2002 and 2005, respectively. HD 128311 b

2196-450: A secondary of magnitude 7.8. The primary is a yellow giant that has cooled and expanded to 10.4 times the diameter of the Sun. Of spectral class G8IV, it is around 121 light-years away, while the secondary is a yellow main sequence star of spectral type G0V. The two are thought to take 120,000 years to orbit each other. Mu Boötis , known as Alkalurops , is a triple star popular with amateur astronomers. It has an overall magnitude of 4.3 and

2318-494: A sickle, which was also held in his left hand. The placement of Arcturus has also been mutable through the centuries. Traditionally, Arcturus lay between his thighs, as Ptolemy depicted him. However, Germanicus Caesar deviated from this tradition by placing Arcturus "where his garment is fastened by a knot". In his Uranometria , Johann Bayer used the Greek letters alpha through to omega and then A to k to label what he saw as

2440-525: A spectral class of K5 and an absolute magnitude of −0.3. Dimmer than Upsilon Boötis is magnitude 4.54 Phi Boötis , with a spectral class of K2 and an absolute magnitude of −0.1. Just slightly dimmer than Phi at magnitude 4.60 is O Boötis , which, like Izar, has a spectral class of K0. O Boötis has an absolute magnitude of 0.2. The other four dim stars are magnitude 4.91 6 Boötis , class K4; magnitude 4.86 20 Boötis , class K3; magnitude 4.81 Omega Boötis , class K4; and magnitude 4.83 A Boötis , class K1. There

2562-424: A telescope. NGC 5466 is classified as a Shapley–Sawyer Concentration Class 12 cluster, reflecting its sparsity. Its fairly large diameter means that it has a low surface brightness , so it appears far dimmer than the catalogued magnitude of 9.1 and requires a large amateur telescope to view. Only approximately 12 stars are resolved by an amateur instrument. Boötes has two bright galaxies. NGC 5248 ( Caldwell 45)

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2684-543: A temple at Canopus , around 146–147 AD, known as the Canobic Inscription . Although the inscription has not survived, someone in the sixth century transcribed it, and manuscript copies preserved it through the Middle Ages. It begins: "To the saviour god, Claudius Ptolemy (dedicates) the first principles and models of astronomy", following by a catalogue of numbers that define a system of celestial mechanics governing

2806-478: A thousand years or more". It was first translated from Arabic into Latin by Plato of Tivoli (Tiburtinus) in 1138, while he was in Spain. Much of the content of the Tetrabiblos was collected from earlier sources; Ptolemy's achievement was to order his material in a systematic way, showing how the subject could, in his view, be rationalized. It is, indeed, presented as the second part of the study of astronomy of which

2928-408: A type Sc emission-line galaxy , NGC 5548 , a type S Seyfert galaxy , NGC 5653 , a type S HII galaxy , NGC 5778 (also classified as NGC 5825), a type E galaxy that is the brightest of its cluster, NGC 5886 , and NGC 5888 , a type SBb galaxy. NGC 5698 is a barred spiral galaxy, notable for being the host of the 2005 supernova SN 2005bc , which peaked at magnitude 15.3. Ptolemy This

3050-467: A very complex theoretical model built in order to explain a false assumption. Ptolemy's date of birth and birthplace are both unknown. The 14th-century astronomer Theodore Meliteniotes wrote that Ptolemy's birthplace was Ptolemais Hermiou , a Greek city in the Thebaid region of Egypt (now El Mansha, Sohag Governorate ). This attestation is quite late, however, and there is no evidence to support it. It

3172-553: A view supported by the Stoics. Although mainly known for his contributions to astronomy and other scientific subjects, Ptolemy also engaged in epistemological and psychological discussions across his corpus. He wrote a short essay entitled On the Criterion and Hegemonikon ( Greek : Περὶ Κριτηρίου καὶ Ἡγεμονικοῡ ), which may have been one of his earliest works. Ptolemy deals specifically with how humans obtain scientific knowledge (i.e.,

3294-518: Is ZZ Boötis , which has two F2-type components of almost equal mass, and ranges in magnitude from a minimum of 6.79 to a maximum of 7.44 over a period of 5.0 days. Two of the brighter Mira-type variable stars in the constellation are R and S Boötis . Both are red giants that range greatly in magnitude—from 6.2 to 13.1 over 223.4 days, and 7.8 to 13.8 over a period of 270.7 days, respectively. Also red giants, V and W Boötis are semi-regular variable stars that range in magnitude from 7.0 to 12.0 over

3416-496: Is 1.76 AU from the host star. The host star, HD 128311, is a K0V-type star located 16.6 parsecs from Earth. It is smaller than the Sun, with a mass of 0.84  M ☉ and a radius of 0.73  R ☉ ; it also appears below the threshold of naked-eye visibility at an apparent magnitude of 7.51. There are several single-planet systems in Boötes. HD 132406 is a Sun-like star of spectral type G0V with an apparent magnitude of 8.45, 231.5 light-years from Earth. It has

3538-467: Is 121 light-years away. Its name is from the Arabic phrase for "club" or "staff". The primary appears to be of magnitude 4.3 and is blue-white. The secondary appears to be of magnitude 6.5, but is actually a close double star itself with a primary of magnitude 7.0 and a secondary of magnitude 7.6. The secondary and tertiary stars have an orbital period of 260 years. The primary has an absolute magnitude of 2.6 and

