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'''Hipparchos''' ([[Latin language|Latinized]] ''Hipparchus'') (ca. [[190 BC|190 B.C.]] - ca. [[120 BC|120 B.C.]]) was a [[Greeks|Greek]] [[astronomer]], [[mathematician]] and [[geographer]].

=== Life and work ===
Hipparchos was born in [[Nicaea]] (Greek ''Nikaia''), ancient district [[Bithynia]] (modern-day [[Iznik]] in province [[Bursa Province|Bursa]], [[Turkey]]). 

Most of what is known about Hipparchos is from [[Strabo]]'s ''Geographica'' (''Geography''), from [[Pliny the Elder]]'s ''Naturalis historia'' (''Natural sciences'') and from [[Ptolemy]]'s ''Almagest''.  The exact dates of his life are not known for sure, but he is believed to have made his observations from [[162 BC|162 B.C.]] to [[126 BC|126 B.C.]]. The date of his birth was calculated by [[Jean Baptiste Joseph Delambre|Delambre]], based on clues in his work. We don't know anything about his youth either.  He probably studied in [[Alexandria]].  After that from [[141 BC|141 B.C.]] to [[126 BC|126 B.C.]] he lived mostly on the island of [[Rhodes]], again in [[Alexandria]], in [[Siracuse]], and around [[130 BC|130 B.C.]] in Babylon.  During this period he made a lot of precise and lasting observations.

Hipparchos is believed to have died on the island of [[Rhodes]], where he spent most of his later life. 

His main original works are lost. His only preserved work is the ''(Commentary) on the Phaenomena of Eudoxus and Aratus'' or ''Commentary on Aratus'', a commentary in 2 books on a poem by [[Aratus]], which describes the [[constellation]]s and the [[star]]s that form them.  This work contains many measurements of [[stellar position]]s.  All his other works were lost in a burning of the Great [[Alexandrian Library]] in [[642]].

Hipparchos is recognised as originator and father of scientific [[astronomy]]. He is believed to be the greatest Greek astronomer observer, and many regard him as the greatest astronomer of ancient times, although [[Cicero]] gave preference to [[Aristarchus of Samos]]. Some put on this place also [[Ptolemy]] of Alexandria.

=== [[measuring instrument|Astronomical instrument]]s and [[astrometry]] ===
Hipparchos had made a lot of astronomical instruments, which were used for a long time with naked-eye observations. About [[150 BC|150 B.C.]] he made the first [[astrolabe]], which was improved in 3rd century by Arab astronomers and brought by them in Europe in [[10th century]]. With an astrolabe Hipparchos was among the first able to measure the geographical [[latitude]] and time. Previously this was done with a ''[[gnomon]]'', but the way this was used changed during his time. They put it in a metallic hemisphere, which was divided inside in concentric circles, and used it as a portable instrument, named ''scaphion'', for determination of geographical coordinates from measured solar altitudes. With this instrument [[Eratosthenes]] of Cyrene [[220 BC|220 B.C.]] had measured the length of Earth's meridian, and after that they used this instrument to survey smaller regions as well.
Ptolemy reported that Hipparchos invented an improved type of [[theodolite]] with which to measure [[angles]].

=== Geometry and trigonometry ===
It is thought that Hipparchos compiled the first [[trigonometry]] tables.  He tabulated values for the chord function, which gave the length of the chord for each angle. In modern terms, the chord of an angle equals twice the [[Trigonometric function|sine]] of half of the angle, e.g., chord(''A'') = 2* sin(''A''/2). He had a method of solving [[spherical triangle]]s. The [[theorem]] in [[plane geometry]] called ''Ptolemy's theorem'' was developed by Hipparchos. This theorem was elaborated on by [[Lazare Carnot|Carnot]]. He was the first to show that the [[stereographic projection]] is [[conformal map|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]].

