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Greek and Hellenistic Astronomy Robert H. van Gent Mathematical Institute Utrecht University “The School of Athens” (Scuola di Atene), fresco made in 1509/11 by Raphael of Urbino in the Apostolic Palace (Vatican City). In the centre Plato (left) and Aristotle (right) are seen debating in the company of numerous illustrious classical scholars and philosophers. Thales of Milete (c. 624-c. 546 BCE) According to the Greek historian Herodotus, the Greek philosopher Thales predicted an eclipse of the Sun (probably the one on 28 May 585 BCE) which occurred during a battle between the Lydians and the Persians. Later sources claim that he visited Egypt where visited the pyramids and computed their heights from their shadows. An often repeated anecdote relates how he, during a nightly stroll, fell into a well and so became the stereotype of the “absent-minded astronomer”. Plato (424/23-348/47 BCE) Established the famous Academy of Athens and is regarded as the founder of Western science and philosophy. Wrote dozens of treatises (“Socratic Dialogues”) on numerous topics. His views on the cosmos and its origin were described in detail in the Timaeus (this book also contains the first part of his famous story of the lost city of Atlantis which was continued in the Critias). Plato also discussed astronomical topics in other works, such as Phaedo, Phaedrus, The Republic (Politeia) and The Laws (Legibus). Plato was a pupil of Socrates (c. 469-399 BCE), his most famous pupil was Aristotle. Oil on popular wood ascribed to Joos van Wassenhove (c. 1475) for the studiolo of Federico II da Montefeltro in Urbino (Louvre, Paris) Aristotle of Stagira (384-322 BCE) Pupil of Plato and founder of the Lyceum of Athens. His works greatly influenced Hellenistic, Islamic and medieval-European philosophy and science. Aristotle’s views on the cosmos are described, together with those of earlier Greek philosophers, in the following works: • De Caelo (“The Heavens”) • Meteorologia (“Meteorological Phenomena”) According to Aristotle all motion below the lunar orb was rectilinear and directed to the centre of the Earth, while all celestial motions were circular, uniform and eternal. According to historical tradition the Macedonian conqueror Alexander the Great (356-323 BCE) was tutored by Aristotle. Oil on popular wood ascribed to Joos van Wassenhove (c. 1475) for the studiolo of Federico II da Montefeltro in Urbino (Louvre, Paris) The Five Regular or Platonic Polyhedrons Described by the Greek mathematician Euclid in the 13th book of the Elements. Plato linked them in the Timaeus (c. 360 BCE) with the four elements of the ‘sublunary’ world. Later philosophers added the dodecahedron to represent the fifth element (quintessence or aether) from which the ‘supralunary’ world is made up. polyhedron F V E element tetrahedron 4 6 4 fire cube 6 12 8 earth octahedron 8 12 6 air dodecahedron 12 30 20 aether icosahedron 20 30 12 water The City of Alexandria The city of Alexandria, founded in 332/31 BCE by Alexander the Great, was laid out according to a rectangular street plan of which the major axis was directed to the direction where the Sun rose on 20 July (the traditional Egyptian New Year’s Day, coinciding with the heliacal rising of the bright star Sirius, the Dog Star) Measurement of the Earth’s Circumference by Eratosthenes of Cyrene (276-194 BCE) Eratosthenes measured the angle α as 7.2°. From this he deduced a circumference of (360/7.2) × 5000 = 250 000 stadia. Assuming 1 stadion ≈ 185.4 m, this then results in a circumference of c. 46 400 km – about 15% too large. Eratosthenes assumed that Alexandria and Syene (in southern Egypt) were 5000 stadia distant from each other and were located on the same meridian. On the day of the summer solstice (c. 21 June) a vertical gnomon in Syene was observed to cast no shadow at noon while a similar vertical gnomon in Alexandria was observed to produce a measurable noon shadow. Eratosthenes’s method was later also applied by Poseidonius of Apameia, Islamic mathematicians and the Dutch astronomer and mathematician Willebrord Snellius. Measuring the Distances of