3660-447: Is Beta Boötis, or Nekkar, a yellow giant of magnitude 3.5 and spectral type G8IIIa. Like Arcturus, it has expanded and cooled off the main sequence —likely to have lived most of its stellar life as a blue-white B-type main sequence star . Its common name comes from the Arabic phrase for "ox-driver". It is 219 light-years away and has a luminosity of 58  L ☉ . Located 86 light-years distant, Gamma Boötis , or Seginus,

3782-472: Is a type Sc galaxy (a variety of spiral galaxy ) of magnitude 10.2. It measures 6.5 by 4.9 arcminutes. Fifty million light-years from Earth, NGC 5248 is a member of the Virgo Cluster of galaxies; it has dim outer arms and obvious H II regions , dust lanes and young star clusters . NGC 5676 is another type Sc galaxy of magnitude 10.9. It measures 3.9 by 2.0 arcminutes. Other galaxies include NGC 5008 ,

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3904-412: Is a close triple star popular with amateur astronomers and the most prominent binary star in Boötes. The primary is a yellow- or orange-hued magnitude 2.5 giant star, the secondary is a magnitude 4.6 blue-hued main-sequence star , and the tertiary is a magnitude 12.0 star. The system is 210 light-years away. The name "Izar" comes from the Arabic word for "girdle" or "loincloth", referring to its location in

4026-471: Is a member of the cluster NGC 5466 . Anomalous Cepheids are metal poor and have masses not much larger than the Sun's, on average, 1.5  M ☉ . BL Boötis type stars are a subtype of RR Lyrae variables. T Boötis was a nova observed in April 1860 at a magnitude of 9.7. It has never been observed since, but that does not preclude the possibility of it being a highly irregular variable star or

4148-428: Is a white giant star of spectral class A7III, with a luminosity 34 times and diameter 3.5 times that of the Sun. It is a Delta Scuti variable , ranging between magnitudes 3.02 and 3.07 every 7 hours. These stars are short period (six hours at most) pulsating stars that have been used as standard candles and as subjects to study asteroseismology . Delta Boötis is a wide double star with a primary of magnitude 3.5 and

4270-399: Is also the brightest star north of the celestial equator , just shading out Vega and Capella . Its name comes from the Greek for "bear-keeper". An orange giant of spectral class K1.5III, Arcturus is an ageing star that has exhausted its core supply of hydrogen and cooled and expanded to a diameter of 27 solar diameters , equivalent to approximately 32 million kilometers. Though its mass

4392-474: Is an accepted version of this page Claudius Ptolemy ( / ˈ t ɒ l ə m i / ; Ancient Greek : Πτολεμαῖος , Ptolemaios ; Latin : Claudius Ptolemaeus ; c.  100  – c.  170 AD) was an Alexandrian mathematician , astronomer , astrologer , geographer , and music theorist who wrote about a dozen scientific treatises , three of which were important to later Byzantine , Islamic , and Western European science. The first

4514-572: Is ancestral to the modern system of constellations but, unlike the modern system, they did not cover the whole sky (only what could be seen with the naked eye in the northern hemisphere). For over a thousand years, the Almagest was the authoritative text on astronomy across Europe, the Middle East, and North Africa. The Almagest was preserved, like many extant Greek scientific works, in Arabic manuscripts;

4636-480: Is approximately one solar mass ( M ☉ ), Arcturus shines with 133 times the luminosity of the Sun ( L ☉ ). Bayer located Arcturus above the Herdman's left knee in his Uranometria . Nearby Eta Boötis , or Muphrid, is the uppermost star denoting the left leg. It is a 2.68-magnitude star 37 light-years distant with a spectral class of G0IV, indicating it has just exhausted its core hydrogen and

4758-415: Is beginning to expand and cool. It is 9 times as luminous as the Sun and has 2.7 times its diameter. Analysis of its spectrum reveals that it is a spectroscopic binary . Muphrid and Arcturus lie only 3.3 light-years away from each other. Viewed from Arcturus, Muphrid would have a visual magnitude of −2½, while Arcturus would be around visual magnitude −4½ when seen from Muphrid. Marking the herdsman's head

4880-624: Is his Geographike Hyphegesis ( Greek : Γεωγραφικὴ Ὑφήγησις ; lit.   ' Guide to Drawing the Earth ' ), known as the Geography , a handbook on how to draw maps using geographical coordinates for parts of the Roman world known at the time. He relied on previous work by an earlier geographer, Marinus of Tyre , as well as on gazetteers of the Roman and ancient Persian Empire . He also acknowledged ancient astronomer Hipparchus for having provided

5002-431: Is in a part of the celestial sphere facing away from the plane of our home Milky Way galaxy , and so does not have open clusters or nebulae. Instead, it has one bright globular cluster and many faint galaxies. The globular cluster NGC 5466 has an overall magnitude of 9.1 and a diameter of 11 arcminutes . It is a very loose globular cluster with fairly few stars and may appear as a rich, concentrated open cluster in

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5124-658: Is known but who likely shared some of Ptolemy's astronomical interests. Ptolemy died in Alexandria c.  168 . Ptolemy's Greek name , Ptolemaeus ( Πτολεμαῖος , Ptolemaîos ), is an ancient Greek personal name . It occurs once in Greek mythology and is of Homeric form . It was common among the Macedonian upper class at the time of Alexander the Great and there were several of this name among Alexander's army, one of whom made himself pharaoh in 323 BC: Ptolemy I Soter ,

