The first scientific measurement of a cosmic distance was made, around 240 BC. of JC, by Eratosthenes de Cirene - director of the Library of Alexandria, at that time the most advanced scientific institution in the world -, who appreciated that on June 21, when the Sun, at noon, was exactly at its zenith in the city of Siena (Egypt), it was not also, at the same time, in Alexandria, about 750 km north of Siena. Eratosthenes concluded that the explanation must be that the surface of the Earth, being round, was always farther from the Sun in some points than in others.
Based on the length of the shadow of Alexandria, at noon at the solstice, the already advanced Geometry was able to answer the question regarding the magnitude in which the Earth's surface curved in the 750 km path between Siena and Alexandria . From this value, the circumference and diameter of the Earth could be calculated, assuming that it had a spherical shape, a fact that the Greek astronomers then accepted without hesitation.
Eratosthenes made the corresponding calculations (in Greek units) and, as far as we can judge, his figures were approximately 12,000 km for the diameter and about 40,000 for the circumference of the Earth. Thus, although perhaps by chance, the calculation was quite correct. Unfortunately, this value for the size of the Earth did not prevail. Approximately 100 years a. from J. C, another Greek astronomer, Posidonio de Apamea, repeated the experience of Eratosthenes, arriving at the very different conclusion that the Earth had an approximate circumference of 29,000 km.
This smallest value was the one that Ptolemy accepted and, therefore, the one that was considered valid during medieval times. Columbus also accepted this figure and, thus, believed that a 3,000-mile trip to the West would lead him to Asia. If he had known the actual size of the earth, perhaps he would not have ventured. Finally, in 1521-1523, the Magellan fleet - or, rather, the only ship left of it - circumnavigated the Earth for the first time, which allowed to restore the correct value, calculated by Eratosthenes.
Based on the diameter of the Earth, Hipparchus of Nicea, approximately 150 years a. from J. C., calculated the Earth-Moon distance. He used the method that had been suggested a century earlier by Aristarchus of Samos, the most daring of Greek astronomers, who had already assumed that the lunar eclipses were due to the Earth being interposed between the Sun and the Moon. Aristarchus discovered that the curve of the Earth's shadow as it crossed in front of the Moon indicated the relative sizes of the Earth and the Moon. From this, the geometric methods offered a way to calculate the distance the Moon was, depending on the diameter of the Earth. Hipparchus, repeating this work, calculated that the distance from the Moon to the Earth was 30 times the diameter of the Earth, this meant that the Moon must be about 348,000 km from Earth. As we see, this calculation is also quite correct.
But finding the distance that separates us from the Moon was all that Greek Astronomy could achieve to solve the problem of the dimensions of the Universe, at least correctly. Aristarchus also made a heroic attempt to determine the Earth-Sun distance. The geometric method he used was absolutely correct in theory, but it involved the measurement of such small differences in angles that, without the use of modern instruments, proved ineffective in providing an acceptable value. According to this measurement, the Sun was about 20 times farther from us than the Moon (when, in fact, it is about 400 times more).
Regarding the size of the Sun, Aristarchus deduced - although his figures were also erroneous - that this size must be at least 7 times larger than that of the Earth, pointing out below that it was illogical to assume that the Sun, of such great dimensions, it revolved around our little Earth, so it decided, at last, that our planet revolved around the Sun.
Unfortunately no one accepted his ideas. Later astronomers, starting with Hipparchus and ending with Claudius Ptolemy, issued all kinds of hypotheses about celestial movements, always based on the notion of a still Earth in the center of the Universe, with the Moon at 384. 000 km away and others bodies beyond it, at an indeterminate distance. This scheme remained until 1543, the year in which Nicolás Copernicus published his book, which returned to give effect to the point of view of Aristarchus and forever dethroned the Earth from its position as the center of the Universe.
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