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Encyclopedia > Hipparchus (astronomer)
Hipparchus.
Hipparchus.

Hipparchus (Greek Ἳππαρχος; c. 190 BCc. 120 BC) was a Greek, astronomer, geographer, and mathematician of the Hellenistic period. Image File history File links Hipparchos_1. ... Image File history File links Hipparchos_1. ... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 240s BC 230s BC 220s BC 210s BC 200s BC - 190s BC - 180s BC 170s BC 160s BC 150s BC 140s BC Years: 195 BC 194 BC 193 BC 192 BC 191 BC - 190 BC - 189 BC 188 BC... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 170s BC 160s BC 150s BC 140s BC 130s BC - 120s BC - 110s BC 100s BC 90s BC 80s BC 70s BC Years: 125 BC 124 BC 123 BC 122 BC 121 BC - 120 BC - 119 BC 118 BC... An astronomer or astrophysicist is a person whose area of interest is astronomy or astrophysics. ... A geographer is a crazy psycho whose area of study is geocrap, the pseudoscientific study of Earths physical environment and human habitat and the study of boring students to death. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The term Hellenistic (established by the German historian Johann Gustav Droysen) in the history of the ancient world is used to refer to the shift from a culture dominated by ethnic Greeks, however scattered geographically, to a culture dominated by Greek-speakers of whatever ethnicity, and from the political dominance...


Hipparchus was born in Nicaea (now Iznik, Turkey), and probably died on the island of Rhodes. He is known to have been a working astronomer at least from 147 BC to 127 BC. Hipparchus is considered the greatest astronomical observer and, by some, the greatest overall astronomer of antiquity. He was the first Greek to develop quantitative and accurate models for the motion of the Sun and Moon. For this he made use of the observations and knowledge accumulated over centuries by the Chaldeans from Babylonia. He was also the first to compile a trigonometric table, which allowed him to solve any triangle. With his solar and lunar theories and his numerical trigonometry, he was probably the first to develop a reliable method to predict solar eclipses. His other achievements include the discovery of precession, the compilation of the first star catalogue of the western world, and, probably, the invention of the astrolabe. It would be three centuries before Claudius Ptolemaeus' synthesis of astronomy would supersede the work of Hipparcus; it is heavily dependent on it. Iznik (which derives from the former Greek name, Nicaea) is a city in Turkey which is known primarily as the site of two major meetings (or Ecumenical councils) in the early history of the Christian church. ... Location map of Rhodes Rhodes, (Greek: Ρόδος (pron. ... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 190s BC 180s BC 170s BC 160s BC 150s BC - 140s BC - 130s BC 120s BC 110s BC 100s BC 90s BC Years: 152 BC 151 BC 150 BC 149 BC 148 BC - 147 BC - 146 BC 145 BC... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 170s BC 160s BC 150s BC 140s BC 130s BC - 120s BC - 110s BC 100s BC 90s BC 80s BC 70s BC Years: 132 BC 131 BC 130 BC 129 BC 128 BC - 127 BC - 126 BC 125 BC... Classical antiquity is a broad term for a long period of cultural history centered on the Mediterranean Sea, which begins roughly with the earliest-recorded Greek poetry of Homer (7th century BC), and continues through the rise of Christianity and the fall of the Western Roman Empire (5th century AD... The Sun is the star of our solar system. ... Bulk silicate composition (estimated wt%) SiO2 44. ... Chaldea, the Chaldees of the KJV Old Testament, was a Hellenistic designation for a part of Babylonia. ... Babylonia, named for its capital city, Babylon, was an ancient state in the south part of Mesopotamia (in modern Iraq), combining the territories of Sumer and Akkad. ... Wikibooks has a book on the topic of Trigonometry Trigonometry (from the Greek trigonon = three angles and metron = measure [1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right triangles). ... Photo taken during the 1999 eclipse. ... Precession refers to a change in the direction of the axis of a rotating object. ... In astronomy, many stars are referred to simply by catalogue numbers. ... A 16th century astrolabe. ... A medieval artists rendition of Claudius Ptolemaeus Claudius Ptolemaeus (Greek: ; c. ...

Contents

Life and work

Relatively little of Hipparchus' direct work survived into modern times. Although he wrote at least fourteen books, only his commentary on the popular astronomical poem by Aratus was preserved by later copyists. Most of what is known about Hipparchus comes from Ptolemy's (2nd century AD) Almagest, with additional references to him by Pappus of Alexandria and Theon of Alexandria (4th century) in their commentaries on the Almagest; from Strabo's Geographia ("Geography"), and from Pliny the Elder's Naturalis historia ("Natural history") (1st century).[1] Aratus (Greek Aratos) (ca. ... A medieval artists rendition of Claudius Ptolemaeus Claudius Ptolemaeus (Greek: ; c. ... The 2nd century is the period from 101 - 200 in accordance with the Julian calendar in the Christian Era. ... Almagest is the Latin form of the Arabic name (al-kitabu-l-mijisti, i. ... Pappus of Alexandria is one of the most important mathematicians of ancient Greek time, known for his work Synagoge or Collection (c. ... Theon (c. ... As a means of recording the passage of time, the 4th century was that century which lasted from 301 to 400. ... The Greek geographer Strabo in a 16th century engraving. ... Pliny the Elder: an imaginative 19c portrait. ... Naturalis Historia Pliny the Elders Natural History is an encyclopedia written by Pliny the Elder. ... The 1st century was that century which lasted from 1 to 100 according the Gregorian calendar. ...


There is a strong tradition that Hipparchus was born in Nicaea (Greek Νικαία), in the ancient district of Bithynia (modern-day Iznik in province Bursa), in what today is Turkey. Bithynia was an ancient region, kingdom and Roman province in the northwest of Asia Minor, adjoining the Propontis, the Thracian Bosporus and the Euxine (today Black Sea). ... shows the Location of the Bursa Province Bursa is a province in western Turkey, along the Sea of Marmara. ...


The exact dates of his life are not known, but Ptolemy attributes astronomical observations to him from 147 BC to 127 BC; earlier observations since 162 BC might also be made by him. The date of his birth (ca. 190 BC) was calculated by Delambre based on clues in his work. Hipparchus must have lived some time after 127 BC because he analyzed and published his latest observations. Hipparchus obtained information from Alexandria as well as Babylon, but it is not known if and when he visited these places. Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 190s BC 180s BC 170s BC 160s BC 150s BC - 140s BC - 130s BC 120s BC 110s BC 100s BC 90s BC Years: 152 BC 151 BC 150 BC 149 BC 148 BC - 147 BC - 146 BC 145 BC... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 170s BC 160s BC 150s BC 140s BC 130s BC - 120s BC - 110s BC 100s BC 90s BC 80s BC 70s BC Years: 132 BC 131 BC 130 BC 129 BC 128 BC - 127 BC - 126 BC 125 BC... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 210s BC 200s BC 190s BC 180s BC 170s BC - 160s BC - 150s BC 140s BC 130s BC 120s BC 110s BC Years: 167 BC 166 BC 165 BC 164 BC 163 BC - 162 BC - 161 BC 160 BC... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 240s BC 230s BC 220s BC 210s BC 200s BC - 190s BC - 180s BC 170s BC 160s BC 150s BC 140s BC Years: 195 BC 194 BC 193 BC 192 BC 191 BC - 190 BC - 189 BC 188 BC... Jean Baptiste Joseph Delambre (September 19, 1749 in Amiens – August 19, 1822 in Paris) was a French mathematician and astronomer. ... Alexandria Modern Alexandria. ... Babylon was a city in Mesopotamia, the ruins of which can be found in present-day Babil Province, Iraq, about 50 miles south of Baghdad. ...


It is not known what Hipparchus' economic means were and how he supported his scientific activities. Also, his appearance is unknown: there are no contemporary portraits. In the 2nd and 3rd centuries coins were made in his honour in Bithynia that bear his name and show him with a globe; this supports the tradition that he was born there. A coin is usually a piece of hard material, generally metal and usually in the shape of a disc, which is issued by a government to be used as a form of money. ... A globe This article is on a planet-representation device. ...