5246-458: Is known that Ptolemy lived in or around the city of Alexandria , in the Roman province of Egypt under Roman rule . He had a Latin name, Claudius, which is generally taken to imply he was a Roman citizen . He was familiar with Greek philosophers and used Babylonian observations and Babylonian lunar theory. In half of his extant works, Ptolemy addresses a certain Syrus, a figure of whom almost nothing

5368-507: Is more common. Arcturus was given such importance in Chinese celestial mythology because of its status marking the beginning of the lunar calendar , as well as its status as the brightest star in the northern night sky. Two constellations flanked Daijiao : Yousheti to the right and Zuosheti to the left; they represented companions that orchestrated the seasons. Zuosheti was formed from modern Zeta , Omicron and Pi Boötis , while Yousheti

5490-960: Is not known." Not much positive evidence is known on the subject of Ptolemy's ancestry, apart from what can be drawn from the details of his name, although modern scholars have concluded that Abu Ma'shar's account is erroneous. It is no longer doubted that the astronomer who wrote the Almagest also wrote the Tetrabiblos as its astrological counterpart. In later Arabic sources, he was often known as "the Upper Egyptian ", suggesting he may have had origins in southern Egypt . Arabic astronomers , geographers , and physicists referred to his name in Arabic as Baṭlumyus ( Arabic : بَطْلُمْيوس ). Ptolemy wrote in Koine Greek , and can be shown to have used Babylonian astronomical data . He might have been

5612-546: Is now so included in the List of IAU-approved Star Names. This star had its angular diameter measured using interferometric observations by the Navy Precision Optical Interferometer . The angular diameter, together with the star's distance, yield a radius 18 times the radius of the Sun . Beta Boötis is 3.2 times more massive than the Sun. At the estimated age of 320 million years , it has evolved into

5734-450: Is of spectral class F0. The secondary and tertiary stars are separated by 2 arcseconds; the primary and secondary are separated by 109.1 arcseconds at an angle of 171 degrees. Nu Boötis is an optical double star. The primary is an orange giant of magnitude 5.0 and the secondary is a white star of magnitude 5.0. The primary is 870 light-years away and the secondary is 430 light-years. Epsilon Boötis , also known as Izar or Pulcherrima ,

5856-400: Is of type K0 and is located 110 parsecs from Earth; it appears at a visual magnitude of 7.96. It is significantly larger than the Sun, with a mass of 1.61  M ☉ and a radius of 4.6 solar radii. Its one planet, discovered in 2011 by the radial velocity method , has a mass of 2.2   M J ; its radius is as yet undetermined. HD 131496 b orbits at a distance of 2.09 AU with

5978-486: Is one bright B-class star in Boötes; magnitude 4.93 Pi Boötis , also called Alazal. It has a spectral class of B9 and is 40 parsecs from Earth. There is also one M-type star, magnitude 4.81 34 Boötis . It is of class gM0. Besides Pulcherrima and Alkalurops, there are several other binary stars in Boötes: 44 Boötis (i Boötis) is a double variable star 42 light-years away. It has an overall magnitude of 4.8 and appears yellow to

6100-659: Is sometimes known as the Apotelesmatika ( Greek : Αποτελεσματικά , lit.   ' On the Effects ' ) but more commonly known as the Tetrábiblos , from the Koine Greek meaning "Four Books", or by its Latin equivalent Quadripartite . The Catholic Church promoted his work, which included the only mathematically sound geocentric model of the Solar System , and unlike most Greek mathematicians , Ptolemy's writings (foremost

6222-407: Is the smaller planet, with a mass of 2.18   M J ; it was discovered through radial velocity observations. It orbits at almost the same distance as Earth, at 1.099 AU; however, its orbital period is significantly longer at 448.6 days. The larger of the two, HD 128311 c, has a mass of 3.21   M J and was discovered in the same manner. It orbits every 919 days inclined at 50°, and

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6344-525: Is the star's Bayer designation . It bore the traditional name Nekkar or Nakkar derived from the Arabic name for the constellation: Al Baḳḳār 'the Herdsman'. In 2016, the International Astronomical Union organized a Working Group on Star Names (WGSN) to catalogue and standardize proper names for stars. The WGSN approved the name Nekkar for this star on 21 August 2016 and it

6466-518: The Almagest ) never ceased to be copied or commented upon, both in late antiquity and in the Middle Ages . However, it is likely that only a few truly mastered the mathematics necessary to understand his works, as evidenced particularly by the many abridged and watered-down introductions to Ptolemy's astronomy that were popular among the Arabs and Byzantines. His work on epicycles has come to symbolize

6588-413: The Almagest , is the only surviving comprehensive ancient treatise on astronomy. Although Babylonian astronomers had developed arithmetical techniques for calculating and predicting astronomical phenomena, these were not based on any underlying model of the heavens; early Greek astronomers, on the other hand, provided qualitative geometrical models to "save the appearances" of celestial phenomena without

6710-662: The Almagest was the first, concerned with the influences of the celestial bodies in the sublunary sphere . Thus explanations of a sort are provided for the astrological effects of the planets , based upon their combined effects of heating, cooling, moistening, and drying. Ptolemy dismisses other astrological practices, such as considering the numerological significance of names, that he believed to be without sound basis, and leaves out popular topics, such as electional astrology (interpreting astrological charts to determine courses of action) and medical astrology , for similar reasons. The great respect in which later astrologers held

