. GREECE

For the Pythagoreans (572-48 BC), the sky as a whole is numbers and it is harmony. I know it preaches equality among all living beings. While they despise the economic profit and consider work is reserved for slaves, they spare no effort to think about impossible matters, from which fundamental concepts such as irrational numbers, conics, infinity. As opposed to this way of thinking, the practical thought of Archimedes (287-212 BC) expressed in his contributions to the engineering, with pulleys and levers, hydrostatic thrust, worm gear, is the antithesis. Thales of Miletus (640 BC), the first of the great astronomers, believed that the Universe was spherical. Aristotle (384 BC) fought the idea of ​​a flat Earth, basing his points of view on the change of positions of stars in the sky with latitude and in the shape circular shape of the Earth’s shadow cast on the Moon during an eclipse. Figure 1.1 Eratosthenes model: the shadow of the sun falls from different ways in Siena and Alexandria, to cause of the shape of the Earth. The angular difference of the rays of the Sun, with respect to the vertical of each place, equals angle AOS, base distance AS. The bow that subtends 7th 1 / 7th grade, is a fiftieth of the circumference.

The director of the Library of Alexandria, Eratosthenes (approximately 280-200 BC. C.), measures the Earth using the height of the Sun at noon. With the shadow of an element vertical projected at two different points, he found a difference in value of 7 1/ 7 for the angular distance between Aswan and Alexandria. As the horizontal distance between the two places was, according to his previous measurements, of 5,000 stadia, he found by methods purely geometric, when trigonometry had not yet been developed, that the total perimeter of the earth’s sphere was 5000 x 360 / 71/7 = 252000 stadiums = 39690 Km Hipparchus (190-120 BC), the most important Greek astronomer, invented trigonometry, he made a catalog of more than 1000 stars and discovered the precession of the earth’s axis. Their His works were the basis for the great work of Ptolemy, which would be written in the second century AD. C. Also other stars were attributed a spherical shape. Anaxagoras held that the Sun was an incandescent rock and Democritus claimed that the Milky Way consisted of numerous stars. One of the greatest contributions of Greek astronomy, among the classical conceptions about the considerations of the Universe as finite and geocentric -al The side of Plato’s Timaeus, Metaphysics, and Aristotle’s Treatise on Heaven and the World was the attempt to explain the motion of the planets by a theory of Hipparchus. (190-125 BC) and Claudius Ptolemy (87-170 AD) who compiled in Almagest the entire astronomical knowledge of the time.

The seven planets, which traditionally included the Earth and the Moon, are moved in seven spheres around the Earth, which occupied the center (system geocentric). From the inside out, the Moon, Mercury, Venus, the Sun, Mars, Jupiter and Saturn. Beyond the orbit of Saturn was the sphere of the fixed stars. The Earth did not occupy the exact center of each orbit, that is, the planetary orbits were somewhat eccentric. Only the Sun and the Moon moved in a circle; the other planets traveled an epicycle whose center slid along a circle called a deferent.

The Ptolemy system is geocentric, and is replaced by the heliocentric of Copernicus. Tycho Brahe proposed an intermediate system, with the Earth as the center, surrounded by the Moon and the Sun, and this in turn is surrounded by the planets. Earth is supposed completely static, while all the celestial bodies revolve around him, being it is the center of the Universe. Note some smaller circles called epicycles and others older, the deferents. The centers of the epicycles of the inner planets are located on the straight Earth Sun, and that of the exteriors, on the deferents. Epicycles and deferents, they are circles, and circles are supposed to be the geometry of perfect motion.

Ptolemy’s theory of epicycles allowed not only to give a theoretical explanation to the movement of the planets, but also get reliable predictions. Epicycles and Equant: the equant, which will be rejected by Copernicus, with circular movements and uniform speed, it explains the “anomalous” trajectory of the Sun around the Earth. at https://www.geogebra.org Alongside the geocentric theory appeared others such as that of Aristarco de Samos (310 a 250 a. C.). According to him the Sun (Helios) was in the center and around him they revolve in a circle planets, including Earth.

The Greeks were also the first to try to measure distances in the cosmos. Aristarchus, applying parallax methods, when projecting the shadow of the Earth on the Moon eclipsed, and that the Moon in eclipses showed the same apparent size as the Sun, he found that the ratio of the Moon-Sun distances was 1/19. The diameter of the Moon, according to him, was 0.36 times that of the Earth, and that of the Sun 6.75 that of this, since both quantities must keep the same proportion of the distances.

The peoples of central and northern Europe a. C. possessed astronomical knowledge that applied to megalithic constructions of the Stone Age. Stonehenge in southern England, which mostly have to do with the movements of the Sun and the Moon.