Hipparchus family background
If you've studied math at a high school level, you probably have experience with trigonometry.
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It's a fascinating branch of mathematics, and it all came about through the genius of Hipparchus of Rhodes. Hipparchus was a Greek scholar considered the greatest astronomical observer in early human history. He made many advances in geography and mathematics, specifically in trigonometry, which he used to construct models to predict solar eclipses. Because math is the language of science, his contributions are particularly important.
His early life is mostly a mystery, but what we do know about him comes from Ptolemy's Almagest. He is mentioned in other writings as well. His image, usually depicted sitting and looking at a globe, has been found on many coins minted between AD and AD. In ancient terms, that's a pretty important acknowledgment of importance. Hipparchus apparently traveled and wrote extensively.
There are records of observations he made in his native Bithynia as well as from the island of Rhodes and the Egyptian city of Alexandria. The only example of his writing that still exists is his Commentary on Aratus and Eudoxus. It's not one of his major writings, but it's still important because it gives us an insight into his work. Hipparchus's major love was mathematics and he pioneered a number of ideas we take for granted today: the division of a circle into degrees and the creation of one of the first trigonometric tables for solving triangles.
In fact, he very likely invented the precepts of trigonometry. It seems that Nicea was proud of Hipparchus as his image was placed on coins between the years and AD. It means that the first coins that honored Hipparchus were minted around years following his death. Hipparchus was able to accurately measure the distance between the earth and the moon.
It was also him who observed a nova, the appearance of a brand new star, as well as the precession of equinoxes.
Hipparchus suspected that the stars might move little by little in relation to one another over long periods of time. He also nursed the hope that people in the future will be able to verify this. This is the very reason why Hipparchus compiled the star catalog that documented the magnitudes and positions of more than stars.
His legacy also bore fruit at about two millennia later when Edmund Halley was able to discover the correct motion of stars in There are times when Ptolemy, the great astronomer himself, literally quoted Hipparchus so people can still read some of the direct thoughts of Hipparchus. Only a few of the original work of Hipparchus has survived.
Hipparchus of rhodes biography of albert bandura: Hipparchus (born, Nicaea, Bithynia [now Iznik, Turkey]—died after bce, Rhodes?) was a Greek astronomer and mathematician who made fundamental contributions to the advancement of astronomy as a mathematical science and to the foundations of trigonometry.
Like others before and after him, he also noticed that the Moon has a noticeable parallax , i. He knew that this is because in the then-current models the Moon circles the center of the Earth, but the observer is at the surface—the Moon, Earth and observer form a triangle with a sharp angle that changes all the time.
From the size of this parallax, the distance of the Moon as measured in Earth radii can be determined. For the Sun however, there was no observable parallax we now know that it is about 8. In the first book, Hipparchus assumes that the parallax of the Sun is 0, as if it is at infinite distance. He then analyzed a solar eclipse, which Toomer presumes to be the eclipse of 14 March BC.
Alexandria and Nicaea are on the same meridian. It has been contended that authors like Strabo and Ptolemy had fairly decent values for these geographical positions, so Hipparchus must have known them too. Hipparchus could draw a triangle formed by the two places and the Moon, and from simple geometry was able to establish a distance of the Moon, expressed in Earth radii.
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Because the eclipse occurred in the morning, the Moon was not in the meridian , and it has been proposed that as a consequence the distance found by Hipparchus was a lower limit. In any case, according to Pappus, Hipparchus found that the least distance is 71 from this eclipse , and the greatest 83 Earth radii. In the second book, Hipparchus starts from the opposite extreme assumption: he assigns a minimum distance to the Sun of Earth radii.
In this case, the shadow of the Earth is a cone rather than a cylinder as under the first assumption. With these values and simple geometry, Hipparchus could determine the mean distance; because it was computed for a minimum distance of the Sun, it is the maximum mean distance possible for the Moon. With his value for the eccentricity of the orbit, he could compute the least and greatest distances of the Moon too.
With this method, as the parallax of the Sun decreases i. Hipparchus thus had the problematic result that his minimum distance from book 1 was greater than his maximum mean distance from book 2. He was intellectually honest about this discrepancy, and probably realized that especially the first method is very sensitive to the accuracy of the observations and parameters.
Ptolemy later measured the lunar parallax directly Almagest V. He criticizes Hipparchus for making contradictory assumptions, and obtaining conflicting results Almagest V. His results were the best so far: the actual mean distance of the Moon is Theon of Smyrna wrote that according to Hipparchus, the Sun is 1, times the size of the Earth, and the Earth twenty-seven times the size of the Moon; apparently this refers to volumes , not diameters.
Similarly, Cleomedes quotes Hipparchus for the sizes of the Sun and Earth as ; this leads to a mean lunar distance of 61 radii. Apparently Hipparchus later refined his computations, and derived accurate single values that he could use for predictions of solar eclipses. See Toomer for a more detailed discussion.
Pliny Naturalis Historia II. X tells us that Hipparchus demonstrated that lunar eclipses can occur five months apart, and solar eclipses seven months instead of the usual six months ; and the Sun can be hidden twice in thirty days, but as seen by different nations.
Ptolemy discussed this a century later at length in Almagest VI. The geometry, and the limits of the positions of Sun and Moon when a solar or lunar eclipse is possible, are explained in Almagest VI. Hipparchus apparently made similar calculations. The result that two solar eclipses can occur one month apart is important, because this can not be based on observations: one is visible on the northern and the other on the southern hemisphere—as Pliny indicates—and the latter was inaccessible to the Greek.
