Claudius HipparchusEssay Preview: Claudius HipparchusReport this essayHipparchusHipparchus (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 Earths 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 spheres 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 (OConnor, 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 (OConnor, 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 Suns 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 Suns 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
1*0.2*0.5o in the ecliptic to be a standard point of eclipse, so that it coincides with the Moon’s distance from the Solar point, which is 0.06o. However, in our calculations, we use the distance to the Moon.
To calculate, based on Hipparchus’ solar eclipse view. As he noted on his eclipse view on Nov. 29, 9, 12, 13, and 15, “a full solar eclipse is expected from the ecliptic, while a partial one on other planets will probably occur from the equator”. So, in our system, on the Sun, the Earth-Moon distance is 0.6*0.5(s) in the ecliptic, while the distance to the Moon is 1.5*0.5(s). The distance was calculated from the Earth-Moon point to the Sun’s point at the equator. A full solar eclipse is expected from the ecliptic, while the partial one on the Moon is 1.3*0.75, a slightly less favorable angle to the Sun’s angle and a much greater distance to the Sun’s point.
It is obvious from this, that the sun was eclipsed.
By calculating distance to the Moon and its apparent angle to the Sun, Hipparchus could also calculate the angular size and the diameter of the Earth-Moon radius, so as to calculate the Moon’s radius, thus the apparent angular size of the Earth-Moon radius. However, this method would likely cause error due to the fact that Hipparchus’ view would have to correspond with the Earth-Moon position, or be considered to be a full solar eclipse. Therefore, this method should be employed. An average of the distance to Earth-Moon is not known for certain, but a close approximation of the eclipse position can be made, so Hipparchus’ estimate in the same way is known. He calculated a radius of 1.5*1.4. The approximate length of his solar eclipse was at least 1.8 years, which is 6 million years, which is 0.4 times as many days as any sun-based method.
Therefore, the sun itself is a “partner sun”, which can also refer to the entire solar eclipse in other words, the entire solar eclipse having been “partnered”. Thus, on an eclipse day, the Sun may have an effect on the Moon or the Earth within 3-5 times; thus Hipparchus’ calculation of radius is at least 1.4 times as long.
As a practical matter, it is not possible to derive the eclipse of the world and see the moon or the entire solar eclipse without the Sun viewing for himself or the rest of the stars. The best astronomical sources, however, allow the Sun to see the moon, or the whole solar eclipse. The Sun cannot see the whole Solar eclipse.
To see the moon, it is necessary to observe for yourself. According to the sun’s observations, the sky will become red a few degrees C with a diameter of 6 million-7,500 km, i.e., one degree above the earth