Claudius Hipparchus

Hipparchus

Hipparchus (190-120 BCE) was a Greek astrologer, astronomer, geographer, and mathematician of the Hellenistic period. Also, he is considered the founder of trigonometry. He was born in Nicaea (now Iznik, Turkey), and he was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Chaldeans from Babylonia. He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. With his solar and lunar theories and his trigonometry, he may have been the first to develop a reliable method to predict solar eclipses. His other reputed achievements include the discovery of Earth's precession, the compilation of the first comprehensive star catalog of the western world, and possibly the invention of the astrolabe, also of the armillary sphere, which he used during the creation of much of the star catalogue. It would be three centuries before Claudius Ptolemaeus synthesis of astronomy would supersede the work of Hipparchus; it is heavily dependent on it in many areas.

The movement of a celestial body through 36o would correspond to a fraction of the celestial sphere's total rotation, equal to 36o/360o = 0.1 revolutions. By accurately measuring this time interval through the night, Hipparchus determined, mathematically, exactly how long a day lasts (in arbitrary units of time), assuming uniform rotation of the celestial sphere. Referring back to the example of 36o, it would have taken any particular star 2.4 hours to move through this angle of 36o. Thus, 36o/360o = 2.4h/x

Solving for x, Hipparchus would have found that the length of one day is 24 hours. Although these calculations are quite simple, the methods for keeping time during Hipparchus era were not nearly as conventional as the accurate stopwatches of today. Sir Isaac Newton, for instance, used the period of his heartbeat as a method of keeping time; Hipparchus would have used a similar technique. Hipparchus found that the position of constellations at night could be used to accurately determine the time, since the Sun would not have been visible.

Perhaps one of Hipparchus more complex discoveries would seem more significant. With the help of Babylonian collections of data, Hipparchus was able to estimate, to a respectable degree, the distance between the Earth and its Moon (O'Connor, J. J. and Robertson, E. F., 1999). However, the circumstances required for such an experiment were very specific. Hipparchus needed a solar eclipse; the Sun, Moon and Earth were to be aligned in a plane, with the Moon in the middle, casting a shadow on Earth. The Babylonians determined the period of solar eclipses is 126 007 days, 1 hour. By using only arithmetic, not simple empirical data, Hipparchus found that the period he determined for solar eclipses coincided beautifully with that of the Babylonians (O'Connor, J. J. and Robertson, E. F., 1999).

During that solar eclipse, probably in 129 BCE, Hipparchus stood at Syene, while another observer stood at Alexandria, two cities in close proximity; the distance between these two cities was known (Churchman, S. and Haynes, M., 1999). At the instant that Hipparchus saw a full eclipse (no direct Sunlight was projected onto him); his fellow observer saw a partial eclipse, in which only one-fifth of the Sun was visible. As Hipparchus already knew, the angular size of the Sun is 0.5o (the Sun's diameter occupies only 0.5o of the 360o of the ecliptic - the circle which the Sun appears to trace out on the celestial sphere). Therefore, the Sun's visible portion, as observed from Alexandria, had an angular size of 0.2*0.5o= 0.1o. By using trigonometry, Hipparchus derived the ratio of the Syene-Alexandria distance to the Earth-Moon distance. Hipparchus estimate

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