Hipparchus is believed to have died on the island of Rhodes, where he spent most of his later life -- Ptolemy attributes observations made on Rhodes in the period from 141 BC to 127 BC to Hipparchus. Location map of Rhodes Rhodes, (Greek: Ρόδος (pron. ... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 190s BC 180s BC 170s BC 160s BC 150s BC - 140s BC - 130s BC 120s BC 110s BC 100s BC 90s BC Years: 146 BC 145 BC 144 BC 143 BC 142 BC - 141 BC - 140 BC 139 BC... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 170s BC 160s BC 150s BC 140s BC 130s BC - 120s BC - 110s BC 100s BC 90s BC 80s BC 70s BC Years: 132 BC 131 BC 130 BC 129 BC 128 BC - 127 BC - 126 BC 125 BC...


Hipparchus' only preserved work is Toon Aratou kai Eudoxou Fainomenoon exegesis ("Commentary on the Phaenomena of Eudoxus and Aratus"). This is a critical commentary in the form of two books on a popular poem by Aratus based on the work by Eudoxus.[2] Hipparchus also made a list of his major works, which apparently mentioned about fourteen books, but which is only known from references by later authors. His famous star catalogue probably was incorporated into the one by Ptolemy, but cannot be independently reconstructed. We know he made a celestial globe; a copy of a copy may have been preserved in the oldest surviving celestial globe accurately depicting the constellations: the globe carried by the Farnese Atlas.[3] Poetry (ancient Greek: poieo = create) is an art form in which human language is used for its aesthetic qualities in addition to, or instead of, its notional and semantic content. ... Aratus (Greek Aratos) (ca. ... Eudoxus of Cnidus (Greek Εύδοξος) (410 or 408 BC - 355 or 347 BC) was a Greek astronomer, mathematician, physician, scholar and friend of Plato. ... Chinese history, astronomers have created celestial globes to assist the observation of the stars. ... The Farnese Atlas at the Museo Archaeologico Nazionale in Naples, Italy. ...


There is evidence, based on references in non-scientific writers such as Plutarch, that Hipparchus was aware of some physical ideas that we consider Newtonian, and some claim that Newton knew this.[4] Classical mechanics is a model of the physics of forces acting upon bodies. ...


Babylonian sources

See also: Babylonian influence on Greek astronomy To meet Wikipedias quality standards, this article or section may require cleanup. ...


Earlier Greek astronomers and mathematicians were influenced by Babylonian astronomy to a limited extent, for instance the period relations of the Metonic cycle and Saros cycle may have come from Babylonian sources. Hipparchus seems to have been the first to exploit Babylonian astronomical knowledge and techniques systematically.[5] He was the first Greek known to divide the circle in 360 degrees of 60 arc minutes (Eratosthenes before him used a simpler sexagesimal system dividing a circle into 60 parts). He also used the Babylonian unit pechus ("cubit") of about 2° or 2½°. The Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the year (specifically, the seasonal tropical year) and the synodic month. ... A Saros cycle is a period of 6585 + 1/3 days (approximately 18 years 10 days and 8 hours) which can be used to predict eclipses of the sun and the moon. ... A degree (in full, a degree of arc, arc degree, or arcdegree), usually symbolized °, is a measurement of plane angle, representing 1/360 of a full rotation. ... A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60) of one degree. ... Eratosthenes (Ἐρατοσθένης) Eratosthenes (Greek ) (276 BC - 194 BC) was a Hellenistic mathematician, geographer and astronomer. ... The sexagesimal (base-sixty) is a numeral system with sixty as the base. ...


Hipparchus probably compiled a list of Babylonian astronomical observations; G. Toomer, a historian of astronomy, has suggested that Ptolemy's knowledge of eclipse records and other Babylonian observations in the Almagest came from a list made by Hipparchus. Hipparchus' use of Babylonian sources has always been known in a general way, because of Ptolemy's statements. However, Franz Xaver Kugler demonstrated that the periods that Ptolemy attributes to Hipparchus had already been used in Babylonian ephemerides, specifically the collection of texts nowadays called "System B" (sometimes attributed to Kidinnu).[6] Franz Xaver Kugler (born 1862 in Königsbach, Germany–died 1929 in Lucerne, Switzerland) was a chemist, mathematician, assyriologist, and Jesuit priest. ... An ephemeris (plural: ephemerides) (from the Greek word ephemeros= daily) was, traditionally, a table providing the positions (given in a Cartesian coordinate system, or in right ascension and declination or, for astrologers, in longitude along the zodiacal ecliptic), of the Sun, the Moon, and the planets in the sky at... Kidinnu (also Kidunnu) (circa 400 BC – possibly 14 August 330 BC) was a Chaldean astronomer and mathematician. ...


Geometry and trigonometry

Hipparchus is recognised as the first mathematician who compiled a trigonometry table, which he needed when computing the eccentricity of the orbits of the Moon and Sun. He tabulated values for the chord function, which gives the length of the chord for each angle. He did this for a circle with a circumference of 21,600 and a radius (rounded) of 3438 units: this circle has a unit length of 1 arc minute along its perimeter. He tabulated the chords for angles with increments of 7.5°. In modern terms, the chord of an angle equals twice the sine of half of the angle, i.e.: Wikibooks has a book on the topic of Trigonometry Trigonometry (from the Greek trigonon = three angles and metron = measure [1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right triangles). ... In astrodynamics, under standard assumptions any orbit must be of conic section shape. ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ... A chord of a curve is a geometric line segment whose endpoints both lie on the curve. ... All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. In mathematics, the trigonometric functions are functions of an angle; they are important when studying triangles and modeling periodic phenomena, among many other applications. ...

chord(A) = 2 sin(A/2).

He described the chord table in a work, now lost, called Toon en kuklooi eutheioon (Of Lines Inside a Circle) by Theon of Alexandria (4th century) in his commentary on the Almagest I.10; some claim his table may have survived in astronomical treatises in India, for instance the Surya Siddhanta. This was a significant innovation, because it allowed Greek astronomers to solve any triangle, and made it possible to make quantitative astronomical models and predictions using their preferred geometric techniques.[7] Theon (c. ... As a means of recording the passage of time, the 4th century was that century which lasted from 301 to 400. ... The Surya Siddhanta is the first Indian astronomical treatise where rules were laid down to determine the true motions of the luminaries, which conforms to their actual positions in the sky. ...


For his chord table Hipparchus must have used a better approximation for π than the one from Archimedes of between 3 + 1/7 and 3 + 10/71; perhaps he had the one later used by Ptolemy: 3;8:30 (sexagesimal) (Almagest VI.7); but it is not known if he computed an improved value himself. When a circles diameter is 1, its circumference is Ï€. The mathematical constant Ï€ is an irrational real number, approximately equal to 3. ... Archimedes (Greek: ) (c. ... The sexagesimal (base-sixty) is a numeral system with sixty as the base. ...


Hipparchus could construct his chord table using the Pythagorean theorem and a theorem known to Archimedes. He also might have developed and used the theorem in plane geometry called Ptolemy's theorem, because it was proved by Ptolemy in his Almagest (I.10) (later elaborated on by Carnot). In mathematics, the Pythagorean theorem or Pythagoras theorem is a relation in Euclidean geometry among the three sides of a right triangle. ... A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ... In mathematics, plane geometry may mean: geometry of the Euclidean plane; or sometimes geometry of a projective plane, most commonly the real projective plane but possibly the complex projective plane, Fano plane or others; or geometry of the hyperbolic plane or two-dimensional spherical geometry. ... In mathematics, Ptolemys theorem is a relation in Euclidean geometry between the four sides and two diagonals or chords of a quadrilateral inscribed in circle. ... Lazare Carnot Lazare Nicolas Marguerite Carnot (Nolay, May 13, 1753 - Magdeburg, August 22, 1823) was a French politician and mathematician. ...


Hipparchus was the first to show that the stereographic projection is conformal, and that it transforms circles on the sphere that do not pass through the center of projection to circles on the plane. This was the basis for the astrolabe. Stereographic projection of a circle of radius R onto the x axis. ... In mathematics, a conformal map is a function which preserves angles. ... A sphere (< Greek σφαίρα) is a perfectly symmetrical geometrical object. ... Two intersecting planes in three-dimensional space In mathematics, a plane is a fundamental two-dimensional object. ... A 16th century astrolabe. ...


Approximations to spherical trigonometry

Besides geometry, Hipparchus also used arithmetic techniques developed by the Chaldeans. He was one of the first Greek mathematicians to do this, and in this way expanded the techniques available to astronomers and geographers. Arithmetic or arithmetics (from the Greek word αριθμός = number) is the oldest and simplest branch of mathematics, used by almost everyone, for tasks ranging from simple daily counting to advanced science and business calculations. ... Chaldea, the Chaldees of the KJV Old Testament, was a Hellenistic designation for a part of Babylonia. ...


