remarkable astronomical achievements of the ancient greeks -- 6/01/16

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Today's selection -- from To Explain the World by Steven Weinberg. A thousand of years before Christopher Columbus, the early Greek philosopher Aristotle laid out the reasons for concluding that the Earth was round, and from that point forward,this became the prevailing view among ancient astronomers and philosophers.

"One of the most remarkable achievements of Greek astronomy was the measurement of the sizes of the Earth, Sun, and Moon, and the distances of the Sun and Moon from the Earth. It is not that the results obtained were numerically accurate. The observations on which these calculations were based were too crude to yield accurate sizes and distances. But for the first time mathe­matics was being correctly used to draw quantitative conclusions about the nature of the world.

"In this work, it was essential first to understand the nature of eclipses of the Sun and Moon, and to discover that the Earth is a sphere. Both the Christian martyr Hippolytus and Aetius, a much-quoted philosopher of uncertain date, credit the earliest understanding of eclipses to Anaxagoras, an Ionian Greek born around 500 BC at Clazomenae (near Smyrna), who taught in Athens. Perhaps relying on the observation of Parmenides that the bright side of the Moon always faces the Sun, Anaxagoras concluded, 'It is the Sun that endows the Moon with its bril­liance.' From this, it was natural to infer that eclipses of the Moon occur when the Moon passes through the Earth's shadow. He is also supposed to have understood that eclipses of the Sun occur when the Moon's shadow falls on the Earth.

Aristotle, with his hand on a bust of Homer  (Rembrandt. 1653)

"On the shape of the Earth, the combination of reason and observation served Aristotle very well. Diogenes Laertius and the Greek geographer Strabo credit Parmenides with knowing, long before Aristotle, that the Earth is a sphere, but we have no idea how (if at all) Parmenides reached this conclusion. In On the Heavens Aristotle gave both theoretical and empirical argu­ments for the spherical shape of the Earth. As we saw in Chap­ter 3, according to Aristotle's a priori theory of matter the heavy elements earth and (less so) water seek to approach the center of the cosmos, while air and (more so) fire tend to recede from it. The Earth is a sphere, whose center coincides with the center of the cosmos, because this allows the greatest amount of the element earth to approach this center. Aristotle did not rest on this theoretical argument, but added empirical evidence for the spherical shape of the Earth. The Earth's shadow on the Moon during a lunar eclipse is curved, and the position of stars in the sky seems to change as we travel north or south:

In eclipses the outline is always curved, and, since it is the in­terposition of the Earth that makes the eclipse, the form of the line will be caused by the form of the Earth's surface, which is therefore spherical. Again, our observation of the stars make[s] it evident, not only that the Earth is circular, but also that it is a circle of no great size. For quite a small change of position on our part to south or north causes a manifest al­teration of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward. Indeed there are some stars seen in Egypt and in the neighborhood of Cyprus that are not seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set.

"It is characteristic of Aristotle's attitude toward mathematics that he made no attempt to use these observations of stars to give a quantitative estimate of the size of the Earth. Apart from this, I find it puzzling that Aristotle did not also cite a phenomenon that must have been familiar to every sailor. When a ship at sea is first seen on a clear day at a great distance it is 'hull down on the horizon' -- the curve of the Earth hides all but the tops of its masts -- but then, as it approaches, the rest of the ship becomes visible.

"Aristotle's understanding of the spherical shape of the Earth was no small achievement. ... I suspect that the persistent belief in the flatness of the Earth may have been due to an obvious problem with a spherical Earth: if the Earth is a sphere, then why do travelers not fall off? This was nicely answered by Aristotle's theory of matter. Aristotle understood that there is no universal direction 'down,' along which objects placed anywhere tend to fall. Rather, everywhere on Earth things made of the heavy elements earth and water tend to fall toward the center of the world, in agreement with observation.

"In this respect, Aristotle's theory that the natural place of the heavier elements is in the center of the cosmos worked much like the modern theory of gravitation, with the important difference that for Aristotle there was just one center of the cosmos, while today we understand that any large mass will tend to contract to a sphere under the influence of its own gravitation."