1. 385L26

2. • Sun risings and settings (E-W) seasonal shifts altitudes • Moon risings, settings (E-W), phases • Stars stars [aplanê astra] 1000 stars in 48 constellations central band of 12 constellations (zodiac) • Planets [planêtes] : Mercury, Venus, Mars, Jupiter, Saturn retrogradations comets meteors occultations, oppositions, eclipses…

3. Anaximander
6th cent. BCE
concentrism; symmetrical distances
Empedokles
ca. 450 BCE
reflected light; solar eclipse
Philolaos
late 5th c. BCE
pyrocentrism; Counter-Earth
Plato
BCE
Spindle of Necessity; geocentric model

4. Anaximander
The stars come to be as a band of fire separated off from the fire in the kosmos and enclosed in dark mist. There are vents, tube-like passages through which stars appear. For this reason, eclipses occur when the vents are blocked. The moon alter- nately appears to wax and wane, as the vents open and close. The band of the sun is 27 times that of the earth; that of the moon is 18 times. Anaximander says that the stars are carried along by the circles and spheres on which each goes.

5. Empedokles
And the Moon cuts off <the Sun’s> rays as <the Sun> goes above <the Moon>, and casts a shadow on as much of the earth as equals the breadth of the pale-faced Moon. (fr. 42) Even so the sunbeam, having struck the broad and mighty circle of the Moon, returns at once, running so as to reach the sky. (fr. 43)

6. Pythagoreans Philolaos (late 5th c. BCE)
Most say that the earth lies at the center of the universe... but the Pythagoreans take the contrary view. At the center, they say, is fire, and the earth is one of the stars, creating night and day by its circular motion around the center. They further construct another earth in opposition to ours to which they give the name "counter-earth."...For since the number 10 is thought to be perfect and to comprise the whole nature of numbers, they say that there are ten bodies which move through the heavens. But since there are only nine visible bodies, they invent a tenth—"counter-earth."

7. Plato ( BCE)
The spindle of Necessity...consists of a large whorl hollowed out, with a second, smaller one fitting exactly into it, the second being hollowed out to hold a third, the third a fourth, and so on up to a total of eight. The first and outermost whorl had the broadest rim; next broadest was the sixth, next the fourth, next the eighth, next the seventh, next the fifth, next the third, and last of all the second. —Republic 10

8. Definitions
celestial sphere : projected sphere of arbitrary radius with Earth at its center. celestial equator : projected circle along the plane of the terrestrial equator intersecting the celestial sphere. ecliptic : apparent path of the Sun on the celestial sphere, relative (23.4˚) to the celestial equator. equinox : point of intersection of the ecliptic with the celestial equator, in spring (vernal equinox) and autumn (autumnal equinox), marking day and night of equal lengths. solstice : highest (summer solstice) and lowest (winter solstice) point reached by the Sun along the ecliptic, marking longest and shortest days. zodiac : twelve 30-degree divisions of plane roughly 8 degrees above and below plane of ecliptic, bearing principal constellati0ns.

9. Platonic Agenda : sôzein ta phainomena
Construct a rational, arithmetic account of observable data: • E-W movement of all celestial bodies around Earth • annual E-W movement of zodiac along ecliptic • W-E movement of Sun, Moon, planets against background of zodiac • varying speeds of planetary motion relative to zodiac (Moon = 1 month; Saturn = 30 years) • stations and retrogression of planets

10. sozein ta phainomena
• universe is rational and accessible as such to rational mind • appearances deceptive and possibly unreal • beneath apparent disorder is uniform, orderly reality • reality is expressible mathematically • in the case of extended objects, expression is geometrical

11. Astronomical Parameters
• universe geocentric • earth spherical (not flat disk) • celestial bodies travel on spheres (not bands) • celestial motion circular • Sun, Venus, Mercury move at roughly same speed • varying speeds of other planets relative to zodiac • movement of Sun, Moon, planets independent and opposite movement of sphere of fixed stars