Ako daleko s

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Ako daleko sú hviezdy
Peter Ballo
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Very Early (Pythagoras 550 BC) Cosmology
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Aristotles reasoning for why the earth is round

• Different stars can be seen, depending on
  location
• below Perfection demands that objects fall
  toward the Earth center, which is only down
  everywhere if Earth is sphere
• 3. right Eclipses would look strange (lunar
  depicted)?

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The Eudoxus model

• Two inner ones turn slowly in opposite
  directions, to account for retrograde, speedup,
  slowdown and ecliptic crossings
• Third one gives Mars year, with axis tipped a
  few degrees, slipping backward on the ecliptic
• Fourth one gives usual diurnal motion

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The Complete Ptolemaic Model
Note the order in which the celestial objects are
lined up and that Moon and Sun need no epicycles
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How Far To Moon? Aristarchuss (270 BC) clever
idea

• if you know the size of the Earth (not very
  well, actually)?
• during a lunar eclipse, measure how many moon
  diameters
• fit into earths (slightly) cone-shaped shadow
  call that n diameters
• now you know the size of the moon too!!!
• so DM DE/n (its a bit trickier due to
  coniness of shadow)?
• now you know the size of the moon too!!!
• knowing angular size of moon
• simple proportion, then dM DM ?

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How Far To Sun? Another of Aristarchuss clever
ideas

• at quarter moon, angle at M to E and S is 90º
• precisely measure angle between M and S
• he measured 87º correct answer is 89.83º
• in modern trigonometry, wed say
• dS dM sec A sec A 1/cos A
• he got dS 19 dM
• correct dS 390 dM

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The Alexandrian School

• Aristarchus of Samos
• Relative Sizes of Earth, Moon and Sun

• Found that Sun is 6-7x larger than the Earth,
  compared to 109x
• The Sun is larger than the Earth!
• Led him to suggest a Sun-centered
  (heliocentric) universe

Earth
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From Sun
From Sun
7 o
Alexandria
7 o
Syene
Distance around Earth 360o/7o x Distance
Syene to Alexandria
50 x 5000 stades !
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Evolution of Greek Cosmologies

• Hipparchus 150 BC (Island of Rhodes)?
• Cataloged Positions and Brightnesses of 850 Stars
• Length of Month and Year, With Errors
• Year Accurate to 6 minutes, Month accurate to
  seconds
• Precession

• Non-Uniform Motion of Sun and Moon
• Solar motion is faster in (northern) winter

• The Eccentric Circle
• Primacy of observation over dogma
• Inter-relation of observation and theory
• The role of the aesthetic in understanding the
  universe

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R
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d
d R/Tan(?) ? R/?
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