ASTRONOMY 9: HISTORY OF COSMOLOGY

Handout #10

J. E. Baker
UC Berkeley, Spring 2000

Cosmology in Ancient Greece: Aristotle and Greek Astronomy

1.

Aristotle (384-322 BC)

• Student of Plato's Academy
• Founded Lyceum
• Worked in almost every field of known science and philosophy!
• Profound influence on development of Western science
• Every effect must have a cause
• Important innovation: universe can be described by natural laws inferred by rational thought
• Aristotle's physics: mostly quite wrong, but strong common-sense appeal
  • Founded science of mechanics (physics of motion)
  • Developed the idea of ``force'', impetus theory of motion (wrong, but widely held even today!)
  • Thought force was required to keep Earthly objects in motion (didn't fully understand inertia)
• Aristotle applies his physics to the cosmos
  • Basic Earthly elements: air, earth, fire, water
  • Terrestrial and celestial physics are very different!
  • Two types of ``natural'' motion

    (a)

    Earth: linear, straight-line, finite motion (air and fire go up, water and earth go down)

    (b)

    Heavens: perfect, eternal, circular motion

  • Bodies are impelled to move to their ``natural'' location
  • Can only have one center $\Rightarrow$ only one world
  • Circular motion must have a corresponding basic element $\Rightarrow$ 5th element (quintessence): ether (heavenly, unchanging)
  • Cosmic division:

    (a)

    Sub-lunary sphere (inside moon's orbit): earthly, changing, becoming, imperfect, made of 4 elements (Ionian)

    (b)

    Celestial realm (moon and beyond): immutable, perfect, made of ether (Eleatic)

  • Objects don't get ``left behind'' $\Rightarrow$ Earth is fixed at the cosmic center
  • Earth known to be spherical on observational grounds:

    (a)

    Circular shadow during lunar eclipse

    (b)

    Different stars become visible when travel north/south

  • Heavens are rotating $\Rightarrow$ Universe must be finite!
  • Space has an unapproachable ``edge''
  • Universe is eternal, uncreated
  • God rules from outside (primary cause of all motion)
  • Appropriates Eudoxus' sphere model to explain planetary motion
  • Better observations require more spheres $\Rightarrow$ 55 total! (Still no explanation for varying brightnesses)
  • Aristotle thinks spheres are physically real
  • No ``Void'' (vacuum), unlike the Atomists

2.

Heraclides of Pontus (c. 388-310 BC)

• Proposed rotating Earth to explain daily rotation of heavens
• Proposed Mercury and Venus orbit Sun, not Earth
• Ideas rejected by Aristotelians

3.

Aristarchus of Samos (approx. 310-230 BC) ``The Ancient Copernicus''

• Measuring the size of the cosmos...
• Estimated size of Moon to be $\approx 1/3$ size of Earth (from lunar eclipse shadow)
• Measured angle between Sun and Moon when Moon is half-full (called ``first quarter'')
• Concluded Sun is 18-20$\times$ further away than Moon
• But apparent (angular) sizes of Sun and Moon are the same $\Rightarrow$ Sun is at least 18 times as big as Moon, or 6 times as big as Earth!
• Used inaccurate data (Moon diameter 2$^\circ$, actually $0.5^\circ$), and method doesn't work well in practice: Sun is actually much bigger still!
• Heliocentric model: Sun is at the center!
• Correct but rejected by Aristotelians, forgotten for 1500 years... Science is not a linear progression of ideas!

4.

Eratosthenes of Cyrene (276-194 BC)

• Clever measurement of the circumference of the earth
• Distance between Alexandria and Syene (now Aswan, Egypt) measured to be 5000 ``stadia'' (Greek unit of length)
• Compare noon shadows at summer solstice, find $7.2^\circ$ difference
• Assume Sun is far away so that rays are parallel
• Circumference is then
  
  $$C = \left(\frac{360^\circ}{7.2^\circ}\right) \times 5000\ \m... ... 50 \times 5000\ \mathrm{stadia} = 250,000\ \mathrm{stadia}.$$
  
  

• Length of stadium is uncertain; result was very accurate if 1 stadium = 157.2 meters:
  
  $$C = (250,000\ \mathrm{stadia})\times 1 = (250,000\ \mathrm{st... ...rm{km}}{1000\ \mathrm{m}}\right) \approx 40,000\ \mathrm{km}$$
  
  

5.

Appollonius of Perga (approx. 262-190 BC)

• Back to the geocentric cosmos
• A new answer to Plato's challenge to ``save the phenomena''
• Different from Eudoxus' ``onion'' cosmos of spheres, more like a Ferris wheel
• Not totally geocentric: introduced ``eccentric circle''
  • Earth remains motionless at cosmic center
  • Planets still move in circles at uniform speed
  • But center of circles is now displaced from Earth!
  • Apparent motion as viewed from Earth is of variable speed
• Also invented epicycle
  • Wheels upon wheels
  • Allows (complicated) explanation of retrograde motion
• ``Theorist'': did not try to apply ideas to observational data

6.

Hipparchus of Rhodes (190-120 BC)

• Great Greek astronomer
• Synthesized Babylonian and Greek data with new Greek geometrical models from Appollonius
  • Model for Sun's motion (eccentric circle)
  • Model for Moon's motion (eccentric + epicycle)
• Also made accurate catalog of 850 star positions
• Discovered precession of equinoxes

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