Download Decline of Western Civilization (extended) knowledge of ancient

Chapter 4: Renaissance Astronomy
Astronomy after Ptolemy [http://www.thenagain.info/WebChron/WestCiv/WestCiv.html]
Decline of Western Civilization (extended)
knowledge of ancient astronomy lost
Islamic Astronomy [Astrolabium.jpg,Astrolabio_andalusí_Toledo_1067.jpg,arabic_astronomers.gif]
Incorporated knowledge (and preserved writings) of Greeks and
other ancient civilizations
Measurements and observations, improved calculations, but no
critical developments in models
First “modern” observatories
a1c4:1
Rebirth of Western Astronomy (~1400) [figure 4-2]
rediscovery of ancient writings
observation/hypothesis testing
challenges to ancient models
only relative motion is observable
beginnings of impetus theory
Ptolemy's geocentric model largely accepted
[fig 4.1 the Universe according to Dante's Devine Comedy]]
a1c4:2
Copernicus (1473-1543, the height of the Renaissance )
heliocentric model (Sun centered) [copernicus.gif]
planets orbit in perfect circles about the Sun
apparent path of the sun is the ecliptic [fig 4-3, zodiac.avi]
model provides apparent paths’ of planets, including prograde
and retrograde motion [figure 4-4, heliocentric_retrograde.mov, copernicus_m.avi,copernicus_v.avi]
sidereal period: 1 actual revolution (P)
longer sidereal period => greater distance from sun
synodic period: apparent period, relative to sun as seen from earth (S)
[fig 4-5,6]
Sidereal period determined from apparent period and earth’s period
Superior Planets
Planet’s orbit about Sun is outside Earth’s orbit about sun
1/P=1/Pearth-1/S
Inferior Planets
Planet’s orbit about Sun is inside Earth’s orbit about sun
1/P=1/Pearth+1/S
a1c4:3
Geometry + Observations → size of a planet’s orbits [figure 4-7]
Greatest Elongation: greatest angular distance between Sun and planet.
Astronomical Unit (AU): Earth’s orbital distance (average distance from the Sun).
Motion and Observations:
Earth Rotates: Daily motion of Sun, Moon, Stars and Planets [diurnal.avi]
Inferior Planet overtakes Earth: Planet undergoes retrograde motion
Earth overtakes Superior Planet : Planet undergoes retrograde motion
Moon’s motion about Earth: Phases of the Moon (and occasional
eclipses) [eclipser_shadowsB_2010_v2.mov]
Earth moves about Sun: Sun appears to move west to east along
ecliptic, through zodiac [zodiac.avi]
Earth's Axis has constant Tilt + Earth's Orbit: Seasons
[seasons_large.mov]
a1c4:4
PLANET
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Synodic Period
(days)
Sidereal Period
(days)
116
584
−
780
399
378
370
367.5
88
225
365
687
4,332
10,750
30,590
59,800
Orbital Distance
(AU)
0.39
0.72
1.0
1.52
5.2
9.6
19.2
30.1
a1c4:5
More on Copernicus’s model
Orbits are perfect circles.
Epicycles were required to account for variation in planet’s orbital speed.
(just as complex as Ptolemy’s model)
[fig4.8]
Astronomical observations did not favor either Copernicus’s
model or Ptolemy’s model.
(Both about as good/bad)
Violation of Aristotle’s theory of motion.
•No stellar parallax is observed (yet)! [fig 4.9, 4.11, parallax.avi, 16_1.mov]
→ not accepted at the time
a1c4:6
Tycho Brahe, the Great Observer (1546-1601)
regular observations of Sun, Moon and Planets
large number of observations
greatest precision to date
did not detect any stellar parallax [parallax.avi]
heliocentric model rejected due to lack of observed stellar parallax
Tycho Brahe’s geocentric model [figure 4-12]
Sun and Moon orbit Earth, while planets orbit sun.
Similar to Ptolemy’s and Copernicus, no more or less accurate.
Tycho met Johannes Kepler 2 years before Tycho’s death.
30 years of Tycho’s observations went to Kepler when Tycho
died.
a1c4:7
Kepler (1571-1630)
colleague of Tycho Brahe
analyzed Tycho Brahe’s vast, accurate collection of astronomical
data =>
Kepler’s Laws of planetary motion, a model for the solar
system
Kepler’s First Law: Orbital shapes are ellipses with the Sun
at one focus [figure 4-13,kepler_1.avi]
An ellipse is a close curve for which the sum of the distances from two fixed
points (the foci) is the same for every point on the curve.
[figure 4-14, ellipse.avi]
semi-major axis: farthest distance from center
eccentricity: how “squashed” the ellipse is
perihelion: point of orbit closest to the sun
aphelion: point of orbit farthest from the sun
complete description of orbit: orbital elements [orbital_elements.avi]
a1c4:8
Kepler’s Second Law: how orbital speed varies along the orbit
equal areas in equal time [figure 4-15,kepler_2.avi, KeplerThird_Nav.swf]
(orbital speed) x (distance to sun) = constant
fastest at perihelion, slowest at aphelion
Kepler’s Third Law: Period-Orbit relation
square of sidereal period proportional to cube of semi-major axis
P 2 ∼ a3
use period in earth-years, a = 1 Astronomical Unit
Astronomical Unit = average Earth-Sun distance
P 2 = a3
[KeplerThird_Nav.swf]
Kepler’s Laws gave better agreement with observation than
any earlier model!
a1c4:9
Galileo (1564-1642)
early use of Astronomical Telescope
stars: not magnified like planets & the moon
Sun & Moon: not perfect smooth spheres [fig 4.16,17]
Jupiter’s satellites: another “center of rotation”[fig 4.18]
phases of Venus: inconsistent with Ptolemy’s model
[fig 4-19, ptolemy_v_phases.avi, copernicus_v_phases.avi]
“Dialogue Concerning the Two Chief World Systems, the Ptolemaic
and the Copernican”
a1c4:10