# 1 Ako ďaleko sú hviezdy Peter Ballo. 2 Very Early (Pythagoras: 550 BC) Cosmology.

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1 Ako ďaleko sú hviezdy Peter Ballo

2 Very Early (Pythagoras: 550 BC) Cosmology

3 Aristotle’s reasoning for why the earth is round 1.Different stars can be seen, depending on location 2.[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)‏

4 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

5 Note the order in which the celestial objects are lined up and that Moon and Sun need no epicycles The Complete Ptolemaic Model

7 How Far To Moon? Aristarchus’s (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 earth’s (slightly) cone-shaped shadow: call that n diameters now you know the size of the moon too!!! so D M = D E /n (it’s 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: d M = D M 

8 How Far To Sun? Another of Aristarchus’s 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, we’d say d S = d M sec A [sec A = 1/cos A] he got d S = 19 d M correct: d S = 390 d M

The Alexandrian School Aristarchus of SamosAristarchus of Samos –Relative Sizes of Earth, Moon and Sun Earth Found that Sun is 6-7x larger than the Earth, compared to 109x Found that Sun is 6-7x larger than the Earth, compared to 109x The Sun is larger than the Earth! The Sun is larger than the Earth! Led him to suggest a Sun-centered (“heliocentric”) universe Led him to suggest a Sun-centered (“heliocentric”) universe

1.71400 1.51200 1.41000 1.3800 1.1600 Diameter of hole /mmLength of tube / mm

From Sun 7 o Alexandria 7 o Syene Distance around Earth = 360 o /7 o x Distance Syene to Alexandria = 50 x 5000 stades ! From Sun

Evolution of Greek Cosmologies Hipparchus150 BC (Island of Rhodes)‏Hipparchus150 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 secondsYear Accurate to 6 minutes, Month accurate to seconds –Precession – Non-Uniform Motion of Sun and Moon Solar motion is faster in (northern) winter Solar motion is faster in (northern) winter – The “Eccentric Circle” Primacy of observation over dogma Primacy of observation over dogma Inter-relation of observation and theory Inter-relation of observation and theory The role of the aesthetic in understanding the universe The role of the aesthetic in understanding the universe

E S V M 46 o 28 o

E M V S M J S 46 o 28 o Daily

M S J S M E Not to scale! V

R d  d = R/Tan()  R/

Cover page from S. Majewski Key Project proposal

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