6832-410: The Geography is likely to be of different dates, in addition to containing many scribal errors. However, although the regional and world maps in surviving manuscripts date from c.  1300 AD (after the text was rediscovered by Maximus Planudes ), there are some scholars who think that such maps go back to Ptolemy himself. Ptolemy wrote an astrological treatise, in four parts, known by

6954-784: The Optics, is a work that survives only in a somewhat poor Latin version, which, in turn, was translated from a lost Arabic version by Eugenius of Palermo ( c.  1154 ). In it, Ptolemy writes about properties of sight (not light), including reflection , refraction , and colour . The work is a significant part of the early history of optics and influenced the more famous and superior 11th-century Book of Optics by Ibn al-Haytham . Ptolemy offered explanations for many phenomena concerning illumination and colour, size, shape, movement, and binocular vision. He also divided illusions into those caused by physical or optical factors and those caused by judgmental factors. He offered an obscure explanation of

7076-457: The Tetrabiblos derived from its nature as an exposition of theory, rather than as a manual. A collection of one hundred aphorisms about astrology called the Centiloquium , ascribed to Ptolemy, was widely reproduced and commented on by Arabic, Latin, and Hebrew scholars, and often bound together in medieval manuscripts after the Tetrabiblos as a kind of summation. It is now believed to be

7198-461: The equator , as it is today, but Ptolemy preferred to express it as climata , the length of the longest day rather than degrees of arc : The length of the midsummer day increases from 12h to 24h as one goes from the equator to the polar circle . One of the places Ptolemy noted specific coordinates for was the now-lost stone tower which marked the midpoint on the ancient Silk Road , and which scholars have been trying to locate ever since. In

7320-519: The harmonic canon (Greek name) or monochord (Latin name), which is an experimental musical apparatus that he used to measure relative pitches, and used to describe to his readers how to demonstrate the relations discussed in the following chapters for themselves. After the early exposition on to build and use monochord to test proposed tuning systems, Ptolemy proceeds to discuss Pythagorean tuning (and how to demonstrate that their idealized musical scale fails in practice). The Pythagoreans believed that

7442-425: The right ascension coordinates of these borders lie between 13 36.1 and 15 49.3 , while the declination coordinates stretch from +7.36° to +55.1°. Covering 907 square degrees, Boötes culminates at midnight around 2 May and ranks 13th in area. Colloquially, its pattern of stars has been likened to a kite or ice cream cone. However, depictions of Boötes have varied historically. Aratus described him circling

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7564-543: The sword or the spear, was represented by Gamma Boötis . Two Chinese constellations have an uncertain placement in Boötes. Kangchi , the lake, was placed south of Arcturus, though its specific location is disputed. It may have been placed entirely in Boötes, on either side of the Boötes-Virgo border, or on either side of the Virgo-Libra border. The constellation Zhouding , a bronze tripod -mounted container used for food,

7686-423: The transit method in 2010, orbits every 2.944 days very close to its Sun, at 0.0376 AU. It is smaller than Jupiter, at 0.884   M J and 0.962   R J . Its star is a K1V-type star of apparent magnitude 12.7, far below naked-eye visibility, and smaller than the Sun at 0.78  M ☉ and 0.765  R ☉ . HD 131496 is also encircled by one planet, HD 131496 b . The star

7808-471: The " foreleg of ox " by Berio. Homer mentions Boötes in the Odyssey as a celestial reference for navigation , describing it as "late-setting" or "slow to set". Exactly whom Boötes is supposed to represent in Greek mythology is not clear. According to one version, he was a son of Demeter , Philomenus , twin brother of Plutus , a plowman who drove the oxen in the constellation Ursa Major . This agrees with

7930-430: The "criterion" of truth), as well as with the nature and structure of the human psyche or soul, particularly its ruling faculty (i.e., the hegemonikon ). Ptolemy argues that, to arrive at the truth, one should use both reason and sense perception in ways that complement each other. On the Criterion is also noteworthy for being the only one of Ptolemy's works that is devoid of mathematics . Elsewhere, Ptolemy affirms

8052-485: The French astronomer Delambre in the early 1800s which were repeated by R.R. Newton. Specifically, it proved Hipparchus was not the sole source of Ptolemy's catalog, as they both had claimed, and proved that Ptolemy did not simply copy Hipparchus' measurements and adjust them to account for precession of the equinoxes, as they had claimed. Scientists analyzing the charts concluded: It also confirms that Ptolemy’s Star Catalogue

8174-425: The Greek term Tetrabiblos (lit. "Four Books") or by its Latin equivalent Quadripartitum . Its original title is unknown, but may have been a term found in some Greek manuscripts, Apotelesmatiká ( biblía ), roughly meaning "(books) on the Effects" or "Outcomes", or "Prognostics". As a source of reference, the Tetrabiblos is said to have "enjoyed almost the authority of a Bible among the astrological writers of

8296-653: The Hyenas", Theta , Iota , Kappa and Lambda Boötis (or Xuange) are a small group of stars in the far north of the constellation. The magnitude 4.05 Theta Boötis has a spectral type of F7 and an absolute magnitude of 3.8. Iota Boötis is a triple star with a primary of magnitude 4.8 and spectral class of A7, a secondary of magnitude 7.5, and a tertiary of magnitude 12.6. The primary is 97 light-years away. The primary and secondary stars are separated by 38.5 arcseconds, at an angle of 33 degrees. The primary and tertiary stars are separated by 86.7 arcseconds at an angle of 194 degrees. Both