=== Apparent motion of the Sun ===
Hipparchos had used almost basic astronomical instruments such as the [[gnomon]], [[astrolabe]], [[armillary sphere]] and so. Before him [[Meton]],  [[Euktemon]] and their students had determined [[440 BC|440 B.C.]] ([[431 BC|431 B.C.]]) the two points of the solstice. Hipparchos on his own in Alexandria [[146 BC|146 B.C.]] determined the [[equinox|equinoctial point]]. He used [[Archimedes]]' observations of solstices. Hipparchos himself made several observations of the [[solstice]]s and [[equinox]]es. From these observations a year after in [[145 BC|145 B.C.]] he also on his own determined the length of the [[tropical year]] to be  T<sub>H</sub> = 365.24653...<sup>d</sup> = 365<sup>d</sup> 5<sup>h</sup> 55 <sup>m</sup> 12 <sup>s</sup> (365<sup>d</sup> + 1/4 - 1/300 = 365.24666...<sup>d</sup> = 365<sup>d</sup> 5<sup>h</sup> 55 <sup>m</sup>), which differes from the actual value (modern estimate) T = 365.24219...<sup>d</sup> = 365<sup>d</sup> 5<sup>h</sup> 48<sup>m</sup> 45<sup>s</sup> by only 6<sup>m</sup> 27<sup>s</sup> (6<sup>m</sup> 15<sup>s</sup>) (365.2423<sup>d</sup> = 365<sup>d</sup> 5<sup>h</sup> 48<sup>m</sup>, by only 7<sup>m</sup>).

When he measured the length of gnomon shadow at solstice he determined the length of tropical year and he was finding times of the known bright star starsets and times of starrises. From all of these measurements he found in [[134 BC|134 B.C.]] the length of [[sidereal year]] to be S<sub>H</sub> = 365<sup>d</sup> 6<sup>h</sup> 10<sup>m</sup> (365.2569444...<sup>d</sup>), which differs from today's S = 365.2563657...<sup>d</sup> = 365<sup>d</sup> 6<sup>h</sup> 9<sup>m</sup> 10<sup>s</sup> for 50<sup>s</sup>. Hipparchos also had measurements of the times of solstices from Aristarchus dating from [[279 BC|279 B.C.]] and from the school of Meton and Euctemon dating from [[431 BC|431 B.C.]]. This was a long enough period of time to allow him to calculate the difference between the length of the sidereal year and the tropical year, and led him to the discovery of precession. When he compared both lengths, he saw the tropical year is shorter for about 20 minutes from sidereal.

Hipparchos described the motion of the [[Sun]] and obtained a value for the eccentricity. It was known that the seasons were of unequal length, not something that would be expected if the Sun moved around the Earth in a circle at uniform speed (of course today we know that the [[planet]]s move in [[ellipse]]s, but this was not discovered until [[Johannes Kepler|Kepler]] published his first two laws of planetary motion in [[1609]]). His solution was to place the Earth not at the center of the Sun's motion, but at distance from the center. This model of the Sun's motion described the actual motion of the Sun fairly well.
Before him the Chaldean astronomers knew the lengths of seasons are not equal. Hipparchos measured the full length of winter and spring to be 184 1/2 days, and of summer and autumn 180 1/2 days. In his geocentrical view, which he preferred, he explained this fact with the apoption that the Earth is not in the centre of Sun's orbit around it, but it lies eccentrically for 1/24 r. With his estimation of the length of seasons he tried to determine, as of today, the eccentricity of Earth's orbit, and according to [[John Dreyer|Dreyer]] he got the incorrect value ''e'' = 0.04166 (which is too large). The questions remains if he is really the author of this estimation.

=== Motion of the Moon ===
Hipparchos also studied the motion of the [[Moon]] and obtained more accurate measurements of some periods of the motion than existed previously, and undertook to find the distances and sizes of the Sun and the Moon. About [[139 BC|139 B.C.]] he determined the length of [[synodic month]] to 23/50<sup>s</sup>. He determined the Moon's horizontal [[parallax]]. He discovered the irregularity in lunar movement, which changes medium lunar longitude and today is called ''equalization of the center'' with a value:

: ''I'' = 377' sin ''m'' + 13' sin 2''m'',

where ''m'' is ''medium [[anomaly]]'' of the Moon.

=== Star catalogue ===
After that he [[135 BC|135 B.C.]] enthusiastic of [[nova]] star in constellation of [[Scorpius]] with [[equatorial armillary sphere]] measured ecliptical coordinates of about 850 (1600 or 1080, which is false quoted many times elsewhere) and till [[129 BC|129 B.C.]] he made first big [[star catalogue]].

This map served him to find any changes on the sky and for great sadness it is not preserved today. His star map was thoroughly modificated as late as 1000 years after [[964]] by A. Ali Sufi and 1500 years after [[1437]] by [[Ulugh Beg]]. Later, [[Edmond Halley|Halley]] would use his star catalog to discover proper motions as well. His work speaks for itself. And another sad fact is that we do not know almost nothing from his life, what was already stressed by [[Fred Hoyle|Hoyle]].

