1. Daily motion of the sky

2. Spin of the Earth

3. Poles and equators

4. Sun’s path at different latitudes

5. Constellations: patterns in the sky

6. Celestial sphere
Horizon
Southern sky

7. Seasonal appearance
Summer
winter

8. Sun’s path in the sky

9. Seasonal position of the Sun

10. Earth’s orbit around the Sun

11. Precession of Earth’s axis

12. Phases of the moon
See the same side of the moon

13. The moon and the Earth
Earthshine
Geometry

14. solar eclipses

15. Earth-moon orbit

16. Lunar eclipse

17. Daily motion of stars Deductions: Earth spins Spherical shape
Moon reflects
Sun’s light
A coordinate
system for the sky

18. Planets as Physical Bodies Rather than Gods
Anaxagoras ( BC)
Diameter D
Hypothesis: Sun is hot piece of stone. How big? How far away?
First day of summer
(June 21) at noon
when Sun Is
highest in the
Sky.
Pay a soldier to pace off: s = 800 km.
r/s = 8d/d = 8  r = 8s = 6400 km;
D/r = 0.5o = 0.5o( rad/180o) = 0.009
 D= 58 km
Anaxagoras concludes that Sun is a flaming rock smaller than Greece.
Meteorite fell
from sky, hot
when found.
Must have come
From the Sun.
Hypothesis:
Sun is hot piece
First day of summer
(June 21) at noon
when Sun Is highest
in the sky (in the
Northern hemisphere).
Pay a man to pace off
s = 800 km. r/s = 8d/d = 8
D/r = 0.5o = 0.5o( rad/180o) = 0.009
Sun is a flaming rock smaller than Greece.
Wrong! But more important is idea that Sun is a physical body, not a God.
Wrong! But more important is idea that Sun is a physical body, not a God.

19. Measure of the Earth and the Moon
During lunar eclipse, shadow cast by Earth is circular  Earth is a sphere.
As seen from Earth
Erastothenes ( BC): If the Sun is much farther away, its rays arrives on parallel lines. Anaxagoras’s problem is then given by the bottom diagram. Alexandria lies north of Syene by a latitude angle arctan(1/8) = 7.2o = 360o/50. Distance from Alexandria to Syene, 800 km, is 1/50 of the polar circumference around the world  2RE = 40,000 km  RE = 6400 km. What Anaxagoras got as the distance to the Sun is actually the radius of the Earth! The Sun must be much farther away!
Erastothenes ( BC): If the Sun is much farther away, then its rays comes nearly on parallel lines, and geometry of Anaxagoras’s problem is actually that of the bottom diagram. In that case, Alexandria lies north of Syene by an angle that is arctan(1/8) = 7.2o = 360o/50. In other words, distance from Alexandria to Syene, 800 km, is 1/50 of the polar circumference around the world  2RE = 40,000 km. (Later, Napoleonic scientists would define meter so that polar circumference of Earth exactly equals 40,000 km.) In any case, this argument yields RE = 6400 km. What Anaxagoras got as the distance to the Sun is actually the radius of the Earth!
Aristarchus ( BC): During lunar eclipse, shadow has inferred diameter 3.7 times larger than diameter DM of the Moon. Thus, DM = 6400 km/3.7 = 1700 km. But DM/rM = 0.5o = rad  rM = 190,000 km = 60 RE.
Aristarchus ( BC): During lunar eclipse, shadow has inferred diameter 3.7 times larger than diameter DM of the Moon. Thus, DM = 2RE/3.7. But DM/rM = 0.5o = rad  rM = 2RE/[(3.7)(0.009)] = 60 RE . (Crucial for Newton) If Sun is much farther than Moon, Sun is much bigger than Earth. Maybe Earth circles Sun.
7.2o
Alexandria
7.2o
Syene

20. Eratosthene: size of the Earth

21. Greek philosophers: constellations & star brightness
Stars and planets

22. Planets: cosmic wanderers

23. Roots of Science in Mysticism
Mystical concepts of elements & reasons for change
Babylonian argument that water = “theory of everything”
Source of all life between Tigris & Euphrates
Capable of change from solid to liquid to gas
Water, Fire, Earth, Air, and Aether/Quintessence (Greece)
Water, Fire, Earth, Metal, and Wood (China)
Numerology & association of metals/elements with planets
Greece: Sun = gold, Moon = silver, Mercury = tin, Venus = copper, Mars = iron, Jupiter = asem, Saturn = lead (7 “planets” = 7 day week); quicksilver  metal
China: Mercury = water, Venus = metal, Mars = fire, Jupiter = wood, Saturn = earth

24. Ptolomy’s geocentric model
Aristarchus’ heliocentric
theory
Hipparcus’s
parallax

25. Ptolomy’s geocentric model: Planets retrograde motion

26. Renaissance: Rise of Modern Science
Despite its brilliance in theory, Greece did not develop modern science because it generally refrained from experimentation.
Despite its many successes in experimentation, China did not develop modern science because it was too practical to tolerate theory.
Islam was crossroad of commerce between East and West.
Islam was exposed to Western tradition (theory) & Eastern tradition (experimentation) in advancing knowledge.
Crusades led to European re-exposure to classical knowledge.
Islam, a more advanced culture than Europe, was subsequently destroyed by Genghis Khan and the Mongol invasion. If Islam had escaped devastation, it might well have invented modern science.
As it was, the opportunity fell to Europe. Besides Copernicus,
the two scientific giants of the Renaissance were
Kepler, transitional figure, three laws of planetary motion;
Galileo, perfect blend of theorist & experimentalist (whose like is not seen again until Fermi).

27. Copernicus’ revolution
Heliocentric model

28. Relative distances Ptolemy Copernicus Modern Mercury 100 430 (.4 AU)
Distance of Mars from the sun (sun-Earth distance = 1 AU)
Distances of Planets from Sun in Earth Radii, (and Astronomical Units)
Ptolemy
Copernicus
Modern
Mercury
100
430 (.4 AU)
9,600 (.4 AU)
Venus
600
820 (.75 AU)
17,000 (.72 AU)
Earth
1,200
1,100 (1 AU)
23,500 (1 AU)
Mars
5,000
1,700 (1.5 AU)
35,700 (1.5 AU)
Jupiter
11,500
6,000 (5.5 AU)
122,000 (5.2 AU)
Saturn
17,000
10,500 (9.5 AU)
224,000 (9.5 AU)
Stars
20,000
too far to measure
6,300,000,000 to nearest star

29. Sidereal vs synodic periods