There is no indication that Hipparchus knew spherical trigonometry, which was first developed by Menelaus of Alexandria in the 1st century. Ptolemy later used spherical trigonometry to compute things like the rising and setting points of the ecliptic, or to take account of the lunar parallax. Hipparchus may have used a globe for these tasks, reading values off coordinate grids drawn on it, or he may have made approximations from planar geometry, or perhaps used arithmetical approximations developed by the Chaldeans. Spherical triangle Spherical trigonometry is a part of spherical geometry that deals with polygons (especially triangles) on the sphere and explains how to find relations between the involved angles. ... Menelaus of Alexandria (born ca. ... The 1st century was that century which lasted from 1 to 100 according the Gregorian calendar. ... The plane of the ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ... This article or section does not cite its references or sources. ...


Lunar and solar theory

Motion of the Moon

Hipparchus also studied the motion of the Moon and confirmed the accurate values for some periods of its motion that Chaldean astronomers had obtained before him. The traditional value (from Babylonian System B) for the mean synodic month is 29 days;31,50,8,20 (sexagesimal) = 29.5305941... d. Expressed as 29 days + 12 hours + 793/1080 hours this value has been used later in the Hebrew calendar (possibly from Babylonian sources). The Chaldeans also knew that 251 synodic months = 269 anomalistic months. Hipparchus extended this period by a factor of 17, because after that interval the Moon also would have a similar latitude, and it is close to an integer number of years (345). Therefore, eclipses would reappear under almost identical circumstances. The period is 126007 days 1 hour (rounded). Hipparchus could confirm his computations by comparing eclipses from his own time (presumably 27 January 141 BC and 26 November 139 BC according to [Toomer 1980]), with eclipses from Babylonian records 345 years earlier (Almagest IV.2; [Jones 2001]). Already al-Biruni (Qanun VII.2.II) and Copernicus (de revolutionibus IV.4) noted that the period of 4,267 lunations is actually about 5 minutes longer than the value for the eclipse period that Ptolemy attributes to Hipparchus. However, the best clocks and timing methods of the age had an accuracy of no better than 8 minutes[citation needed]. Modern scholars agree that Hipparchus rounded the eclipse period to the nearest hour, and used it to confirm the validity of the traditional values, rather than try to derive an improved value from his own observations. From modern ephemerides [Chapront et al. 2002] and taking account of the change in the length of the day (see ΔT) we estimate that the error in the assumed length of the synodic month was less than 0.2 seconds in the 4th century BC and less than 0.1 seconds in Hipparchus' time. Bulk silicate composition (estimated wt%) SiO2 44. ... In Egyptian mythology, Month is an alternate spelling for Menthu. ... The Hebrew calendar (Hebrew: ) or Jewish calendar is the annual calendar used in Judaism. ... In Egyptian mythology, Month is an alternate spelling for Menthu. ... In Egyptian mythology, Month is an alternate spelling for Menthu. ... January 27 is the 27th day of the year in the Gregorian calendar. ... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 190s BC 180s BC 170s BC 160s BC 150s BC - 140s BC - 130s BC 120s BC 110s BC 100s BC 90s BC Years: 146 BC 145 BC 144 BC 143 BC 142 BC - 141 BC - 140 BC 139 BC... November 26 is the 330th day (331st on leap years) of the year in the Gregorian calendar. ... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 180s BC 170s BC 160s BC 150s BC 140s BC - 130s BC - 120s BC 110s BC 100s BC 90s BC 80s BC Years: 144 BC 143 BC 142 BC 141 BC 140 BC - 139 BC - 138 BC 137 BC... A statue of Biruni adorns the southwest entrance of Laleh Park in Tehran. ... Nicolaus Copernicus (in Latin; Polish Miko&#322;aj Kopernik, German Nikolaus Kopernikus - February 19, 1473 &#8211; May 24, 1543) was a Polish astronomer, mathematician and economist who developed a heliocentric (Sun-centered) theory of the solar system in a form detailed enough to make it scientifically useful. ... Delta T and delta-T are ASCII substitutes for the formal &#916;T, which is Terrestrial Time minus Universal Time. ... (2nd millennium BC - 1st millennium BC - 1st millennium) The 4th century BC started on January 1, 400 BC and ended on December 31, 301 BC. // Overview Events Bust of Alexander the Great in the British Museum. ...


Orbit of the Moon

It had been known for a long time that the motion of the Moon is not uniform: its speed varies. This is called its anomaly, and it repeats with its own period; the anomalistic month. The Chaldeans took account of this arithmetically, and used a table giving the daily motion of the Moon according to the date within a long period. The Greeks however preferred to think in geometrical models of the sky. Apollonius of Perga had at the end of the 3rd century BC proposed two models for lunar and planetary motion: In Egyptian mythology, Month is an alternate spelling for Menthu. ... Apollonius of Perga [Pergaeus] (c. ... (2nd millennium BC - 1st millennium BC - 1st millennium) The 3rd century BC started on January 1, 300 BC and ended on December 31, 201 BC. // Events The Pyramid of the Moon, one of several monuments built in Teotihuacán Teotihuacán, Mexico begun The first two Punic Wars between Carthage...

  1. In the first, the Moon would move uniformly along a circle, but the Earth would be eccentric, i.e., at some distance of the center of the circle. So the apparent angular speed of the Moon (and its distance) would vary.
  2. The Moon itself would move uniformly (with some mean motion in anomaly) on a secondary circular orbit, called an epicycle, that itself would move uniformly (with some mean motion in longitude) over the main circular orbit around the Earth, called deferent; see deferent and epicycle.

Apollonius demonstrated that these two models were in fact mathematically equivalent. However, all this was theory and had not been put to practice. Hipparchus was the first to attempt to determine the relative proportions and actual sizes of these orbits. In the Ptolemaic system of astronomy, the epicycle (literally: on the cycle in Greek) was a geometric model to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ...


Hipparchus devised a geometrical method to find the parameters from three positions of the Moon, at particular phases of its anomaly. In fact, he did this separately for the eccentric and the epicycle model. Ptolemy describes the details in the Almagest IV.11. Hipparchus used two sets of three lunar eclipse observations, which he carefully selected to satisfy the requirements. The eccentric model he fitted to these eclipses from his Babylonian eclipse list: 22/23 December 383 BC, 18/19 June 382 BC, and 12/13 December 382 BC. The epicycle model he fitted to lunar eclipse observations made in Alexandria at 22 September 201 BC, 19 March 200 BC, and 11 September 200 BC. Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 430s BC 420s BC 410s BC 400s BC 390s BC - 380s BC - 370s BC 360s BC 350s BC 340s BC 330s BC Years: 388 BC 387 BC 386 BC 385 BC 384 BC - 383 BC - 382 BC 381 BC... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 430s BC 420s BC 410s BC 400s BC 390s BC - 380s BC - 370s BC 360s BC 350s BC 340s BC 330s BC Years: 387 BC 386 BC 385 BC 384 BC 383 BC - 382 BC - 381 BC 380 BC... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 430s BC 420s BC 410s BC 400s BC 390s BC - 380s BC - 370s BC 360s BC 350s BC 340s BC 330s BC Years: 387 BC 386 BC 385 BC 384 BC 383 BC - 382 BC - 381 BC 380 BC... September 22 is the 265th day of the year in the Gregorian calendar (266th in leap years). ... Centuries: 4th century BC - 3rd century BC - 2nd century BC Decades: 250s BC 240s BC 230s BC 220s BC 210s BC - 200s BC - 190s BC 180s BC 170s BC 160s BC 150s BC Years: 206 BC 205 BC 204 BC 203 BC 202 BC - 201 BC - 200 BC 199 BC... March 19 is the 78th day of the year in the Gregorian calendar (79th in leap years). ... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 250s BC 240s BC 230s BC 220s BC 210s BC - 200s BC - 190s BC 180s BC 170s BC 160s BC 150s BC Years: 205 BC 204 BC 203 BC 202 BC 201 BC - 200 BC - 199 BC 198 BC... September 11 is the 254th day of the year in the Gregorian calendar (255th in leap years). ... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 250s BC 240s BC 230s BC 220s BC 210s BC - 200s BC - 190s BC 180s BC 170s BC 160s BC 150s BC Years: 205 BC 204 BC 203 BC 202 BC 201 BC - 200 BC - 199 BC 198 BC...

