Hipparchos

Life and work

Hipparchus was born in Nicaea (Greek Nikaia), ancient district Bithynia (modern-day İznik[?]) in province Bursa, Turkey).

Most of what is known about Hipparchus is from Ptolemy's Almagest, and in addition from Strabo's Geographia and from Pliny the Elder's Naturalis historia. The exact dates of his life are not known for sure, but he is believed to have made his observations from 162 BC to 127 BC. The date of his birth (circa 190 BC) 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 BC to 127 BC he lived mostly on the island of Rhodes, again in Alexandria, in Siracuse[?], and around 130 BC in Babylon. During this period he made a lot of precise and lasting observations.

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

Hipparchus' only preserved work is the (Commentary) on the Phaenomena of Eudoxus and Aratus [Manitius 1894], a critical commentary in two books on a popular poem by Aratus which is based on the work of Eudoxus of Cnidus, which describes the constellations and the stars that form them. Hipparchus compiled a list of his works, and apparently he wrote 14 other major books, but these were lost like so many other classical Greek works in the Roman period or early Middle Ages (see Library of Alexandria).

Hipparchus 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

Hipparchus and his predecessors used simple astronomical instruments such as the gnomon and armillary sphere. Hipparchus is credited with the invention or improvement of several astronomical instruments, which were used for a long time with naked-eye observations. About 150 BC he made the first "astrolabion", which may have been an armillary sphere or the planar instrument known today as astrolabe. With an astrolabe Hipparchus was 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. 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 had measured the length of Earth's meridian, and after that they used this instrument to survey smaller regions as well. Ptolemy reported that Hipparchus invented an improved type of theodolite with which to measure angles.

Geometry and trigonometry

It is thought that Hipparchus compiled the first trigonometry tables, when computing the eccentricity of the orbit of the Sun. 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 Hipparchus. This theorem was elaborated on by Carnot. 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.

Apparent motion of the Sun

Before him the school of Meton[?] and Euktemon[?] had observed a solstice (June 27, 432 BC proleptic julian calendar), and Aristarchos in 280 BC, and he refers to Archimedes as well. Hipparchus himself observed a solstice in 135 BC and on other occasions. He found observations of the moment of equinox more accurate, and he observed many during his lifetime. From these observations he determined (according to Ptolemy, Almagest III.1) that the tropical year was about 1/300 of a day shorter than the conventional length of 365 + 1/4 day (365^d + 1/4 - 1/300 = 365.2466...^d = 365^d 5^h 55^m). This differes from the actual value (modern estimate) of 365.2423^d = 365^d 5^h 48^m, by only 7^m.

Between the solstice observation of Meton and his own, there were 297 years spanning 108478 days. This implies a tropical year of 365.24579... days = 365^d;14,44,51 (sexagesimal; = 365^d + 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 Hipparchos is 365 + 1/4 + 1/288 days (= 365.253472... days = 365d6h5m), but this may be a corruption of another value attributed to a Babylonian source: 365 + 1/4 + 1/144 days (= 365.25694... days = 365d6h10m). It is not clear if this would be a value for the sidereal year (actual value at his time (modern estimate) 365.2565^d), but the sources appear to be unreliable anyway [Prof. Alexander Jones, personal communication 19-Jun-2003].

Before him the Chaldean astronomers knew the lengths of 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. That were unexpected if the Sun moved around the Earth in a circle at uniform speed. His solution was to place the Earth not at the center of the Sun's motion, but at some distance from the center. Thus he introduced the concept of excentricity. 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 Kepler published his first two laws of planetary motion in 1609). The value for the excentricity attributed to him by Ptolemy (also see Dreyer[?]) 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°ree; 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 questions remains if Hipparchus is really the author of the values provided by Ptolemy.

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 (especially Kidinnu) had obtained before him. The traditional value for the mean synodic month is 29d;31,50,28,20 (sexagesimal) = 29.53059429... d . Expressed as 29d + 12h + 793/1080 h this value has been used later in the Hebrew calendar (possibly from Babylonian sources). The Chaldeans also knew that 251 synodic months = 269 anomalystic 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^d1^h (rounded). Hipparchus could confirm his computations by comparing eclipses from his own time (139 BC), with eclipses from Babylonian records 345 years earlier (Ptolemy, Almagest IV.2; [G.J.Toomer 1981]; [A.Jones 2001]). From modern ephemerides [Chapront et al. 2002] and taking account of the change in the length of the day (see Delta-T) we estimate that the error in the assumed length of the synodic month was less than 0.2^s in the 4^th BC and less than 0.1^s in Hipparchus' time.

Distances and sizes of the Sun and Moon

Hipparchus also undertook to find the distances and sizes of the Sun and the Moon. He determined the Moon's horizontal parallax, which leads to a distance for the Moon.

Star catalogue

After that he 135 BC 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 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

Hipparchus had in 134 BC 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 Hipparchus drew position of every star on the basis of its celestial latitude, (its angular distance from the ecliptic plane) and its celestial longitude (its angular distance from a reference point, for which he chose the 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 a coordinate net not until Hipparchus.

Hipparchus 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 more accurate data than 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 BC - 130 BC)

Hipparchus 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 Hipparchus 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 BC 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 BC. 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-260 BC) 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 2000 BC 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) - Hipparchus' commentary contains many precise times for rising, culmination, and setting of the constellations treated inn the Phaenomena, and these are likely to have been based on measurements of stellar positions[?] - and Enoptron (Mirror of Nature) of Eudoxus of Cnidus, who had near Cyzicus on the southern coast of the Marmara Sea 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", 46" or 47" (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, Hipparchus and the observations of Agrippa and Menelaus of Alexandria from the early 1st century and he finally confirmed Hipparchus 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 Hipparchus' 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 Hipparchus' 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 Hipparchus' 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.

Celestial coordinate systems

Delambre in his Histoire de l'Astronomie Ancienne (1817) concluded that Hipparchus knew and used a real (celestial) equatorial coordinate system, directly with the right ascension and declination (or with its complement, polar distance). After that Otto Neugebauer[?] (1899-1990) in his A History of Ancient Mathematical Astronomy (1975) rejected Delambre's claims.

An astrometric project of the Hipparcos Space Astrometry Mission of the European Space Agency (ESA) was named after him.

See also:

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

External links

General:

• Hipparchus mentioned in a history of mankind: http://www.hkupasteur.hku.hk/hkuip/causeries/Antiquity
• A brief view by Carmen Rush on Hipparchus' 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/Hipparchus
• University of Cambridge's page: http://www.hps.cam.ac.uk/starry/Hipparchus
• University of Cambridge's page about Hipparchus' sole surviving work: http://www.hps.cam.ac.uk/starry/hipppoem
• University of Oregon[?]'s page: http://zebu.uoregon.edu/~js/glossary/hipparchus

Precession:

• Cavendish Laboratory briefly about Hipparchus' 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 Hipparchus's understanding of the precession: http://www.well.com/user/davidu/appendix4

Literature

Edition and translation: Karl Manitius[?]: In Arati et Eudoxi Phaenomena, Leipzig, 1894.

G.J.Toomer (1978): Hipparchus in "Dictionary of Scientific Biography" 15, 207..224

G.J.Toomer (1981): "Hipparchus' Empirical Basis for his Lunar Mean Motions", Centaurus 24, 97..109 .

A.Jones: Hipparchus in "Encyclopedia of Astronomy and Astrophysics", Nature Publishing Group, 2001.

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.