Wednesday, August 29, 2007

Hipparchus (190-125 BCE)


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Hipparchus (Greek: Hipparcos), Greek astronomer, mathematician and geographer, born: 190 B.C., Antigoneia since the year 30 Nicaea (Greek: Nikaia) when Cisimah gave its name, ancient district Bithynia, (modern-day Iznik) in province Bursa, in modern day Turkey, died: 120 B.C., probably the island of Rhodes. The exact dates of his life are not known for sure, but he is believed to have observed from 162 to 126 B.C. Date of his birth was calculated by J. B. J. Delambre, based on clues in his work. We don't know anything about his youth either. Most of what is known about Hipparchus is from Strabo's Geographica (Geography), from Pliny the Elder's Naturalis historia (Natural sciences) and from Ptolemy's Almagest. He probably studied in Alexandria. His main original works are lost. His only preserved work is the Commentary on Aratus, a commentary on a poem by Aratus which describes the constellations and the stars which comprise them. This work contains many measurements of stellar positions. For his accession he holds the place of originator and father of scientific astronomy. He is believed to be the greatest Greek astronomer observer and he is at the same time entitled the greatest astronomer of ancient times, although Cicero still though about Aristarchus of Samos. Some put on this place also Ptolemy of Alexandria.

Hipparchus had ranked stars after their brightness in six magnitude classes, what we, as magnitudes , still use today since Ptolemy. He arranged value of 1 to 20 brightest stars, to weaker ones value of 2 and so forth to the stars with a class of 6, which can be barely seen. Later astronomers with telescopes and photographic plates and with other measuring devices for the light had extended a luminosity with a density of light current j of a star on the Earth. Observations with measuring devices for the light had shown that the density of light current of a star with a magnitude 1m is hundred times greater of a star with a magnitude 6m.

Hipparchus had made a lot of astronomical instruments, which were used for a long time with naked-eye observations. About 150 B.C. he made first astrolabe, which was improved in 3rd century by Arab astronomers and brought by them in Europe in 10th century. With astrolabe Hipparchus was able to measure among the first the geographical latitude and time. Gnomon was changed during his time. They put it in a metallic hemisphere, which was devided inside in concentric circles and it used 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 make smaller maps. Hipparchus had proposed to determine the geographical longitudes of several cities at solar eclipses. In fact eclipse doesn't arise simultaneously in all points of the center of the lunar shadow, but his method would give the most accurate data as would any previous one, if it would be correctly carried out. But his method unfortunately never saw its proper usage and for this reason maps were rather inaccurate.

It is thought that Hipparchus compiled the first catalog of stars, and also 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 of A = 2sin(A/2). He had a method of solving spherical triangles. Theorem in plane geometry called Ptolemy's theorem was developed by Hipparchus. This theorem was elaborated on by Lazare Carnot.

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 B.C. an estimation for the length of siderical year to be Sk = 365.2576388d = 365d 6h 11m with an error of 110s. 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. Hipparchus had used almost the basic astronomical instruments gnomon, atrolabe, armiral sphere and so. Before him Meton and his students had determined 440 B.C. the two points of the solstice. Hipparchus on his own in Alexandria 146 B.C. determined the equinoctial point. He used Archimedes' observations of solstices. Year after 145 B.C. also on his own he determined the length of tropical year to be:

TH = 365.24653...d = 365d5h55m12s (TH = 365.24653...d = 365d5h55h elsewhere), which differs from today's T = 365.24219...d = 365d5h48m45s for only 6m27s (6m15s). Before him the Chaldean astronomers knew the lengths of seasons are not equal. Hipparchus fully measured the length of winter and spring to be 184 1/2 days, summer and autumn 180 1/2 days. In his geocentrical view, which he preferred, he explained this fact with adoption 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, linear eccentricity of Earth's orbit and according to J. L. E. Dreyer he got the incorrect value e = 0.04166. The question is if he is really author of this estimation? After that he lived from 141 B.C. to 126 B.C. mostly on the island of Rhodes, again in Alexandria and in Syracuse and around 130 B.C. in Babylon made a lot of precise and lasting observations. When he measured the length of gnomen 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 134 B.C. found the length of siderical year to be SH = 365.2569444...d = 365d6h10m, which differs from today's S = 365.2563657...d = 365d6h9m10s for 50s. Hipparchus 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 siderical. And as first in the history he correctly explained this with retrogradical movement of vernal point V over the ecliptic for about 45" or 46" (36" or 3/4' according to Ptolemy) per annum (today's value is 50,387", 50,26") and he showed the Earth's axis is not fixed in space. After that he 135 B.C. enthusiastic of nova star in constellation of Scorpion with equatorial armiral sphere measured ecliptic 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 modified as late as 1000 years after 964 by A. Ali Sufi and 1500 years after 1437 by M. T. ibn Sh. ibn T. Ulugh Beg. Later, Edmond 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. In his star map Hipparchus 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). This system 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 Hipparchus. By comparing his own measurements of the position of the equinoxes to the star Spica with those of Euclid's contemporaries Timocharis of Alexandria and Aristil 150 years earlier, and the records of Chaldean astronomers and specially Kidinnu's records he still later observed that the equinox had moved 2o relative to Spica. He also noticed this motion in other stars. He obtained a value of not less than 1o in a century. The modern value is 1o 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 couldn't put together Eudoxus' detailed statements with his own observations and observations of that time. From all this he found that coordinates of stars and Sun had systematically changed. Their celestial latitudes L remained unchanged, but their celestial longitudes B had reduced as would equinoctial points, intersections of ecliptic and celestial equator, move with progressive velocity every year for 1/100'. After him many Greek and Arab astronomers had confirmed this phenomenon. Ptolemy compared his catalogue with those of Aristil, 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 25,777 years encircle ecliptical pole. The diameter of these circles is equal to the inclination of ecliptic. The equinoctial points in this time traverse the whole ecliptic and they move for 1o in a century. This velocity is equal to Hipparchus' one. Because of these accordances Delambre, P. Tannery and other French historians 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 V 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 oscillation 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. Luni-solar precession causes the motion of point V by the ecliptic in the opposite direction of 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 the ecliptical plane swings from its central position for + or - 4o in 60,000 years. The angle between ecliptic and celestial equator e = 23o 26' is reducing for 0.47" per annum. Besides the point V slides by equator for p=0.108" per annum now in the same direction as Sun. The sum of precessions gives an annual general precession in longitude P = 50,288" which causes the origination of tropical year.

Hipparchus 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 Johannes 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.

Hipparchus 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 moon. About 139 B.C. he determined the length of synodic month to 23/50s. 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. [This article is licensed under the GNU Free Documentation License and uses material adapted in whole or in part from the Wikipedia article on Hipparchus.]

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