Griechische Astronomie: Hipparchos
Hipparchus before-mentioned, who 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, detected a new star that came into existence during his lifetime; the movement of this star in its line of radiance led him to wonder whether this was a frequent occurrence, whether the stars that we think to be fixed are also in motion; and consequently he did a bold thing, that would be reprehensible even for God - he dared to schedule the stars for posterity, and tick off the heavenly bodies by name in a list, devising machinery by means of which to indicate their several positions and magnitudes, in order that from that time onward it might be possible easily to discern not only whether stars perish and are born, but whether some are in transit and in motion, and also whether they increase and decrease in magnitude - thus bequeathing the heavens as a legacy to all mankind, supposing anybody had been found to claim that inheritance! Pliny, Natural History, Book 2) 77 AD on Hipparchus
Hipparchus of Rhodes (called also Hipparchus of Nicaea or Hipparchus of Bithynia) (c. 190 – 120 BC) is one of the greatest astronomers of all times. He was born in Nicaea in Bithynia (today Turkey) and he made astronomical observations in Nicaea, Rhodes and in Alexandria.
Ptolemy produced with the Almagest the most important book of astronomy for around 1500 years but for this work the contribution of the earlier work of Hipparchus was very important. Almost none of Hipparchus books survived except a commentary on Phainomena of Eudoxus and Aratus of Soli. We know the work of Hipparchus from Ptolemy's Almagest and from comments of others.
The Chord, Crd(a), that was calculated by Hipparchus as a function of the angle a.
Hipparchus generated a Chord table that is in principle a sine table. He used linear interpolation to construct the “chord function”, which is similar to a sinusoidal function, to compute positions of celestial bodies.
It is not known just when the systematic use of the 360° circle came into mathematics, but it seems to be due largely to Hipparchus in connection with his table of chords. It is possible that he took over from Hypsicles, who earlier had divided the day into 360 parts, a sub-division that may have been suggested by Babylonian astronomy. Hipparchus was a transitional figure between Babylonian astronomy and the work of Ptolemy. Boyer 1991
Based on Babylonian observations, he improved the accuracy of the length of the lunar, solar and sidereal years. He estimated the solar year with an accuracy which is only 6 1/2 minutes different from the current value. For the lunar month he obtained a value of 29 days, 12 hours, 44 minutes and 2 ½ seconds, only less than 1 second from the current value!
The tropical (solar) year is the period of the Sun's apparent revolution from an equinox to the same equinox again (The time reference that we use in everyday life), and the sidereal year is the period of the Sun's apparent revolution from a fixed star to the same fixed star.
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 produced until 129 BC a catalogue of 850 stars after observing 134 BC a new star in the sky. This catalogue was of high precision and used even by the astronomer Edmund Halley. Hipparchus compared his star positions with those of Timocharis and Aristillus. He could not find any stars that had appeared or disappeared in the last 150 years but all the stars seemed to have changed their places with reference to that point in the heavens where the ecliptic is 90° from the poles of the earth i.e. the equinox. He found that this could be explained by a motion of the equinox in the direction of the apparent diurnal motion of the stars. He found the precession of the equinoxes, which takes place at the rate of 52",1 every year due to a steady revolution of the earth's pole round the pole of the ecliptic once in 26000 years in the opposite direction to the planetary revolutions.
The precession, a very slow conical motion around the orbital axis. It takes 26000 years for the axis to make one full circle!
(The Precession was probably known to the Chaldean Astronomers much earlier). What Hipparchus observed of course was not the motion of the Earth itself but a movement of the celestial equator relative to the ecliptic.
Hipparchus determined the distance from the Earth to the Moon from observations of a solar eclipse in Syene and in Alexandria.
During a solar eclipse that was a total eclipse at Syene and a partial eclipse at Alexandria an observer in Syene saw the entire Sun blocked by the Moon while at the same time another observer at Alexandria saw 1/5th of the Sun's disk, that is 1/5th of 30 arcminutes of the Sun's disk was visible. The Sun's angular diameter is 30 arcminutes or 1/2 degree. The angular size of the visible Sun seen at Alexandria therefore is 0.1 degree. This angle expressed in radians and applying the small angle approximation gives the ratio of the Syene-Alexandria distance to the Earth-Moon distance. Hipparchus determined the the earth-moon distance of 250000 miles, a very good approximation.
Hipparchus, according to Ptolemy, considered that the Earth is not the center of the circular orbit of the Sun. From his observations Hipparchus used epicycles and deferents to describe the elliptic motion of the planets and the moon, an idea that later Ptolemy used in his model. Hipparchus measurements were so accurate that he knew that his model is only an approximation especially for the complicated motion of the moon.
It is strange but he was so accurate using real scientific methods so that finally he rejected the correct Heliocentric model of Aristarchus. In this way he probably contributed through his influence later on Ptolemy that the Heliocentric model was not accepted. The problem is that the lack of astronomical instruments like the telescope and the real incredible distances of the stars did not permit to confirm a Heliocentric model since phenomena like the Parallax could not be seen at that time. Hipparchus was probably the greatest Astronomer of antiquity but as his work survived mainly in the Almagest of Ptolemy it is Ptolemy who was one if not the most influential astronomer in history.
Information about Hipparchus from
Pappus of Alexandria
Theon of Alexandria
Pliny the Elder, Naturalis historia
Carl B. Boyer, A History of Mathematics. John Wiley & Sons, Inc. 1991
George Forbes, History of Astronomy.
Dennis W. Duke, Hipparchus’ Coordinate System, Archive for the History of Exact Sciences, 56 (2002) 427-433. (PDF File)
Greek Astronomy , Heath, Dover Publications, Incorporated, 1991 reprint (from 1932 original)
From Eudoxus to Einstein: A History of Mathematical Astronomy C.M. Linton. Cambridge, UK ; New York : Cambridge University Press, 2004
Hipparcos Space Astrometry Mission
Lunar Crater Hipparchus is the Moon landing place in Tintin's On a marché sur la Lune (Explorers on the Moon).
Medieval Greece / Byzantine Empire