  • For the eccentric model, Hipparchus found for the ratio between the radius of the eccenter and the distance between the center of the eccenter and the center of the ecliptic (i.e., the observer on Earth): 3144 : 327+2/3 ;
  • and for the epicycle model, the ratio between the radius of the deferent and the epicycle: 3122+1/2 : 247+1/2 .

The somewhat weird numbers are due to the cumbersome unit he used in his chord table. The results are distinctly different. This is partly due to some sloppy rounding and calculation errors, for which Ptolemy criticised him (he himself made rounding errors too). Anyway, Hipparchus found inconsistent results; he later used the ratio of the epicycle model (3122+1/2 : 247+1/2), which is too small (60 : 4;45 hexadecimal): Ptolemy established a ratio of 60 : 5+1/4 . See [Toomer 1967].


Apparent motion of the Sun

Before Hipparchus, Meton, Euctemon, and their pupils at Athens had made a solstice observation (i.e., timed the moment of the summer solstice) on June 27, 432 BC (proleptic Julian calendar). Aristarchus of Samos is said to have done so in 280 BC, and Hipparchus also had an observation by Archimedes. Hipparchus himself observed the summer solstice in 135 BC, but he found observations of the moment of equinox more accurate, and he made many during his lifetime. Ptolemy gives an extensive discussion of Hipparchus' work on the length of the year in the Almagest III.1, and quotes many observations that Hipparchus made or used, spanning 162 BC to 128 BC. Meton of Athens was a mathematician, astronomer and engineer who lived in Athens in the 5th century BCE. He is best known for the 19-year Metonic Cycle which he introduced into the Athenian luni-solar calendar as a method of calculating dates. ... For the crater, see Euctemon (crater). ... Athens (Greek: Αθήνα, Athína IPA: ) is the capital and largest city of Greece and the birthplace of democracy. ... This article or section needs a complete rewrite for the reasons listed on the talk page. ... June 27 is the 178th day of the year (179th in leap years) in the Gregorian calendar, with 187 days remaining. ... Centuries: 6th century BC - 5th century BC - 4th century BC Decades: 480s BC 470s BC 460s BC 450s BC 440s BC - 430s BC - 420s BC 410s BC 400s BC 390s BC 380s BC Years: 437 BC 436 BC 435 BC 434 BC 433 BC 432 BC 431 BC 430 BC... The proleptic Julian calendar is produced by extending the Julian calendar to dates preceding its official introduction in 45 BC. Historians since Bede have traditionally represented the years preceding AD 1 as 1 BC, 2 BC, etc. ... Statue of Aristarchus at Aristoteles University in Thessaloniki, Greece Aristarchus (310 BC - c. ... Centuries: 4th century BC - 3rd century BC - 2nd century BC Decades: 330s BC 320s BC 310s BC 300s BC 290s BC - 280s BC - 270s BC 260s BC 250s BC 240s BC 230s BC 285 BC 284 BC 283 BC 282 BC 281 BC 280 BC 279 BC 278 BC 277... Archimedes (Greek: ) (c. ... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 180s BC 170s BC 160s BC 150s BC 140s BC - 130s BC - 120s BC 110s BC 100s BC 90s BC 80s BC Years: 140 BC 139 BC 138 BC 137 BC 136 BC - 135 BC - 134 BC 133 BC... An equinox is one of two opposite points on the celestial sphere where the celestial equator and ecliptic intersect. ... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 210s BC 200s BC 190s BC 180s BC 170s BC - 160s BC - 150s BC 140s BC 130s BC 120s BC 110s BC Years: 167 BC 166 BC 165 BC 164 BC 163 BC - 162 BC - 161 BC 160 BC... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 170s BC 160s BC 150s BC 140s BC 130s BC - 120s BC - 110s BC 100s BC 90s BC 80s BC 70s BC Years: 133 BC 132 BC 131 BC 130 BC 129 BC - 128 BC - 127 BC 126 BC...


Ptolemy quotes an equinox timing by Hipparchus (at 24 March 146 BC at dawn) that differs from the observation made on that day in Alexandria (at 5h after sunrise): Hipparchus may have visited Alexandria but he did not make his equinox observations there; presumably he was on Rhodes (at the same geographical longitude). He may have used his own armillary sphere or an equatorial ring for these observations. Hipparchus (and Ptolemy) knew that observations with these instruments are sensitive to a precise alignment with the equator. The real problem however is that atmospheric refraction lifts the Sun significantly above the horizon: so its apparent declination is too high, which changes the observed time when the Sun crosses the equator. Worse, the refraction decreases as the Sun rises, so it may appear to move in the wrong direction with respect to the equator in the course of the day - as Ptolemy mentions; however, Ptolemy and Hipparchus apparently did not realize that refraction is the cause. March 24 is the 83rd day of the year in the Gregorian Calendar (84th in leap years). ... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 190s BC 180s BC 170s BC 160s BC 150s BC - 140s BC - 130s BC 120s BC 110s BC 100s BC 90s BC Years: 151 BC 150 BC 149 BC 148 BC 147 BC - 146 BC - 145 BC 144 BC... Alexandria Modern Alexandria. ... The Equator is an imaginary circle drawn around a planet (or other astronomical object) at a distance halfway between the poles. ... The straw seems to be broken, due to refraction of light as it emerges into the air. ... In astronomy, declination (dec) is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. ...


At the end of his career, Hipparchus wrote a book called Peri eniausíou megéthous ("On the Length of the Year") about his results. The established value for the tropical year, introduced by Callippus in or before 330 BC (possibly from Babylonian sources, see above), was 365 + 1/4 days. Hipparchus' equinox observations gave varying results, but he himself points out (quoted in Almagest III.1(H195)) that the observation errors by himself and his predecessors may have been as large as 1/4 day. So he used the old solstice observations, and determined a difference of about one day in about 300 years. So he set the length of the tropical year to 365 + 1/4 - 1/300 days (= 365.24666... days = 365 days 5 hours 55 min, which differs from the actual value (modern estimate) of 365.24219... days = 365 days 5 hours 48 min 45 s by only about 6 min). A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). ... Callippus (or Calippus) (circa 370 B.C.–circa 300 B.C.) was a Greek astronomer. ... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 380s BC 370s BC 360s BC 350s BC 340s BC - 330s BC - 320s BC 310s BC 300s BC 290s BC 280s BC 335 BC 334 BC 333 BC 332 BC 331 BC - 330 BC - 329 BC 328 BC 327...


Between the solstice observation of Meton and his own, there were 297 years spanning 108,478 days. This implies a tropical year of 365.24579... days = 365 days;14,44,51 (sexagesimal; = 365 days + 14/60 + 44/602 + 51/603), and this value has been found on a Babylonian clay tablet [A. Jones, 2001]. This is an indication that Hipparchus' work was known to Chaldeans.


Another value for the year that is attributed to Hipparchus (by the astrologer Vettius Valens in the 1st century) is 365 + 1/4 + 1/288 days (= 365.25347... days = 365 days 6 hours 5 min), but this may be a corruption of another value attributed to a Babylonian source: 365 + 1/4 + 1/144 days (= 365.25694... days = 365 days 6 hours 10 min). It is not clear if this would be a value for the sidereal year (actual value at his time (modern estimate) ca. 365.2565 days), but the difference with Hipparchus' value for the tropical year is consistent with his rate of precession (see below). Vettius Valens (ca. ... The 1st century was that century which lasted from 1 to 100 according the Gregorian calendar. ... The sidereal year is the time for the Sun to return to the same position in respect to the stars of the celestial sphere. ... Precession refers to a change in the direction of the axis of a rotating object. ...