8418-543: The Lambda Boötis stars are a much rarer class whose members can be found both inside and outside the Delta Scuti instability strip. Lambda Boötis stars are dwarf stars that can be either spectral class A or F. Like BL Boötis-type stars they are metal-poor. Scientists have had difficulty explaining the characteristics of Lambda Boötis stars, partly because only around 60 confirmed members exist, but also due to heterogeneity in

8540-461: The Quadrant, was a constellation created near Beta Boötis from faint stars. It was designated in 1795 by Jérôme Lalande , an astronomer who used a quadrant to perform detailed astronometric measurements . Lalande worked with Nicole-Reine Lepaute and others to predict the 1758 return of Halley's Comet . Quadrans Muralis was formed from the stars of eastern Boötes, western Hercules and Draco . It

8662-455: The Sun or Moon illusion (the enlarged apparent size on the horizon) based on the difficulty of looking upwards. The work is divided into three major sections. The first section (Book II) deals with direct vision from first principles and ends with a discussion of binocular vision. The second section (Books III-IV) treats reflection in plane, convex, concave, and compound mirrors. The last section (Book V) deals with refraction and includes

8784-461: The Wise, who composed the book of the Almagest ". Abu Ma'shar recorded a belief that a different member of this royal line "composed the book on astrology and attributed it to Ptolemy". Historical confusion on this point can be inferred from Abu Ma'shar's subsequent remark: "It is sometimes said that the very learned man who wrote the book of astrology also wrote the book of the Almagest . The correct answer

8906-422: The ability to make any predictions. The earliest person who attempted to merge these two approaches was Hipparchus , who produced geometric models that not only reflected the arrangement of the planets and stars but could be used to calculate celestial motions. Ptolemy, following Hipparchus, derived each of his geometrical models for the Sun, Moon, and the planets from selected astronomical observations done in

9028-423: The appearances and disappearances of stars over the course of the solar year. The Planisphaerium ( Greek : Ἅπλωσις ἐπιφανείας σφαίρας , lit.   ' Flattening of the sphere ' ) contains 16 propositions dealing with the projection of the celestial circles onto a plane. The text is lost in Greek (except for a fragment) and survives in Arabic and Latin only. Ptolemy also erected an inscription in

9150-449: The brighter members of the constellation. In the modern constellation, it marks the head of Boötis the herdsman. Based upon parallax measurements obtained by the Gaia spacecraft, this star is approximately 235 light-years (72 parsecs ) from the Sun. The magnitude of the star is reduced by 0.06 from extinction caused by intervening gas and dust. β Boötis ( Latinised to Beta Boötis )

9272-636: The constellation's name. The ancient Greeks saw the asterism now called the " Big Dipper " or "Plough" as a cart with oxen. Some myths say that Boötes invented the plow and was memorialized for his ingenuity as a constellation. Another myth associated with Boötes by Hyginus is that of Icarius , who was schooled as a grape farmer and winemaker by Dionysus . Icarius made wine so strong that those who drank it appeared poisoned , which caused shepherds to avenge their supposedly poisoned friends by killing Icarius. Maera , Icarius' dog, brought his daughter Erigone to her father's body, whereupon both she and

9394-466: The constellation. The name "Pulcherrima" comes from the Latin phrase for "most beautiful", referring to its contrasting colors in a telescope. The primary and secondary stars are separated by 2.9 arcseconds at an angle of 341 degrees; the primary's spectral class is K0 and it has a luminosity of 200  L ☉ . To the naked eye, Izar has a magnitude of 2.37. Nearby Rho and Sigma Boötis denote

9516-458: The data needed to compute the positions of the Sun, Moon and planets, the rising and setting of the stars, and eclipses of the Sun and Moon, making it a useful tool for astronomers and astrologers. The tables themselves are known through Theon of Alexandria 's version. Although Ptolemy's Handy Tables do not survive as such in Arabic or in Latin, they represent the prototype of most Arabic and Latin astronomical tables or zījes . Additionally,

9638-432: The dog died by suicide . Zeus then chose to honor all three by placing them in the sky as constellations: Icarius as Boötes, Erigone as Virgo , and Maera as Canis Major or Canis Minor . Following another reading, the constellation is identified with Arcas and also referred to as Arcas and Arcturus, son of Zeus and Callisto . Arcas was brought up by his maternal grandfather Lycaon , to whom one day Zeus went and had

9760-402: The earliest surviving table of refraction from air to water, for which the values (with the exception of the 60° angle of incidence) show signs of being obtained from an arithmetic progression. However, according to Mark Smith, Ptolemy's table was based in part on real experiments. Ptolemy's theory of vision consisted of rays (or flux) coming from the eye forming a cone, the vertex being within

9882-469: The elevation of the north celestial pole for a few cities. Although maps based on scientific principles had been made since the time of Eratosthenes ( c.  276  – c.  195 BC ), Ptolemy improved on map projections . The first part of the Geography is a discussion of the data and of the methods he used. Ptolemy notes the supremacy of astronomical data over land measurements or travelers' reports, though he possessed these data for only