=== Brightness of stars ===
Hipparchos had in [[134 BC|134 B.C.]] ranked stars in six magnitude classes according to their brightness: he assigned the value of 1 to the 20 brightest stars, to weaker ones a value of 2, and so forth to the stars with a class of 6, which can be barely seen with the naked eyes. This was later adopted by [[Ptolemy]], and modern astronomers with [[telescope]]s, [[photographic plate]]s, and with other light detectors, extended this system and put it on a quantitative basis; see [[Apparent magnitude]].  

=== Geography ===
In his star map Hipparchos drew position of every star on the basis of its celestial latitude, (its angular distance from the [[celestial equator]]) and its celestial longitude (its angular distance from an arbitrary point, for instance as is custom in astronomy from vernal equinox). The system from his star map was also transferred to maps for Earth. Before him longitudes and latitudes were used by [[Dicaearchus]] of [[Messina, Italy|Messana]], but they got their meanings in coordinate net not until Hipparchos.

Hipparchos had proposed to determine the geographical longitudes of several cities at [[solar eclipse]]s. An eclipse does not occur simultaneously at all places on Earth, and their difference in longitude can be computed from the difference in time when the eclipse is observed. His method would give the most accurate data as would any previous one, if it would be correctly carried out. But it was never properly applied, and for this reason maps remained rather inaccurate until modern times.

=== Precession of the equinoxes (146 B.C.-130 B.C.)===
Hipparchos is perhaps most famous for having been the first to measure the [[precession]] of the [[equinox]]es. There is some suggestion that the [[Babylonian literature and science|Babylonians]] may have known about precession but it appears that Hipparchos was to first to really understand it and measure it. According to [[Albategnius|al-Battani]] [[Chaldea|Chaldean]] astronomers had distinguished the [[tropical year|tropical]] and [[sidereal year|siderical year]]. He stated they had around [[330 BC|330 B.C.]] an estimation for the length of the sidereal year to be  S<sub>K</sub> = 365<sup>d</sup> 6<sup>h</sup> 11<sup>m</sup> (= 365.2576388<sup>d</sup>) with an error of (about) 110<sup>s</sup>. This phenomenon was probably also known to [[Kidinnu]] around [[314 BC|314 B.C.]]. A. Biot and Delambre attribute the discovery of precession also to old Chinese astronomers.

By comparing his own measurements of the position of the equinoxes to the star Spica during a lunar eclipse at the time of equinox with those of Euclid's contemporaries [[Timocharis]] (circa [[320 BC|320 B.C.]]-[[260 BC|260 B.C.]]) of Alexandria and [[Aristyllus]] 150 years earlier, the records of Chaldean astronomers and specially Kidinnu's records and observations of a temple in [[Thebes]], Egypt that was built in around [[3200 BC|3200 B.C.]] he still later observed that the equinox had moved 2&deg; relative to Spica. He also noticed this motion in other stars. He obtained a value of not less than 1&deg; in a century. The modern value is 1&deg; in 72 years. 

He also knew the works ''Phainomena'' (''Phenomena'') and ''Enoptron'' (''Mirror of Nature'') of [[Eudoxus of Cnidus]], who had near [[Cyzicus]] on the southern coast of the Sea of Marmara his school and through Aratus' astronomical epic poem ''Phenomena'' Eudoxus' sphere, which was made from metal or stone and where there were marked constellations, brightest stars, [[tropic of Cancer]] and [[tropic of Capricorn]]. These comparisons embarrassed him because he couln't put together Eudoxus' detailed statements with his own observations and observations of that time. From all this he found that coordinates of the stars and the Sun had systematically changed. Their celestial latitudes &lambda; ramained unchanged, but their celestial longitudes &beta; had reduced as would equinoctial points, intersections of ecliptic and celestial equator, move with progressive velocity every year for 1/100'.