Orbit of the Sun

Before Hipparchus the Chaldean astronomers knew that the lengths of the seasons are not equal. Hipparchus made equinox and solstice observations, and according to Ptolemy (Almagest III.4) determined that spring (from spring equinox to summer solstice) lasted 94 + 1/2 days, and summer (from summer solstice to autumn equinox) 92 + 1/2 days. This is an unexpected result given a premise of the Sun moving around the Earth in a circle at uniform speed. Hipparchus' solution was to place the Earth not at the center of the Sun's motion, but at some distance from the center. This model described the apparent motion of the Sun fairly well (of course today we know that the planets like the Earth move in ellipses around the Sun, but this was not discovered until Johannes Kepler published his first two laws of planetary motion in 1609). The value for the eccentricity attributed to Hipparchus by Ptolemy is that the offset is 1/24 of the radius of the orbit (which is too large), and the direction of the apogee would be at longitude 65.5° from the vernal equinox. Hipparchus may also have used another set of observations (94 + 1/4 and 92 + 3/4 days), which would lead to different values. The question remains if Hipparchus is really the author of the values provided by Ptolemy, who found no change three centuries later, and added lengths for the autumn and winter seasons. A season is one of the major divisions of the year, generally based on yearly periodic changes in weather. ... The eight planets and three dwarf planets of the Solar System. ... The ellipse and some of its mathematical properties. ... Johannes Kepler (December 27, 1571 – November 15, 1630), a key figure in the scientific revolution, was a German mathematician, astronomer, astrologer, and an early writer of science fiction stories. ... // Events April 4 – King of Spain signs an edit of expulsion of all moriscos from Spain April 9 – Spain recognizes Dutch independence May 23 - Official ratification of the Second Charter of Virginia. ... In astrodynamics, under standard assumptions any orbit must be of conic section shape. ... This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ... Illumination of Earth by Sun on the day of equinox The vernal equinox (or spring equinox) marks the beginning of astronomical spring. ...


Distance, parallax, size of the Moon and Sun

Hipparchus also undertook to find the distances and sizes of the Sun and the Moon. He published his results in a work of two books called Peri megethoon kai 'apostèmátoon ("On Sizes and Distances") by Pappus in his commentary on the Almagest V.11; Theon of Smyrna (2nd century) mentions the work with the addition "of the Sun and Moon". On Sizes and Distances [of the Sun and Moon] (Peri megethoon kai apostèmátoon) is a text by the ancient Greek astronomer Hipparchus. ... Theon of Smyrna (ca. ... The 2nd century is the period from 101 - 200 in accordance with the Julian calendar in the Christian Era. ...


Hipparchus measured the apparent diameters of the Sun and Moon with his diopter. Like others before and after him, he found that the Moon's size varies as it moves on its (eccentric) orbit, but he found no perceptible variation in the apparent diameter of the Sun. He found that at the mean distance of the Moon, the Sun and Moon had the same apparent diameter; at that distance, the Moon's diameter fits 650 times into the circle, i.e., the mean apparent diameters are 360/650 = 0°33'14". In statistics, mean has two related meanings: the average in ordinary English, which is also called the arithmetic mean (and is distinguished from the geometric mean or harmonic mean). ...


Like others before and after him, he also noticed that the Moon has a noticeable parallax, i.e., that it appears displaced from its calculated position (compared to the Sun or stars), and the difference is greater when closer to the horizon. He knew that this is because the Moon circles the center of the Earth/Moon center of gravity, which is below the earth's surface, but the observer is at the surface -- the Moon, Earth and observer form a triangle with a sharp angle that changes all the time. From the size of this parallax, the distance of the Moon as measured in Earth radii can be determined. For the Sun however, there was no observable parallax (we now know that it is about 8.8", more than ten times smaller than the resolution of the unaided eye). This article or section does not cite its references or sources. ... The Pleiades, an open cluster of stars in the constellation of Taurus. ... In classical geometry, a radius of a circle or sphere is any line segment from its center to its boundary. ...


In the first book, Hipparchus assumes that the parallax of the Sun is 0, as if it is at infinite distance. He then analyzed a solar eclipse, presumably that of 14 March 190 BC. It was total in the region of the Hellespont (and in fact in his birth place Nicaea); at the time the Romans were preparing for war with Antiochus III in the area, and the eclipse is mentioned by Livy in his Ab Urbe Condita VIII.2. It was also observed in Alexandria, where the Sun was reported to be obscured 4/5ths by the Moon. Alexandria and Nicaea are on the same meridian. Alexandria is at about 31° North, and the region of the Hellespont at about 41° North; authors like Strabo and Ptolemy had fairly decent values for these geographical positions, and presumably Hipparchus knew them too. So Hipparchus could draw a triangle formed by the two places and the Moon, and from simple geometry was able to establish a distance of the Moon, expressed in Earth radii. Because the eclipse occurred in the morning, the Moon was not in the meridian, and as a consequence the distance found by Hipparchus was a lower limit. In any case, according to Pappus, Hipparchus found that the least distance is 71 (from this eclipse), and the greatest 81 Earth radii. March 14 is the 73rd day of the year in the Gregorian Calendar (74th in leap years) with 292 days remaining in the year. ... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 240s BC 230s BC 220s BC 210s BC 200s BC - 190s BC - 180s BC 170s BC 160s BC 150s BC 140s BC Years: 195 BC 194 BC 193 BC 192 BC 191 BC - 190 BC - 189 BC 188 BC... Hellespont (i. ... Silver coin of Antiochus III Antiochus III the Great, (ruled 223 - 187 BC), younger son of Seleucus II Callinicus, became ruler of the Seleucid kingdom as a youth of about eighteen in 223 BC. (His traditional designation, the Great, stems from a misconception of Megas Basileus (Great king), the traditional... A portrait of Titus Livius made long after his death. ... Ab urbe condita (AUC or a. ... This article is about the astronomical concept. ...


In the second book, Hipparchus starts from the opposite extreme assumption: he assigns a (minimum) distance to the Sun of 470 Earth radii. This would correspond to a parallax of 7', which is apparently the greatest parallax that Hipparchus thought would not be noticed (for comparison: the typical resolution of the human eye is about 2'; Tycho Brahe made naked eye observation with an accuracy down to 1'). In this case, the shadow of the Earth is a cone rather than a cylinder as under the first assumption. Hipparchus observed (at lunar eclipses) that at the mean distance of the Moon, the diameter of the shadow cone is 2+½ lunar diameters. That apparent diameter is, as he had observed, 360/650 degrees. With these values and simple geometry, Hipparchus could determine the mean distance; because it was computed for a minimum distance of the Sun, it is the maximum mean distance possible for the Moon. With his value for the eccentricity of the orbit, he could compute the least and greatest distances of the Moon too. According to Pappus, he found a least distance of 62, a mean of 67+1/3, and consequently a greatest distance of 72+2/3 Earth radii. With this method, as the parallax of the Sun decreases (i.e., its distance increases), the minimum limit for the mean distance is 59 Earth radii - exactly the mean distance that Ptolemy later derived. Tycho Brahe Monument of Tycho Brahe and Johannes Kepler in Prague   , born Tyge Ottesen Brahe (December 14, 1546 – October 24, 1601), was a Danish (Scanian) nobleman best known today as an early astronomer, though in his lifetime he was also well known as an astrologer and alchemist. ... In geometry, a (general) conical surface is the unbounded surface formed by the union of all the straight lines that pass through a fixed point — the apex or vertex — and any point of some fixed space curve — the directrix — that does not contain the apex. ... A right circular cylinder An elliptic cylinder In mathematics, a cylinder is a quadric, i. ...


Hipparchus thus had the problematic result that his minimum distance (from book 1) was greater than his maximum mean distance (from book 2). He was intellectually honest about this discrepancy, and probably realized that especially the first method is very sensitive to the accuracy of the observations and parameters (in fact, modern calculations show that the size of the solar eclipse at Alexandria must have been closer to 9/10ths and not the 4/5ths reported to Hipparchus).


Ptolemy later measured the lunar parallax directly (Almagest V.13), and used the second method of Hipparchus' with lunar eclipses to compute the distance of the Sun (Almagest V.15). He criticizes Hipparchus for making contradictory assumptions, and obtaining conflicting results (Almagest V.11): but apparently he failed to understand Hipparchus' strategy to establish limits consistent with the observations, rather than a single value for the distance. His results were the best so far: the actual mean distance of the Moon is 60.3 Earth radii, within his limits from Hipparchus' second book.