10004-425: The empirical musical relations he identified by testing pitches against each other: He was able to accurately measure relative pitches based on the ratios of vibrating lengths two separate sides of the same single string , hence which were assured to be under equal tension, eliminating one source of error. He analyzed the empirically determined ratios of "pleasant" pairs of pitches, and then synthesised all of them into

10126-419: The eye, and the base defining the visual field. The rays were sensitive, and conveyed information back to the observer's intellect about the distance and orientation of surfaces. Size and shape were determined by the visual angle subtended at the eye combined with perceived distance and orientation. This was one of the early statements of size-distance invariance as a cause of perceptual size and shape constancy,

10248-491: The fifth magnitude, making a total of 29 stars easily visible to the naked eye . In ancient Babylon , the stars of Boötes were known as SHU.PA. They were apparently depicted as the god Enlil , who was the leader of the Babylonian pantheon and special patron of farmers. Boötes may have been represented by the animal foreleg constellation in ancient Egypt, resembling that of an ox sufficiently to have been originally proposed as

10370-567: The first pharaoh of the Ptolemaic Kingdom . Almost all subsequent pharaohs of Egypt, with a few exceptions, were named Ptolemy until Egypt became a Roman province in 30 BC, ending the Macedonian family's rule. The name Claudius is a Roman name, belonging to the gens Claudia ; the peculiar multipart form of the whole name Claudius Ptolemaeus is a Roman custom, characteristic of Roman citizens. This indicates that Ptolemy would have been

10492-570: The form of a bear was almost killed by her son, who was out hunting. Zeus rescued her, taking her into the sky where she became Ursa Major, "the Great Bear". Arcturus, the name of the constellation's brightest star, comes from the Greek word meaning "guardian of the bear". Sometimes Arcturus is depicted as leading the hunting dogs of nearby Canes Venatici and driving the bears of Ursa Major and Ursa Minor . Several former constellations were formed from stars now included in Boötes. Quadrans Muralis ,

10614-506: The herdsman's waist. Rho is an orange giant of spectral type K3III located around 160 light-years from Earth. It is ever so slightly variable, wavering by 0.003 of a magnitude from its average of 3.57. Sigma, a yellow-white main-sequence star of spectral type F3V, is suspected of varying in brightness from 4.45 to 4.49. It is around 52 light-years distant. Traditionally known as Aulād al Dhiʼbah ( أولاد الضباع – aulād al dhiʼb ), "the Whelps of

10736-483: The highest honour. Despite being a minority position among ancient philosophers, Ptolemy's views were shared by other mathematicians such as Hero of Alexandria . There are several characters and items named after Ptolemy, including: Beta Bo%C3%B6tis Beta Boötis , Latinized from β Boötis , and also named Nekkar / ˈ n ɛ k ɑːr / , is a star in the northern constellation of Boötes . It has an apparent visual magnitude of 3.5, making it one of

10858-553: The history of science". One striking error noted by Newton was an autumn equinox said to have been observed by Ptolemy and "measured with the greatest care" at 2pm on 25 September 132, when the equinox should have been observed around 9:55am the day prior. In attempting to disprove Newton, Herbert Lewis also found himself agreeing that "Ptolemy was an outrageous fraud," and that "all those result capable of statistical analysis point beyond question towards fraud and against accidental error". The charges laid by Newton and others have been

10980-433: The host star's light may be caused by magnetic interactions with the planet. Carbon monoxide is present in the planet's atmosphere. Tau Boötis b does not transit its star, rather, its orbit is inclined 46 degrees. Like Tau Boötis b, HAT-P-4b is also a hot Jupiter. It is noted for orbiting a particularly metal-rich host star and being of low density. Discovered in 2007, HAT-P-4 b has a mass of 0.68   M J and

11102-599: The introduction to the Handy Tables survived separately from the tables themselves (apparently part of a gathering of some of Ptolemy's shorter writings) under the title Arrangement and Calculation of the Handy Tables . The Planetary Hypotheses ( Greek : Ὑποθέσεις τῶν πλανωμένων , lit.   ' Hypotheses of the Planets ' ) is a cosmological work, probably one of the last written by Ptolemy, in two books dealing with

11224-417: The literature. Lambda has an absolute magnitude of 1.8. There are two dimmer F-type stars , magnitude 4.83 12 Boötis , class F8; and magnitude 4.93 45 Boötis , class F5. Xi Boötis is a G8 yellow dwarf of magnitude 4.55, and absolute magnitude is 5.5. Two dimmer G-type stars are magnitude 4.86 31 Boötis , class G8, and magnitude 4.76 44 Boötis , class G0. Of apparent magnitude 4.06, Upsilon Boötis has

11346-500: The mathematics of music should be based on only the one specific ratio of 3:2, the perfect fifth , and believed that tunings mathematically exact to their system would prove to be melodious, if only the extremely large numbers involved could be calculated (by hand). To the contrary, Ptolemy believed that musical scales and tunings should in general involve multiple different ratios arranged to fit together evenly into smaller tetrachords (combinations of four pitch ratios which together make

11468-555: The modern title is thought to be an Arabic corruption of the Greek name Hē Megistē Syntaxis (lit. "The greatest treatise"), as the work was presumably known in Late Antiquity . Because of its reputation, it was widely sought and translated twice into Latin in the 12th century , once in Sicily and again in Spain. Ptolemy's planetary models, like those of the majority of his predecessors, were geocentric and almost universally accepted until