the Moon and the Sun by Aristarchus of Samos (c. 310-c. 230 BCE) Aristarchus measured the elongation (angle between the Moon and the Sun) when the Moon is exactly half lit as 87°. From this he inferred that the distance to the Sun was between 18 and 20 times the lunar distance [in reality, the distance ratio is about 390]. From observations of lunar eclipses Aristarchus determined the ratio of the diameters of the Earth and the Moon as c. 2.85. From the angular diameter of the Moon (½°) the distance to the Moon can then be inferred. By using a wrong value (2°) Aristarchus computed a distance of 20 terrestrial radii, whereas the true distance is about 60 terrestrial radii. Claudius Ptolemy of Alexandria (c. 100-175 CE) Author of several works which defined the mathematical sciences in the Late Classical, Islamic and European world until well into the Renaissance: • Mathematike Syntaxis (Almagest) • Hypotheseis ton planomenon (Hypotheses regarding the movements of the planets) • Apotelesmatika (Tetrabiblos, Quadripartitium) • Geographike Hypogesis (Geographia, Cosmographia) • Harmonikon (Harmonics) • Optics Oil on popular wood ascribed to Joos van Wassenhove (c. 1475) for the studiolo of Federico II da Montefeltro in Urbino (Louvre, Paris) The “known world” according to the 1482 printed edition of the Cosmographia of Claudius Ptolemy The geocentric or Ptolemaic world system Andreas Cellarius, Harmonia Macrocosmica, Amsterdam, 1660 As Babylonian astronomers had already noted, the outer planets (Mars, Jupiter and Saturn) do not move in uniform speed and direction with respect to the fixed stars, but, at times, are also observed to become stationary or move in opposite (westward or retrograde) direction. The inner planets (Mercury and Venus) were observed to exhibit similar movements with respect to the Sun. The apparent motion of a planet according to the epicycle model of Ptolemy The apparent motion of a planet according to the heliocentric model of Copernicus The geocentric world system of Claudius Ptolemy (Note that in this simplified diagram the outer planets are not correctly placed in their epicycles – the lines connecting the planets with their deferent circles should be parallel with the Earth-Sun line) The Motion of the Outer Planets (Mars, Jupiter, Saturn) According to Claudius Ptolemy The planet (P) is assumed to move with a constant speed (equal to that of the mean Sun) on a small circle (epicycle), which in turn moves on a larger circle (deferent) with the Earth (O) placed at a small distance from the centre (M). As seen from the equant point (E), the centre (C) of the epicycle moves with a uniform speed. The Motions of the Sun, the Moon and the Planets According the Geometric-Kinematical Models of Claudius Ptolemy Summary of the Contents of the Almagest I & II III IV to VI VII & VIII IX to XIII – introductory chapters on spherical trigonometry – theory of the Sun‘s apparent motion – theory of the Moon’s motion and luni-solar eclipses – the fixed stars, the constellations and the Milky Way – theory of planetary motion The Sun, the Moon and the Planets The Geocentric World System @ Dennis Duke http://www.csit.fsu.edu/~dduke/ The Dimensions of the Cosmos According to Claudius Ptolemy distance (Earth radii) Planet min mean max diameter (Earth = 1) Moon 33 48 64 1/4 + 1/24 Mercury 64 115 166 1/27 166 622½ 1079 1/4 + 1/20 Sun 1160 1210 1260 5 + 1/2 Mars 1260 5040 8820 1 + 1/7 Jupiter 8820 11503 14189 4 + 1/3 + 1/40 Saturn 14189 17026 Venus 19865 4 + 1/ 4 + 1/20 The relative dimensions of the celestial bodies in the world system of Claudius Ptolemy Andreas Cellarius, Harmonia Macrocosmica (Amsterdam, 1660) Some Astronomical Instruments Described by Claudius Ptolemy Cunningham, The Cosmographical Glasse (1559) 19th-century engraving of an astronomer at the observatory of Alexandria The Antikythera Mechanism Discovered in 1900/01 in a Roman shipwreck (c. 80 BCE) off the coast of the Greek island of Antikythera. Recent investigations indicate that it was a complex and highly sophisticated mechanical device capable of displaying various calendars and the movements of the Sun, the Moon and the five then known planets.