Theon of Smyrna wrote that according to Hipparchus, the Sun is 1,880 times the size of the Earth, and the Earth twenty-seven times the size of the Moon; apparently this refers to volumes, not diameters. From the geometry of book 2 it follows that the Sun is at 2,550 Earth radii, and the mean distance of the Moon is 60½ radii. Similarly, Cleomedes quotes Hipparchus for the sizes of the Sun and Earth as 1050:1; this leads to a mean lunar distance of 61 radii. Apparently Hipparchus later refined his computations, and derived accurate single values that he could use for predictions of solar eclipses. Theon of Smyrna (ca. ... Volume is a quantification of how much space a certain region occupies. ... Diameter is an AAA (authentication, authorization and accounting) protocol for applications such as network access or IP mobility. ... Cleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies. ...


See [Toomer 1974] for a more detailed discussion.


Eclipses

Pliny (Naturalis Historia II.X) tells us that Hipparchus demonstrated that lunar eclipses can occur five months apart, and solar eclipses seven months (instead of the usual six months); and the Sun can be hidden twice in thirty days, but as seen by different nations. Ptolemy discussed this a century later at length in Almagest VI.6. The geometry, and the limits of the positions of Sun and Moon when a solar or lunar eclipse is possible, are explained in Almagest VI.5. Hipparchus apparently made similar calculations. The result that two solar eclipses can occur one month apart is important, because this can not be based on observations: one is visible on the northern and the other on the southern hemisphere - as Pliny indicates -, and the latter was inaccessible to the Greek. Pliny the Elder: an imaginative 19c portrait. ...


Prediction of a solar eclipse, i.e., exactly when and where it will be visible, requires a solid lunar theory and proper treatment of the lunar parallax. Hipparchus must have been the first to be able to do this. A rigorous treatment requires spherical trigonometry, but Hipparchus may have made do with planar approximations. He may have discussed these things in Peri tes kata platos meniaias tes selenes kineseoos ("On the monthly motion of the Moon in latitude"), a work mentioned in the Suda. Spherical triangle Spherical trigonometry is a part of spherical geometry that deals with polygons (especially triangles) on the sphere and explains how to find relations between the involved angles. ... Suda (Σουδα or alternatively Suidas) is a massive 10th century Byzantine Greek historical encyclopædia of the ancient Mediterranean world. ...


Pliny also remarks that "he also discovered for what exact reason, although the shadow causing the eclipse must from sunrise onward be below the earth, it happened once in the past that the moon was eclipsed in the west while both luminaries were visible above the earth." (translation H. Rackham (1938), Loeb Classical Library 330 p.207). Toomer (1980) argued that this must refer to the large total lunar eclipse of 26 November 139 BC, when over a clean sea horizon as seen from the citadel of Rhodes, the Moon was eclipsed in the northwest just after the Sun rose in the southeast. This would be the second eclipse of the 345-year interval that Hipparchus used to verify the traditional Babylonian periods: this puts a late date to the development of Hipparchus' lunar theory. We do not know what "exact reason" Hipparchus found for seeing the Moon eclipsed while apparently it was not in exact opposition to the Sun. Parallax lowers the altitude of the luminaries; refraction raises them, and from a high point of view the horizon is lowered. The Loeb Classical Library is a series of books, today published by the Harvard University Press, which present important works of ancient Greek and Latin Literature in a way designed to make the text accessible to the broadest possible audience, by presenting the original Greek or Latin text on each... November 26 is the 330th day (331st on leap years) of the year in the Gregorian calendar. ... Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 180s BC 170s BC 160s BC 150s BC 140s BC - 130s BC - 120s BC 110s BC 100s BC 90s BC 80s BC Years: 144 BC 143 BC 142 BC 141 BC 140 BC - 139 BC - 138 BC 137 BC... Opposition is a term used in positional astronomy and astrology. ...


Astronomical instruments and astrometry

Hipparchus and his predecessors mostly used simple instruments for astronomical calculations and observations, such as the gnomon, the astrolabe, and the armillary sphere. The gnomon is the part of a sundial which casts the shadow. ... A 16th century astrolabe. ... Armillary sphere An armillary sphere (also known as spherical astrolabe) is a model of the celestial sphere, invented by Eratosthenes in 255 BC. Its name comes from the Latin armilla (circle, bracelet), since it has a skeleton made of graduated metal circles linking the poles and representing the equator, the...


Hipparchus is credited with the invention or improvement of several astronomical instruments, which were used for a long time for naked-eye observations. According to Synesius of Ptolemais (4th century) he made the first astrolabion: this may have been an armillary sphere (which Ptolemy however says he constructed, in Almagest V.1); or the predecessor of the planar instrument called astrolabe (also mentioned by Theon of Alexandria). With an astrolabe Hipparchus was the first to be able to measure the geographical latitude and time by observing stars. Previously this was done at daytime by measuring the shadow cast by a gnomon, or with the portable instrument known as scaphion. Synesius (c. ... As a means of recording the passage of time, the 4th century was that century which lasted from 301 to 400. ... Armillary sphere An armillary sphere (also known as spherical astrolabe) is a model of the celestial sphere, invented by Eratosthenes in 255 BC. Its name comes from the Latin armilla (circle, bracelet), since it has a skeleton made of graduated metal circles linking the poles and representing the equator, the... A 16th century astrolabe. ... Theon (c. ... Latitude, usually denoted symbolically by the Greek letter φ, gives the location of a place on Earth north or south of the Equator. ... Two distinct views exist on the meaning of time. ... The gnomon is the part of a sundial which casts the shadow. ... The scaphion was a portable gnomon, developed by hellenistic astronomers. ...

Hipparchus' equatorial ring.
Hipparchus' equatorial ring.

Ptolemy mentions (Almagest V.14) that he used a similar instrument as Hipparchus, called dioptra, to measure the apparent diameter of the Sun and Moon. Pappus of Alexandria described it (in his commentary on the Almagest of that chapter), as did Proclus (Hypotyposis IV). It was a 4-foot rod with a scale, a sighting hole at one end, and a wedge that could be moved along the rod to exactly obscure the disk of Sun or Moon. Image File history File links Equatorial_ring. ... Image File history File links Equatorial_ring. ... A dioptra is a instrument dating back to ancient Greece, at least 300 B.C.E. It is said to have been long used by Greek astronomers, such as Hipparchus(sometimes credited with inventing it). ... Pappus of Alexandria is one of the most important mathematicians of ancient Greek time, known for his work Synagoge or Collection (c. ... Proclus Lycaeus (February 8, 412 – April 17, 485), surnamed The Successor or diadochos (Greek Πρόκλος ὁ Διάδοχος Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major Greek philosophers (see Damascius). ...


Hipparchus also observed solar equinoxes, which may be done with an equatorial ring: its shadow falls on itself when the Sun is on the equator (i.e., in one of the equinoctial points on the ecliptic), but the shadow falls above or below the opposite side of the ring when the Sun is south or north of the equator. Ptolemy quotes (in Almagest III.1 (H195)) a description by Hipparchus of an equatorial ring in Alexandria; a little further he describes two such instruments present in Alexandria in his own time. An equinox is one of two opposite points on the celestial sphere where the celestial equator and ecliptic intersect. ... The Equator is an imaginary circle drawn around a planet (or other astronomical object) at a distance halfway between the poles. ... The plane of the ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ...


Geography

Hipparchus applied his knowledge of spherical angles to the problem of denoting locations on the Earth's surface. Before him a grid system had been used by Dicaearchus of Messana, but Hipparchus was the first to apply mathematical rigor to the determination of the latitude and longitude of places on the Earth. Hipparchus wrote a critique in three books on the work of the geographer Eratosthenes of Cyrene (3rd century BC), called Pròs tèn 'Eratosthénous geografían ("Against the Geography of Eratosthenes"). It is known to us from Strabo of Amaseia, who in his turn criticised Hipparchus in his own Geografia. Hipparchus apparently made many detailed corrections to the locations and distances mentioned by Eratosthenes. It seems he did not introduce many improvements in methods, but he did propose a means to determine the geographical longitudes of different cities at lunar eclipses (Strabo Geografia 7). A lunar eclipse is visible simultaneously on half of the Earth, and the difference in longitude between places can be computed from the difference in local time when the eclipse is observed. His approach would give accurate results if it were correctly carried out but the limitations of timekeeping accuracy in his era made this method impractical. Dicaearchus (also Dicearchos, Dicearchus or Dikæarchus, Greek Δικαιαρχος; circa 350 BC – circa 285 BC) was a Greek philosopher, cartographer, geographer, mathematician and author. ... Location within Italy Messina with a population of about 260,000 is the third largest city on the island of Sicily, Italy and the capital of the province of Messina. ... Latitude, usually denoted symbolically by the Greek letter φ, gives the location of a place on Earth north or south of the Equator. ... Longitude, sometimes denoted by the Greek letter λ, describes the location of a place on Earth east or west of a north-south line called the Prime Meridian. ... Eratosthenes (Ἐρατοσθένης) Eratosthenes (Greek ) (276 BC - 194 BC) was a Hellenistic mathematician, geographer and astronomer. ... (2nd millennium BC - 1st millennium BC - 1st millennium) The 3rd century BC started on January 1, 300 BC and ended on December 31, 201 BC. // Events The Pyramid of the Moon, one of several monuments built in Teotihuacán Teotihuacán, Mexico begun The first two Punic Wars between Carthage... The Greek geographer Strabo in a 16th century engraving. ... Map of Earth showing lines of latitude (horizontally) and longitude (vertically), Eckert VI projection; large version (pdf, 1. ... Chicago from the air. ... An eclipse refers to the phenomenon of one body passing into the shadow cast by another body. ...