11590-408: The most prominent 35 stars in the constellation, with subsequent astronomers splitting Kappa, Mu, Nu and Pi as two stars each. Nu is also the same star as Psi Herculis. John Flamsteed numbered 54 stars for the constellation. Located 36.7 light-years from Earth, Arcturus, or Alpha Boötis, is the brightest star in Boötes and the fourth-brightest star in the sky at an apparent magnitude of −0.05; It

11712-477: The motions of the Sun, Moon, planets, and stars. In 2023, archaeologists were able to read a manuscript which gives instructions for the construction of an astronomical tool called a meteoroscope ( μετεωροσκόπιον or μετεωροσκοπεῖον ). The text, which comes from an eighth-century manuscript which also contains Ptolemy's Analemma , was identified on the basis of both its content and linguistic analysis as being by Ptolemy. Ptolemy's second most well-known work

11834-414: The naked eye. The primary is of magnitude 5.3 and the secondary is of magnitude 6.1; their orbital period is 220 years. The secondary is itself an eclipsing variable star with a range of 0.6 magnitudes; its orbital period is 6.4 hours. It is a W Ursae Majoris variable that ranges in magnitude from a minimum of 7.1 to a maximum of 6.5 every 0.27 days. Both stars are G-type stars. Another eclipsing binary star

11956-466: The north pole, herding the two bears. Later ancient Greek depictions, described by Ptolemy, have him holding the reins of his hunting dogs (Canes Venatici) in his left hand, with a spear, club, or staff in his right hand. After Hevelius introduced Mons Maenalus in 1681, Boötes was often depicted standing on the Peloponnese mountain. By 1801, when Johann Bode published his Uranographia , Boötes had acquired

12078-461: The observations were taken at 12:30pm. The overall quality of Ptolemy's observations has been challenged by several modern scientists, but prominently by Robert R. Newton in his 1977 book The Crime of Claudius Ptolemy , which asserted that Ptolemy fabricated many of his observations to fit his theories. Newton accused Ptolemy of systematically inventing data or doctoring the data of earlier astronomers, and labelled him "the most successful fraud in

12200-402: The primary and tertiary appear white in a telescope, but the secondary appears yellow-hued. Kappa Boötis is another wide double star. The primary is 155 light-years away and has a magnitude of 4.5. The secondary is 196 light-years away and has a magnitude of 6.6. The two components are separated by 13.4 arcseconds, at an angle of 236 degrees. The primary, with spectral class A7, appears white and

12322-401: The radius of the sphere of the fixed stars was 20 000 times the radius of the Earth. The work is also notable for having descriptions on how to build instruments to depict the planets and their movements from a geocentric perspective, much as an orrery would have done for a heliocentric one, presumably for didactic purposes. The Analemma is a short treatise where Ptolemy provides

12444-486: The reappearance of heliocentric models during the scientific revolution . Under the scrutiny of modern scholarship, and the cross-checking of observations contained in the Almagest against figures produced through backwards extrapolation, various patterns of errors have emerged within the work. A prominent miscalculation is Ptolemy's use of measurements that he claimed were taken at noon, but which systematically produce readings now shown to be off by half an hour, as if

12566-538: The secondary appears bluish. An apparent magnitude 4.18 type A0p star , Lambda Boötis is the prototype of a class of chemically peculiar stars, only some of which pulsate as Delta Scuti -type stars. The distinction between the Lambda Boötis stars as a class of stars with peculiar spectra, and the Delta Scuti stars whose class describes pulsation in low-overtone pressure modes, is an important one. While many Lambda Boötis stars pulsate and are Delta Scuti stars, not many Delta Scuti stars have Lambda Boötis peculiarities, since

12688-405: The secondary literature, while noting that issues with the accuracy of Ptolemy's observations had long been known. Other authors have pointed out that instrument warping or atmospheric refraction may also explain some of Ptolemy's observations at a wrong time. In 2022 the first Greek fragments of Hipparchus' lost star catalog were discovered in a palimpsest and they debunked accusations made by

12810-404: The sole planet discovered in the system, orbits at a distance of 0.046 AU every 3.31 days. Discovered through radial velocity measurements, it has a mass of 5.95 Jupiter masses ( M J ). This makes it a hot Jupiter . The host star and planet are tidally locked , meaning that the planet's orbit and the star's particularly high rotation are synchronized. Furthermore, a slight variability in

12932-474: The spanning of more than 800 years; however, many astronomers have for centuries suspected that some of his models' parameters were adopted independently of observations. Ptolemy presented his astronomical models alongside convenient tables, which could be used to compute the future or past position of the planets. The Almagest also contains a star catalogue , which is a version of a catalogue created by Hipparchus . Its list of forty-eight constellations

13054-451: The spheres ). Although Ptolemy's Harmonics never had the influence of his Almagest or Geography , it is nonetheless a well-structured treatise and contains more methodological reflections than any other of his writings. In particular, it is a nascent form of what in the following millennium developed into the scientific method, with specific descriptions of the experimental apparatus that he built and used to test musical conjectures, and

13176-400: The star HD 136418 at a distance of 1.32 AU with a period of 464.3 days. Its host star is a magnitude 7.88 G5-type star, 98.2 parsecs from Earth. It has a radius of 3.4  R ☉ and a mass of 1.33  M ☉ . WASP-14 b is one of the most massive and dense exoplanets known, with a mass of 7.341   M J and a radius of 1.281   R J . Discovered via

