Chapter 7.

Ptolemaic System of the World

7.1. Babylonian and Egyptian Observations of Planetary Motion

• Observed motions of Sun, Moon, and five naked-eye planets, all wander among stars
• Sun and Moon move eastward on celestial sphere never changing their course; mostly uniform
• Inferior planets move eastward relative zodiac stars; then reverse moving westward (retrograde motion)
• Superior planets generally move eastward relative zodiac stars; brief period of retrograde motion westward near opposition
• All planets move through different angles in same interval of time over synodic periods; move swiftly some times and slowly at other times
• All planets display noticeable variations in brightness over synodic period

7.2. Hellenistic Period of Greek Science

• Aristarchus of Samos (ca. 310 - ca. 230 B.C.)
  • Proposed Sun as center of planetary motion
  • In treatise, On the Sizes and Distances of the Sun and Moon, he estimated that Sun is 20 times farther from Earth than Moon (closer to 400)
  • Since both have approximately same angular size, the Sun must be 20 times larger than Moon or about 7 times Earth's diameter (closer to 109 times)
  • Apparently thought it natural to put largest and only self-luminous body in Solar System, the Sun, at the center
  • Explained daily movement of the heavens by rotation of Earth on its axis
  • Explained planetary motions by they and Earth revolving about Sun
  • Greeks (Anaxagoras) were aware that Moon, and possibly planets, "shine" by reflecting sunlight; notion probably arrived at by observing lunar eclipses
  • May have recognized that stars were self-luminous and conceivably like the Sun only farther away (speculation)
• Objections to Aristarchus's heliocentric concept
  • Why don't we sense motion, must be very fast?
  • Why don't unattached objects on Earth's surface sail past us in opposite direction?
  • Strongest argument was failure to see parallactic shifts of nearby stars relative to distant stars
  • Parallax, apparent shift in position of foreground object (nearby stars) relative to background objects (distant stars) due to motion of observer (Earth's orbital motion)
  • Foreground stars do show parallactic shift; even nearby stars so far away that parallactic shift extremely small; measured in modern times with large telescopes
• Fact that parallactic phenomenon used as criticism suggests that Greeks aware that stars are not all at same distance from Earth (speculation)
  • Reasoning: if all stars of same brightness, therefore faint stars more distant ones
  • Reasonable assumption that leads to search for parallactic shifts; totally false premise, because stars that appear bright are intrinsically bright, while stars that appear faint are intrinsically faint
  • Even though Greeks suspected stars not at same distances, apparently did not realize that even nearest stars are incredibly distant; parallactic shifts not visible to naked eye
• Greek astronomy in Alexandria - example of Hellenistic culture's spread throughout eastern Mediterranean
  • Museum and its associated Library established in Alexandria after 300 B.C.
  • One of most famous centers of learning in the ancient world; center for scientific and mathematical research
  • Eratosthenes (273-193 B.C.)
    • Knowing that Earth was a sphere
    • Knowing that Sun at least 20 times farther away than Moon (nearer 400) from work of Aristarchus (ca. 320-ca. 250 B.C.)
    • Reasoned that rays of sunlight ought to be parallel when they reach Earth
    • Chose observing stations at Alexandria and Syene to the south, which are nearly on same meridian of longitude
    • Chose local noon on day of summer solstice, which comes at same moment for both sites
    • Knowing Sun passes very near zenith at local noon at Syene on summer solstice
    • Had observer in Alexandria observe Sun; about 7o south of zenith
    • Had measurers pace distance between two cities; about 4900 stadia (1 stadium = 0.16 km)
    • Knowing that a straight line cuts two parallel lines at equal angles
    • Reasoned that angle at Earth's center is equal to zenith angle, 7o
    • Calculated circumference: C/4900 stadia = 360o/7o, C = 252,000 stadia (40,320 km, present value 40,030 km)

7.3. Ptolemy

• Within couple of centuries after Aristarchus, heliocentric system lost out to geocentric until its revival by Copernicus
• Generations of astronomers at Museum tried to remove discrepancies between geocentric concept and observed planetary motions
• Revised geocentric model based on earlier natural philosophers
  • Heraclides (ca. 388-ca. 315 B.C.)
  • Apollonius (ca. 261-ca. 190 B.C.)
  • Hipparchus (ca. 190-120 B.C.)
• Claudius Ptolemy (ca. 100-ca. 170 A.D.)
  • System used combinations of circles and off-center motions
  • Published 150 A.D. (Syntaxis of Astronomy, astronomical encyclopedia)
• Acceptable conceptual scheme: Ptolemaic system had to accurately represent many small cyclic changes and large general motions observer
• Ptolemaic scheme did, final version dominated philosophical thought for 13 centuries until time of Copernicus.
• Ptolemy's geocentric system
  • Each planet moves uniformly on small circle, epicycle, which in turn moves uniformly on circumference of large circle, deferent
  • Combinations of sizes and rates of uniform motion for epicycle and deferent, produce mostly direct planetary motions, occasionally retrograde
  • On side of epicycle farthest from Earth, planet appears to move in same direction as deferent--eastward, or direct
  • On side of epicycle closest to Earth, planet appears to slow down, temporarily halt, reverse direction, halt once more, resume direct motion
  • On epicycle planet sometimes nearer, sometimes farther from Earth, results in brightness variations
• Refinements on basic epicycle-deferent model
  • Observed irregular rates of motion for planets required eccentric motion, (Hipparchus)
    • Earth not located at center of deferent (eccentric deferent)
    • Planet appears to go fastest when closest to Earth
  • Planets motion even more irregular than accounted for by eccentric deferent
    • Assumed planets' motions are uniform not as viewed from either Earth or center of eccentric deferent
    • Assumed uniform as seen from point on other side of center of deferent from Earth, equant

7.4. Greek Cosmology

• Two-sphere geometry, large but not infinite; Universe centered on Earth
• Terrestrial and celestial physics not the same in all probability
• Geocentric motion
• Ptolemaic model (Plato, 400 B.C. to Ptolemy, 150 A.D.)
• Matter composed of four elements, earth, water, air, and fire; no voids, space defined by where matter is located