And as first in the history he correctly explained this with [[retrograde motion|retrogradical]] movement of [[vernal point]] &gamma; over the ecliptic for about 45" or 46" (36" or 3/4' according to Ptolemy) per annum (today's value is &Psi;'=50.387", 50.26") and he showed the Earth's axis is not fixed in space. 
After him many Greek and Arab astronomers had confirmed this phenomenon.
Ptolemy compared his catalogue with those of Aristyllus, Timocharis, Hipparchos and the observations of [[Agrippa]] and [[Menelaus]] of Alexandria from the early [[1st century]] and he finally confirmed Hipparchos empirical fact that poles of celestial equator in one Platonic year or approximately in 25777 years encircle [[ecliptical pole]]. The diameter of these cicles is equal to the inclination of ecliptic. The equinoctial points in this time traverse the whole ecliptic and they move for 1&deg; in a century. This velocity is equal to Hipparchos' one. Because of these accordances Delambre, P. Tannery and other French historian of astronomy had wrongly jumped to conclusions that Ptolemy recorded his star catalogue from Hipparchos' one with an ordinary extrapolation. This was not known until [[1898]] when Marcel Boll and the others had found that Ptolemy's catalogue differs from Hipparchos' one not only in the number of stars but otherwise. 

This phenomenon was named by Ptolemy just because the vernal point &gamma; leads the Sun. In [[Latin language|Latin]] ''praecesse'' means to overtake or to outpass and today means to twist or to turn too. Its own name shows this phenomenon was discovered practically before its theoretical explanation, otherwise would be named with a better term. Many later astronomers, physicists and mathematicians had occupied themselves with this problem, practically and theoretically. The phenomenon itself had opened many new promising solutions in several branches of [[celestial mechanics]]: Thabit's theory of trepidation and oscilation of equinoctial points, [[Isaac Newton|Newton's]] [[gravitation|general gravitational law]], which had explained it in full, [[Leonhard Euler|Euler's]] kinematic equations and [[Joseph Louis Lagrange|Lagrange's]] [[Lagrangian mechanics|equations of motion]], [[Jean Le Rond d'Alembert|d'Alembert's]] dynamical theory of the movement of the rigid body, some algebraic solutions for special cases of precession, [[John Flamsteed|Flamsteed's]] and [[James Bradley|Bradley's]] difficulties in making of precise telescopic star catalogues, [[Friedrich Bessel|Bessel's]] and [[Simon Newcomb|Newcomb's]] measurements of precession and finally the precession of perihelion in [[Albert Einstein|Einstein's]] [[General relativity|General Theory of Relativity]].

[[Lunisolar precession]] causes the motion of point &gamma; by the ecliptic in the opposite direction od apparent solar year's movement and the circulation of [[celestial pole]]. This circle becomes a spiral because of additional ascendancy of the planets. This is [[planetary precession]] where ecliptical plane swings from its central position for &plusmn;4&deg; in 60000 years. The angle between ecliptic and celestial equator &epsilon; = 23&deg; 26' is reduceing for 0.47" per annum. Besides the point &gamma; slides by equator for ''p'' = 0.108" per annum now in the same direction as the Sun. The sum of precessions gives an annual ''general precession in longitude'' &Psi; = 50.288" which causes the origination of tropical year.


=== '''See also:''' ===
*[[Apparent magnitude]]
*[[Astrometry]]
*[[Geminus]] (of Rhodes) ([[10 BC]] - circa [[60]]) 
*[[Mira]]
*[[Mithraism]]
*[[Star catalogue]]s

=== External links ===

'''General:'''
* Hipparchos mentioned as Hipparchos in a history of mankind: http://www.hkupasteur.hku.hk/hkuip/causeries/Antiquity.html
* A brief view by Carmen Rush on Hipparchos' stellar catalogue:  http://ottawa.rasc.ca/astronomy/astro_facts/hipparcus.html
* A lot of original Wikipedian article (upto 2002-09-20) was transformed here (''this is pretty much encouraging for us [[Wikipedia:Wikipedians|Wikipedians]], but we must consider Hoyle's note that many defectiveness or inaccuracies may still be present inhere''): http://www.malaspina.com/site/person_639.asp
* [[University of St. Andrews]]' page: http://www-groups.dcs.st-and.ac.uk/history/Mathematicians/Hipparchos.html
* [[University of Cambridge]]'s page: http://www.hps.cam.ac.uk/starry/Hipparchos.html
* University of Cambridge's page about Hipparchos' sole surviving work: http://www.hps.cam.ac.uk/starry/hipppoem.html
* [[University of Oregon]]'s page: http://zebu.uoregon.edu/~js/glossary/Hipparchos.html
'''Precession:'''
* Cavendish Laboratory briefly about Hipparchos' [[celestial dynamics]] and generally about the precession of the Earth's main axis: http://www.inference.phy.cam.ac.uk/teaching/dynamics/p0.html
* David Ulansey about Hipparchos's understanding of the precession:
http://www.well.com/user/davidu/appendix4.html