13298-433: The stars of Boötes existed in the modern constellation's north; they are all representations of weapons. Tianqiang , the spear , was formed from Iota , Kappa and Theta Boötis ; Genghe , variously representing a lance or shield , was formed from Epsilon , Rho and Sigma Boötis . There were also two weapons made up of a singular star. Xuange , the halberd , was represented by Lambda Boötis , and Zhaoyao , either

13420-440: The structure of the universe and the laws that govern celestial motion . Ptolemy goes beyond the mathematical models of the Almagest to present a physical realization of the universe as a set of nested spheres, in which he used the epicycles of his planetary model to compute the dimensions of the universe. He estimated the Sun was at an average distance of 1 210 Earth radii (now known to actually be ~23 450 radii), while

13542-517: The subject of wide discussions and received significant push back from other scholars against the findings. Owen Gingerich , while agreeing that the Almagest contains "some remarkably fishy numbers", including in the matter of the 30-hour displaced equinox, which he noted aligned perfectly with predictions made by Hipparchus 278 years earlier, rejected the qualification of fraud. Objections were also raised by Bernard Goldstein , who questioned Newton's findings and suggested that he had misunderstood

13664-496: The supremacy of mathematical knowledge over other forms of knowledge. Like Aristotle before him, Ptolemy classifies mathematics as a type of theoretical philosophy; however, Ptolemy believes mathematics to be superior to theology or metaphysics because the latter are conjectural while only the former can secure certain knowledge. This view is contrary to the Platonic and Aristotelian traditions, where theology or metaphysics occupied

13786-573: The third part of the Geography , Ptolemy gives instructions on how to create maps both of the whole inhabited world ( oikoumenē ) and of the Roman provinces, including the necessary topographic lists, and captions for the maps. His oikoumenē spanned 180 degrees of longitude from the Blessed Islands in the Atlantic Ocean to the middle of China , and about 80 degrees of latitude from Shetland to anti-Meroe (east coast of Africa ); Ptolemy

13908-430: The transit method, it orbits 0.036 AU from its host star with a period of 2.24 days. WASP-14 b has a density of 4.6 grams per cubic centimeter, making it one of the densest exoplanets known. Its host star, WASP-14 , is an F5V-type star of magnitude 9.75, 160 parsecs from Earth. It has a radius of 1.306  R ☉ and a mass of 1.211  M ☉ . It also has a very high proportion of lithium . Boötes

14030-427: The west, Ursa Major to the northwest, Draco to the northeast, and Hercules, Corona Borealis and Serpens Caput to the east. The three-letter abbreviation for the constellation, as adopted by the International Astronomical Union in 1922, is "Boo". The official constellation boundaries, as set by Belgian astronomer Eugène Delporte in 1930, are defined by a polygon of 16 segments. In the equatorial coordinate system ,

14152-567: Was formed from modern Eta , Tau and Upsilon Boötis . Dixi , the Emperor's ceremonial banquet mat, was north of Arcturus, consisting of the stars 12 , 11 and 9 Boötis . Another northern constellation was Qigong , the Seven Dukes , which mostly straddled the Boötes-Hercules border. It included either Delta Boötis or Beta Boötis as its terminus. The other Chinese constellations made up of

14274-556: Was his astronomical treatise now known as the Almagest , originally entitled Mathematical Treatise ( Greek : Μαθηματικὴ Σύνταξις , Mathēmatikḗ Syntaxis ). The second is the Geography , which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world . The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This

14396-456: Was named for the son of Lycaon, Maenalus . The mountain, one of Diana 's hunting grounds, was also holy to Pan . The stars of Boötes were incorporated into many different Chinese constellations . Arcturus was part of the most prominent of these, variously designated as the celestial king's throne ( Tian Wang ) or the Blue Dragon 's horn ( Daijiao ); the name Daijiao , meaning "great horn",

14518-464: Was not based solely on data from Hipparchus’ Catalogue. ... These observations are consistent with the view that Ptolemy composed his star catalogue by combining various sources, including Hipparchus’ catalogue, his own observations and, possibly, those of other authors. The Handy Tables ( Greek : Πρόχειροι κανόνες ) are a set of astronomical tables, together with canons for their use. To facilitate astronomical calculations, Ptolemy tabulated all

14640-463: Was originally called Le Mural by Jean Fortin in his 1795 Atlas Céleste ; it was not given the name Quadrans Muralis until Johann Bode 's 1801 Uranographia . The constellation was quite faint, with its brightest stars reaching the 5th magnitude. Mons Maenalus , representing the Maenalus mountains, was created by Johannes Hevelius in 1687 at the foot of the constellation's figure. The mountain

14762-475: Was sometimes cited as the stars 1 , 2 and 6 Boötis . However, it has also been associated with three stars in Coma Berenices . Boötes is also known to Native American cultures . In Yup'ik language , Boötes is Taluyaq , literally " fish trap ," and the funnel-shaped part of the fish trap is known as Ilulirat. Boötes is a constellation bordered by Virgo to the south, Coma Berenices and Canes Venatici to

14884-499: Was well aware that he knew about only a quarter of the globe, and an erroneous extension of China southward suggests his sources did not reach all the way to the Pacific Ocean. It seems likely that the topographical tables in the second part of the work (Books 2–7) are cumulative texts, which were altered as new knowledge became available in the centuries after Ptolemy. This means that information contained in different parts of

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