Prediction of a solar eclipse, i. Hipparchus must have been the first to be able to do this. A rigorous treatment requires spherical trigonometry , thus those who remain certain that Hipparchus lacked it must speculate that he may have made do with planar approximations. Pliny also remarks that "he also discovered for what exact reason, although the shadow causing the eclipse must from sunrise onward be below the earth, it happened once in the past that the Moon was eclipsed in the west while both luminaries were visible above the earth" translation H.
Rackham , Loeb Classical Library p. Toomer argued that this must refer to the large total lunar eclipse of 26 November BC, when over a clean sea horizon as seen from Rhodes, the Moon was eclipsed in the northwest just after the Sun rose in the southeast. We do not know what "exact reason" Hipparchus found for seeing the Moon eclipsed while apparently it was not in exact opposition to the Sun.
Parallax lowers the altitude of the luminaries; refraction raises them, and from a high point of view the horizon is lowered. Hipparchus and his predecessors used various instruments for astronomical calculations and observations, such as the gnomon , the astrolabe , and the armillary sphere. Hipparchus is credited with the invention or improvement of several astronomical instruments, which were used for a long time for naked-eye observations.
According to Synesius of Ptolemais 4th century he made the first astrolabion : this may have been an armillary sphere which Ptolemy however says he constructed, in Almagest V. With an astrolabe Hipparchus was the first to be able to measure the geographical latitude and time by observing fixed stars. Previously this was done at daytime by measuring the shadow cast by a gnomon, by recording the length of the longest day of the year or with the portable instrument known as a scaphe.
Ptolemy mentions Almagest V. It was a four-foot rod with a scale, a sighting hole at one end, and a wedge that could be moved along the rod to exactly obscure the disk of Sun or Moon. Hipparchus also observed solar equinoxes , which may be done with an equatorial ring : its shadow falls on itself when the Sun is on the equator i.
Ptolemy quotes in Almagest III. Hipparchus applied his knowledge of spherical angles to the problem of denoting locations on the Earth's surface. Before him a grid system had been used by Dicaearchus of Messana , but Hipparchus was the first to apply mathematical rigor to the determination of the latitude and longitude of places on the Earth.
It is known to us from Strabo of Amaseia, who in his turn criticised Hipparchus in his own Geographia. Hipparchus apparently made many detailed corrections to the locations and distances mentioned by Eratosthenes. It seems he did not introduce many improvements in methods, but he did propose a means to determine the geographical longitudes of different cities at lunar eclipses Strabo Geographia 1 January A lunar eclipse is visible simultaneously on half of the Earth, and the difference in longitude between places can be computed from the difference in local time when the eclipse is observed.
His approach would give accurate results if it were correctly carried out but the limitations of timekeeping accuracy in his era made this method impractical. Late in his career possibly about BC Hipparchus compiled his star catalog. Scholars have been searching for it for centuries. Hipparchus also constructed a celestial globe depicting the constellations, based on his observations.
His interest in the fixed stars may have been inspired by the observation of a supernova according to Pliny , or by his discovery of precession, according to Ptolemy, who says that Hipparchus could not reconcile his data with earlier observations made by Timocharis and Aristillus. For more information see Discovery of precession.
In Raphael 's painting The School of Athens , Hipparchus may be depicted holding his celestial globe, as the representative figure for astronomy.
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It is not certain that the figure is meant to represent him. Previously, Eudoxus of Cnidus in the fourth century BC had described the stars and constellations in two books called Phaenomena and Entropon. Aratus wrote a poem called Phaenomena or Arateia based on Eudoxus's work. Hipparchus wrote a commentary on the Arateia —his only preserved work—which contains many stellar positions and times for rising, culmination, and setting of the constellations, and these are likely to have been based on his own measurements.
According to Roman sources, Hipparchus made his measurements with a scientific instrument and he obtained the positions of roughly stars. This same Hipparchus, who can never be sufficiently commended, And the same individual attempted, what might seem presumptuous even in a deity, viz. In this way it might be easily discovered, not only whether they were destroyed or produced, but whether they changed their relative positions, and likewise, whether they were increased or diminished; the heavens being thus left as an inheritance to any one, who might be found competent to complete his plan.
It is unknown what instrument he used.
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The armillary sphere was probably invented only later—maybe by Ptolemy years after Hipparchus. The historian of science S. Hoffmann found clues that Hipparchus may have observed the longitudes and latitudes in different coordinate systems and, thus, with different instrumentation. Hipparchus is conjectured to have ranked the apparent magnitudes of stars on a numerical scale from 1, the brightest, to 6, the faintest.
In this only work by his hand that has survived until today, he does not use the magnitude scale but estimates brightnesses unsystematically. During the Hellenistic period, few Greek astronomers were as distinguished and influential as Hipparchus. Over the course of his life, Hipparchus would be a very accomplished astronomer and mathematician. He is believed to have been the founder of trigonometry and, although he made the discovery somewhat by accident, he is credited for revealing the precession of the equinoxes.
Not much is known about the early days of Hipparchus since no records exist and, for that matter, there is reason to believe they were necessarily kept in the first place. We do know he was born around B. His body of work was more than merely impressive and it is commonly argued that he is the greatest of all astronomers from antiquity.
Hipparchus was able to become the very first astronomer to actually craft completely accurate models detailing the motion of the moon and the sun. Not all of his models survived to the modern day so he may have made numerous other discoveries that have become lost to history. He was eventually able to come up with a means of predicting solar eclipses thanks in large part to his knowledge about astronomy and his innovative discoveries in trigonometry.
The various different discoveries made about the moon were quite impressive. He was able to determine the motion and orbit of the moon.