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Hipparchos (Latinized Hipparchus) (ca. 190 B.C. - ca. 120 B.C.) was a Greek astronomer, mathematician and geographer.

Table of contents 1 Life and work 2 Astronomical instruments and astrometry 3 Geometry and trigonometry 4 Apparent motion of the Sun 5 Motion of the Moon 6 Star catalogue 7 Brightness of stars 8 Geography 9 Precession of the equinoxes (146 B.C.-130 B.C.) 10 See also: 11 External links

Life and work

Hipparchos was born in Nicaea (Greek Nikaia), ancient district Bithynia (modern-day Iznik[?] in 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 B.C. to 126 B.C.. The date of his birth was calculated by 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 B.C. to 126 B.C. he lived mostly on the island of Rhodes, again in Alexandria, in Siracuse[?], and around 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 constellations and the stars that form them. This work contains many measurements of stellar positions[?]. 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.

Astronomical instruments and astrometry

Hipparchos had made a lot of astronomical instruments, which were used for a long time with naked-eye observations. About 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 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 sine of half of the angle, e.g., chord(A) = 2* sin(A/2). He had a method of solving spherical triangles[?]. The theorem in plane geometry called Ptolemy's theorem was developed by Hipparchos. This theorem was elaborated on by Carnot. He 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.

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 B.C. (431 B.C.) the two points of the solstice. Hipparchos on his own in Alexandria 146 B.C. determined the equinoctial point. He used Archimedes' observations of solstices. Hipparchos himself made several observations of the solstices and equinoxes. From these observations a year after in 145 B.C. he also on his own determined the length of the tropical year to be T_H = 365.24653...^d = 365^d 5^h 55 ^m 12 ^s (365^d + 1/4 - 1/300 = 365.24666...^d = 365^d 5^h 55 ^m), which differes from the actual value (modern estimate) T = 365.24219...^d = 365^d 5^h 48^m 45^s by only 6^m 27^s (6^m 15^s) (365.2423^d = 365^d 5^h 48^m, by only 7^m).

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 sunsets and times of sunrises. From all of these measurements he found in 134 B.C. the length of sidereal year to be S_H = 365^d 6^h 10^m (365.2569444...^d), which differs from today's S = 365.2563657...^d = 365^d 6^h 9^m 10^s for 50^s. Hipparchos also had measurements of the times of solstices from Aristarchus dating from 279 B.C. and from the school of Meton and Euctemon dating from 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 planets move in ellipses, but this was not discovered until 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 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 B.C. he determined the length of synodic month to 23/50^s. 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 2m,

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

Star catalogue

After that he 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 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, 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 Hoyle.

Brightness of stars

Hipparchos had in 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 telescopes, photographic plates, 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 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 eclipses. 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 equinoxes. There is some suggestion that the Babylonians may have known about precession but it appears that Hipparchos was to first to really understand it and measure it. According to al-Battani Chaldean astronomers had distinguished the tropical and siderical year. He stated they had around 330 B.C. an estimation for the length of the sidereal year to be S_K = 365^d 6^h 11^m (= 365.2576388^d) with an error of (about) 110^s. This phenomenon was probably also known to Kidinnu around 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 B.C.-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 B.C. he still later observed that the equinox had moved 2° relative to Spica. He also noticed this motion in other stars. He obtained a value of not less than 1° in a century. The modern value is 1° 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 λ ramained unchanged, but their celestial longitudes β 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 retrogradical movement of vernal point γ over the ecliptic for about 45" or 46" (36" or 3/4' according to Ptolemy) per annum (today's value is Ψ'=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° 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 γ leads the Sun. In 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, Newton's general gravitational law, which had explained it in full, Euler's kinematic equations and Lagrange's equations of motion, d'Alembert's dynamical theory of the movement of the rigid body, some algebraic solutions for special cases of precession, Flamsteed's and Bradley's difficulties in making of precise telescopic star catalogues, Bessel's and Newcomb's[?] measurements of precession and finally the precession of perihelion in Einstein's General Theory of Relativity.

Lunisolar precession[?] causes the motion of point γ 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 ±4° in 60000 years. The angle between ecliptic and celestial equator ε = 23° 26' is reduceing for 0.47" per annum. Besides the point γ 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 Ψ = 50.288" which causes the origination of tropical year.

See also:

• Apparent magnitude
• Astrometry
• Geminus[?] (of Rhodes) (10 BC - circa 60)
• Mira
• Mithraism
• Star catalogues

External links

General:

• Hipparchos mentioned as Hipparchos in a history of mankind: http://www.hkupasteur.hku.hk/hkuip/causeries/Antiquity
• A brief view by Carmen Rush on Hipparchos' stellar catalogue: http://ottawa.rasc.ca/astronomy/astro_facts/hipparcus
• A lot of original Wikipedian article (upto 2002-09-20) was transformed here (this is pretty much encouraging for us 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
• University of Cambridge's page: http://www.hps.cam.ac.uk/starry/Hipparchos
• University of Cambridge's page about Hipparchos' sole surviving work: http://www.hps.cam.ac.uk/starry/hipppoem
• University of Oregon[?]'s page: http://zebu.uoregon.edu/~js/glossary/Hipparchos

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
• David Ulansey about Hipparchos's understanding of the precession:

http://www.well.com/user/davidu/appendix4