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Arquivo para September 9th, 2019

A worldview beyond time

09 Sep

Aristarchus of Samos (320 BC – 250 BC) organized a cosmology far ahead of his time, what was known to date was the studies of Pythagoras (571-390 BC) and Heraclides (390-310 BC), who claimed that the stars were immobile that the earth was the center of the universe, only Mercury and Venus would orbit around the sun. While flourishing Euclid’s Geometry (300 BC – ?).
Aristarchus which also had works on optics, music and mechanics, astronomy and astrology, invited by Ptalomeu I will compose the famous Academy of Alexandria, and his influence on the Renaissance will in particular influence his studies on proportions and projections, and although others are cited, Piero dela Francesca (1415-1942) is the great success of Euclidean geometry in the Quattrocent Renaissance.
Aristarchus’ view far ahead of his time was that the earth revolved around the south, and the moon revolved around the earth, thought of two experiments to measure Earth’s radio and the distance from Earth to the Sun.
The experiment thought was to build a tower facing the sea and knowing the height of the tower and the angle between the sea horizon (where there is less distortion thinking the earth as a sphere), can similarity of triangles calculate the radius of the Earth, the The error was small for the measurement difficulties of the time, very close to the 6 378 km of the equatorial radius.
If an object is 1 ° from some measurement point, that object is necessarily 57 times its size, because the tangent of 1 ° is about 0.01745 (see figure) see figure and so Aristarchus calculated the radius of the earth.
The second experiment, knowing the radius of the earth was to find the distance to the sun, he knew that during the full moon, under the average 31 minute angle of the arc (half of 1) tells us that this measurement will be 115 times its diameter, and we can find the distance from the earth to the moon, using again the tangent (he found an angle of 87º) one can measure the distance to the sun that gave 7 million and 300 thousand kilometers, in fact the angle was 89º853´, and the distance between the earth and the sun is 150 million km.
Carl Sagan makes a beautiful presentation and Aristarchus of Samos and his worldview beyond his time:

Source: Costa, J. R. V. Aristarco de Samos e a distância Terra-Sol. Astronomia no Zênite, jul 2000. Disponível em: http://www.zenite.nu/aristarco-de-samos-e-a-distancia-terra-sol/