Star catalogue

Late in his career (about 135 BC?) Hipparchus compiled a star catalogue. He also constructed a celestial globe depicting the constellations, based on his observations. His interest in the fixed stars may have been inspired by the observation of a supernova (according to Pliny), or by his discovery of precession (according to Ptolemy, who says that Hipparchus could not reconcile his data with earlier observations made by Timocharis and Aristyllos; for more information see Discovery of precession). Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 180s BC 170s BC 160s BC 150s BC 140s BC - 130s BC - 120s BC 110s BC 100s BC 90s BC 80s BC Years: 140 BC 139 BC 138 BC 137 BC 136 BC - 135 BC - 134 BC 133 BC... A fixed star is a celestial object that does not seem to move (in comparison to the other stars of the night sky). ... Multiwavelength X-ray image of the remnant of Keplers Supernova, SN 1604. ... Timocharis of Alexandria (circa 320 BC - 260 BC) was a Greek astronomer and philosopher. ... Precession of the equinoxes is caused by a polar motion, a change in the orientation of the Earths axis. ...


Previously, Eudoxus of Cnidus in the 4th century B.C. had described the stars and constellations in two books called Phaenomena and Entropon. Aratus wrote a poem called Phaenomena or Arateia based on Eudoxus' work. Hipparchus wrote a commentary on the Arateia - his only preserved work - which contains many stellar positions and times for rising, culmination, and setting of the constellations, and these are likely to have been based on his own measurements. Eudoxus of Cnidus (Greek &#917;&#973;&#948;&#959;&#958;&#959;&#962;) (410 or 408 BC - 355 or 347 BC) was a Greek astronomer, mathematician, physician, scholar and friend of Plato. ... Aratus (Greek Aratos) (ca. ...


Hipparchus made his measurements with an equatorial armillary sphere, and obtained the positions of maybe about 850 stars. It is disputed which coordinate system he used. Ptolemy's catalogue in the Almagest, which is derived from Hipparchus' catalogue, is given in ecliptic coordinates. However Delambre in his Histoire de l'Astronomie Ancienne (1817) concluded that Hipparchus knew and used the equatorial coordinate system, a conclusion challenged by Otto Neugebauer in his A History of Ancient Mathematical Astronomy (1975). Hipparchus seems to have used a mix of ecliptic coordinates and equatorial coordinates: in his commentary on Eudoxos he provides the polar distance (equivalent to the declination in the equatorial system) and the ecliptic longitude. Armillary sphere An armillary sphere (also known as spherical astrolabe) is a model of the celestial sphere, invented by Eratosthenes in 255 BC. Its name comes from the Latin armilla (circle, bracelet), since it has a skeleton made of graduated metal circles linking the poles and representing the equator, the... The ecliptic coordinate system is a celestial coordinate system that uses the ecliptic for its fundamental plane. ... The equatorial coordinate system is probably the most widely used celestial coordinate system, whose equatorial coordinates are: declination () right ascension () -also RA-, or hour angle () -also HA- It is the most closely related to the geographic coordinate system, because they use the same fundamental plane, and the same poles. ... The ecliptic coordinate system is a celestial coordinate system that uses the ecliptic for its fundamental plane. ... The equatorial coordinate system is probably the most widely used celestial coordinate system, whose equatorial coordinates are: declination () right ascension () -also RA-, or hour angle () -also HA- It is the most closely related to the geographic coordinate system, because they use the same fundamental plane, and the same poles. ... In astronomy, declination (dec) is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. ...


Hipparchus' original catalogue has not been preserved today. However, an analysis of an ancient statue of Atlas (the so-called Farnese Atlas) published in 2005 shows stars at positions that appear to have been determined using Hipparchus' data. [1]. In Greek mythology, Atlas was one of the primordial Titans. ... The Farnese Atlas at the Museo Archaeologico Nazionale in Naples, Italy. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ...


As with most of his work, Hipparchus star catalogue has been adopted and expanded by Ptolemy. It has been strongly disputed how much of the star catalogue in the Almagest is due to Hipparchus, and how much is original work by Ptolemy. Statistical analysis (e.g. by Bradly Schaeffer, and others) shows that the classical star catalogue has a complex origin. Ptolemy has even been accused of fraud for stating that he re-measured all stars: many of his positions are wrong and it appears that in most cases he used Hipparchus' data and precessed them to his own epoch three centuries later, but using an erroneous (too small) precession constant.


In any case the work started by Hipparchus has had a lasting heritage, and has been worked on much later by Al Sufi (964), and by Ulugh Beg as late as 1437. It was superseded only by more accurate observations after invention of the telescope. Al Sufi from The Depiction of Celestial Constellations Abd Al-Rahman Al Sufi ( December 7, 903 &#8211; May 25, 986) was a Persian astronomer also known as Abd ar-Rahman as-Sufi, or Abd al-Rahman Abu al-Husain, and known in the west as Azophi. ... Events Nicephorus II begins campaign to recapture Cilicia. ... Ulugh Beg, here depicted on a Soviet stamp, was one of Islams greatest astronomers during the Middle Ages. ... // Events foundation of All Souls College, University of Oxford. ... 50 cm refracting telescope at Nice Observatory. ...


Stellar magnitude

Hipparchus ranked stars in six magnitude classes according to their brightness: he assigned the value of one to the twenty brightest stars, to weaker ones a value of two, and so forth to the stars with a class of six, which can be barely seen with the naked eye. A similar system is still used today. // Headline text HEY!! HOW ARE YOU ALL?? Its nice of you to come read this page. ...


Precession of the equinoxes (146 BC-130 BC)

See also Discovery of precession

Hipparchus is perhaps most famous for having discovered the precession of the equinoxes. His two books on precession, On the Displacement of the Solsticial and Equinoctial Points and On the Length of the Year, are both mentioned in the Almagest of Claudius Ptolemy. According to Ptolemy, Hipparchus measured the longitude of Spica and other bright stars. Comparing his measurements with data from his predecessors, Timocharis and Aristillus, he realized that Spica had moved 2° relative to the autumnal equinox. He also compared the lengths of the tropical year (the time it takes the Sun to return to an equinox) and the sidereal year (the time it takes the Sun to return to a fixed star), and found a slight discrepancy. Hipparchus concluded that the equinoxes were moving ("precessing") through the zodiac, and that the rate of precession was not less than 1° in a century. Precession of the equinoxes is caused by a polar motion, a change in the orientation of the Earths axis. ... Precession refers to a change in the direction of the axis of a rotating object. ... An equinox is one of two opposite points on the celestial sphere where the celestial equator and ecliptic intersect. ... Almagest is the Latin form of the Arabic name (al-kitabu-l-mijisti, i. ... A medieval artists rendition of Claudius Ptolemaeus Claudius Ptolemaeus (Greek: ; c. ... Spica (α Vir / α Virginis / Alpha Virginis) is the brightest star in the constellation Virgo, and one of the brightest stars in the nighttime sky. ... Timocharis of Alexandria (circa 320 BC - 260 BC) was a Greek astronomer and philosopher. ... For the crater, see Aristillus (crater). ... Illumination of Earth by Sun on the day of equinox The autumnal equinox (or fall equinox) marks the beginning of astronomical autumn. ... A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). ... The orbital period is the time it takes a planet (or another object) to make one full orbit. ...


Ptolemy followed up on Hipparchus' work in the 2nd century. He confirmed that precession affected the entire sphere of fixed stars (Hipparchus had speculated that only the stars near the zodiac were affected), and concluded that 1° in 100 years was the correct rate of precession. The modern value is 1° in 72 years.


Hipparchus and astrology

As far as is known, Hipparchus never wrote about astrology, i.e. the application of astronomy to the practice of divination. Nevertheless the work of Hipparchus dealing with the calculation and prediction of celestial positions would have been very useful to those engaged in astrology. Astrology developed in the Greco-Roman world during the Hellenistic period, borrowing many elements from Babylonian astronomy; some historians have suggested that Hipparchus played a key role in this. Remarks made by Pliny the Elder in his Natural History Book 2.24, suggest that some ancient authors did regard Hipparchus as an important figure in the history of astrology. Pliny claimed that Hipparchus "can never be sufficiently praised, no one having done more to prove that man is related to the stars and that our souls are a part of heaven." Hand-coloured version of the anonymous Flammarion woodcut. ... This article is about the religious practice of divination. ... Hand-coloured version of the anonymous Flammarion woodcut. ... In modern Olympic and amateur wrestling, Greco-Roman wrestling is a particular style and variation. ... The term Hellenistic (established by the German historian Johann Gustav Droysen) in the history of the ancient world is used to refer to the shift from a culture dominated by ethnic Greeks, however scattered geographically, to a culture dominated by Greek-speakers of whatever ethnicity, and from the political dominance... Babylonia was an ancient state in Iraq), combining the territories of Sumer and Akkad. ... Pliny the Elder: an imaginative 19c portrait. ... For the span of recorded history starting roughly 5,000-5,500 years ago, see Ancient history. ... The History of astrology encompasses a great span of human history and many cultures. ...


Named after Hipparchus

The ESA's Hipparcos Space Astrometry Mission was named after him, as are the Hipparchus lunar crater and the asteroid 4000 Hipparchus. The European Space Agency (ESA), established in 1975, is an inter-governmental organization dedicated to the exploration of space, currently with 17 member states. ... Hipparcos (for High Precision Parallax Collecting Satellite) was an astrometry mission of the European Space Agency (ESA) dedicated to the measurement of stellar parallax and the proper motions of stars. ... Hipparchus is the degraded remnant of a lunar crater. ... 253 Mathilde, a C-type asteroid. ...


See also

// Headline text HEY!! HOW ARE YOU ALL?? Its nice of you to come read this page. ... This article does not cite its references or sources. ... The History of astrology encompasses a great span of human history and many cultures. ... Geminus of Rhodes was a Greek astronomer and mathematician. ... Centuries: 2nd century BC - 1st century BC - 1st century Decades: 60s BC 50s BC 40s BC 30s BC 20s BC - 10s BC - 0s 10s 20s 30s 40s Years: 15 BC 14 BC 13 BC 12 BC 11 BC 10 BC 9 BC 8 BC 7 BC 6 BC 5 BC... Events Boudicca sacks London (approximate date). ... Chandra X-ray Image of Mira Mira (ο Cet / 68 Ceti / HD14386 / HIP10826 / ADS 1778 AP / Omicron Ceti) is a binary star in the constellation Cetus consisting of the red giant, Mira A or just Mira, and a white dwarf, Mira B or VZ Ceti. ... Mithras and the Bull: This fresco from the mithraeum at Marino, Italy (3rd century) shows the tauroctony and the celestial lining of Mithras cape Mithraism was a mystery religion prominent in the Roman world. ... In astronomy, many stars are referred to simply by catalogue numbers. ...

Notes

  1. ^ For general information on Hipparchus see the following biographical articles: G. J. Toomer, "Hipparchus" (1978); and A. Jones, "Hipparchus."
  2. ^ Modern edition: Karl Manitius (In Arati et Eudoxi Phaenomena, Leipzig, 1894).
  3. ^ B. E. Schaefer, "Epoch of the Constellations on the Farnese Atlas."
  4. ^ Lucio Russo, The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had To Be Reborn, (Berlin: Springer, 2004). ISBN 3-540-20396-6.
  5. ^ For more information see G. J. Toomer, "Hipparchus and Babylonian astronomy."
  6. ^ Franz Xaver Kugler, Die Babylonische Mondrechnung ("The Babylonian lunar computation"), Freiburg im Breisgau, 1900.
  7. ^ Toomer, "The Chord Table of Hipparchus" (1973).

Lucio Russo is an Italian physician, mathematician, and science historian. ...

References

  • Edition and translation: Karl Manitius: In Arati et Eudoxi Phaenomena, Leipzig, 1894.
  • J. Chapront, M. Chapront Touze, G. Francou (2002): A new determination of lunar orbital parameters, precession constant, and tidal acceleration from LLR measurements. Astron.Astrophys. 387, 700-709.
  • A. Jones: "Hipparchus." In Encyclopedia of Astronomy and Astrophysics. Nature Publishing Group, 2001.
  • Patrick Moore (1994): Atlas of the Universe, Octopus Publishing Group LTD (Slovene translation and completion by Tomaž Zwitter and Savina Zwitter (1999): Atlas vesolja), 225.
  • B.E. Schaefer (2005): "The Epoch of the Constellations on the Farnese Atlas and their Origin in Hipparchus's Lost Catalogue." Journal for the History of Astronomy 36, 1-29.
  • N.M. Swerdlow (1969): "Hipparchus on the distance of the sun." Centaurus 14, 287-305.
  • G.J. Toomer (1967): "The Size of the Lunar Epicycle According to Hipparchus." Centaurus 12, 145-150.
  • G.J. Toomer (1973): "The Chord Table of Hipparchus and the Early History of Greek Trigonometry." Centaurus 18, 6-28.
  • G.J. Toomer (1974): "Hipparchus on the Distances of the Sun and Moon." Archives for the History of the Exact Sciences 14, 126-142.
  • G.J. Toomer (1978): "Hipparchus." In Dictionary of Scientific Biography 15: 207-224.
  • G.J. Toomer (1980): "Hipparchus' Empirical Basis for his Lunar Mean Motions," Centaurus 24, 97-109.
  • G.J. Toomer (1988): "Hipparchus and Babylonian Astronomy." In A Scientific Humanist: Studies in Memory of Abraham Sachs, ed. Erle Leichty, Maria deJ. Ellis, and Pamel Gerardi. Philadelphia: Occasional Publications of the Samuel Noah Kramer Fund, 9.

External links

General

  • [4] O'Connor, John J., and Edmund F. Robertson. "Hipparchus (astronomer)". MacTutor History of Mathematics archive.
  • [5] Biographical page at the University of Cambridge
  • [6] University of Cambridge's Page about Hipparchus' sole surviving work
  • [7] Biographical page at the University of Oregon
  • [8] Biography of Hipparchus on Fermat's Last Theorem Blog

The University of Cambridge, located in Cambridge, England, is the second-oldest university in the English-speaking world. ... The University of Oregon is a public university located in Eugene, Oregon. ...

Precession

Celestial bodies

The University of Arizona (UA or U of A) is a land-grant and space-grant public institution of higher education and research located in Tucson, Arizona, United States. ...

Star catalogue

The Farnese Atlas at the Museo Archaeologico Nazionale in Naples, Italy. ...


  Results from FactBites:
 
Hipparchus (astronomer) Encyclopedia (0 words)
Hipparchus is believed to have died on the island of Rhodes, where he spent most of his later life -- Ptolemy attributes observations made on Rhodes in the period from 141 BC to 127 BC to Hipparchus.
Hipparchus was the first to show that the stereographic projection is conformal, and that it transforms circles on the sphere that do not pass through the center of projection to circles on the plane.
Hipparchus ranked stars in six magnitude classes according to their brightness: he assigned the value of one to the twenty brightest stars, to weaker ones a value of two, and so forth to the stars with a class of six, which can be barely seen with the naked eye.
Hipparchus the Astronomer (0 words)
Hipparchus discovered the precession of the equinoxes and was influential in the development of trigonometry, redefined and formalized the projection as a method for solving complex astronomical problems without spherical trigonometry and probably proved its main characteristics.
Hipparchus determined the distance from the Earth to the Moon from observations of a solar eclipse in Syene and in Alexandria.
Hipparchus, according to Ptolemy, considered that the Earth is not the center of the circular orbit of the Sun.
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