Transcript Slide 1

Another demonstration-- Earth was round:
•the altitudes of stars change
with latitude—Greeks sailed the
seas!
•Erasthatenes (who?) first realized
this several decades earlier
Star Trails Above Mauna Kea
Credit & Copyright: Peter Michaud (Gemini Observatory), AURA, NSF
Star trails from the Oregon Star party:
http://www.keteu.org/images/astro/osp-trails.web.jpg
Eratosthenes (250 B.C)
•measured the
circumference of the
Earth--Used "the shadow in
the well" method.
•At S, sun is straight
overhead.
•At A, sun is at an angle
to zenith (about 7o)
•Here, a is the same as
b.
•Proportion: AS/b =
360/(circumference of
Earth).
Aristarchus of Samos (300 B.C.):
•"Heliocentric" arguments.
determined relative
distances of the Earth and
the sun,
•Based on angles between
Earth Moon and Sun at
various phases.
•From size of eclipse
shadow, determined
relative sizes of Earth
moon…and sun!
•Deduced: sun is 90 x
farther than moon, moon
is 1/3 size of earth, sun is
about 30 x as large.
• angles are harder to
measure than it looks
here!
•Concluded earth must
orbit much larger sun!
But….Aristotle argued for the
Geocentric Model
Observed no stellar parallaxes
no winds—shouldn’t 1000
km/hr wind blow as earth spins
through it?
spinning Earth would hurl its
inhabitants into space.
No mechanism to keep it in a
circular orbit.
Click on image to play MPEG move on
the web.
From: www-astronomy.mps.ohio-state.edu
Main difficulty with Geocentric
Model: Retrograde motion
•Why do some celestial
objects move in
backward loops?
•“obvious” solution was
“wheels upon wheels”
•But how many wheels?
From: http://www.earth.uni.edu/~morgan/astro/course/retrograde_mars.jpg
Ptolemy’s Geocentric Model
•Plato, Eudoxes,
Aristotle, and finally
Ptolemy (100AD)
developed geocentric
“systems”
•These used Deferents
(large orbits) and
epicycles (small orbits”
•The trick was to use
these to make accurate
predictions of positions
in the future
•i.e. Mars will be near
Antares in Scorpius on
winter solstice…etc.
Ptolemy’s was most accurate…
•Ptolemy (pronounced Tolemy)
was professor in Alexandria
during the Roman Era.
•A mathematician, physicist,
astronomer, and foremost
geographer of his era.
•Created elaborate system of 88
epicycles and deferents, not
precisely centered on earth, to
model the motion of the
heavens.
•Proved accurate in making
predictions for over a thousand
years
Dark Ages-Aristotelian beliefs
Mandatory
•The defeat of the Rome and
the empire by Germanic tribes
(Aric the brave!) led to
withdrawal of roman troops
across Europe
•Infrastructure, commerce,
education, and defense of cities
crumbled to dust….
•Highly divided Christian Europe
was battling Vikings from the
North, Mongols from the east,
and the Plague.
•The Church began to seize
power through various means…
http://www.coam.org.uk/Events/event2006/Dark%20Ages.jpg
http://www.newizv.ru/images/photos/other/20050126210812_4-VIKINGS.jpg
Copernicus (1473 - 1534)
• by 1400 the planetary positions were
no longer predicted by the
“almagest”
• Copernicus Proposed all the
following “fix”:
1. Earth spins on its axis once every 23
hrs, 56 min
2. Earth and all known planets orbited
the sun in circular orbits with sun at
center.
3. distant stars were so far that no
parallax could be seen .
4. Polar axis precessed every 26,000
years.
5. All the above just a mathematical
model to make accurate
predictions…easier than updating the
Ptolemaic model
So was Copernicus or Ptolemy’s
model correct?
•Tycho Brahe, Johanes Kepler, and
Galileo were the greatest contributors
to the debate.
•Brahe (pronounced Bray) was the last
and greatest pre-telescopic astronomer.
•Brahe felt that better observations
were needed .
•interested in proving that the “Tyconic
Universe" was correct
Johannes Kepler (1571 - 1630)
•Mathematician...sought out Brahe
for his famous data, and was hired
by Brahe to fit data to the tyconic
model universe. But….
•Kepler was trying to fit data to the
“Kepler model" Universe
•the orbits of the six known planets
fit into the largest spheres which
could be inscribed into the six
regular geometric solids
•--crazy by today's standards, but at
least the orbits were centered on the
sun!
•Wrote: Harmony of the worlds
relating music, geometry, astronomy
Kepler and Brahe...continued
•Brahe died and family wouldn't
release data after Brahe died
(don’t ask how he died). :
•Eventually Kepler "acquired"
Brahe's data and found that:
•--the orbit of Mars just isn't a
circle!
•Plato was wrong!
•The door to a true
understanding of the solar
system was now wide open!
Brahe’s tombstone, from: www.nada.kth.se/~fred/tycho/tychotomb.jpg
Kepler’s results
• From Brahe’s data, Kepler
deduced three laws:
1. Planets orbit the sun in
Ellipses with the sun at one
focus
2. A line joining a planet and
the sun sweeps out equal
areas in equal times
These three relations are now
known as Kepler's three laws.
Extra for experts: x and y are the positions
of the Earth with 0,0 at intersection of
major and minor axis.
Kepler’s third law
1. The cube of a planets semimajor axis is proportional to
the square of its orbital
period a3 = T2
2. a = semi-major axis –also
average distance from
planet to sun (also written as
d or r). Units are AU’s.
3. T = orbital period (also
written as P). Units are
years.
4. Newton later used this
A graph of semi-major axis cubed on
discovery to develop and
vertical axis, and orbital period squared on
prove the law of universal horizontal axis. Clearly not a coincidence!
gravitation.
After Kepler
•an accurate description of the
Solar system
•definitive proof that the Earth
orbited the sun, and spun on its
axis (most of that due to
Galileo—stay tuned!
Missing: an explanation of Why
the planets orbited the sun and
why Kepler's mysterious laws
NASA’s Project
were true!
Kepler—to detect
terrestrial planets
orbiting other stars!
Galileo(1564 -1642)
•Mathematician, physicist,
astronomer
•If you take a course in either
Area, Galileo’s name comes up
often
•Heard about telescope and
built one to explore the heavens
•Proved the Copernican model
and developed physics to
explain Earth could orbit sun,
etc.
•Paid a price for his curiosity
What did Galileo observe with his
telescope?
•Venus had
phases like the
Moon:
•Size always
changed with
phase
•At Crescent
Phase Venus was
always closest to
Earth
•At Full Phase,
Venus was always
farthest
from: http://astro.ysc.go.jp/venus-phases.jpg
Conclusion?
•Venus orbited
sun:
•Not the Earth
•Clearly not in
keeping with the
official Geocentric
model!
•What else could
be wrong?
The Trial of Galileo
Jupiter has moons that Orbit Jupiter( not the Sun)
photo from:
http://www.ladeltascience.com/astronomy/kisatchie04/ju
piterand moons.jpg
The Galilean
Moons
The Sun has spots
http://solar.physics.montana.edu/canfield/ssu_images/sunspots.gif
the Moon has craters
•So the Moon was
a world like the
Earth…
•Not a perfect
geometric object
as Plato taught.
Plato to Galileo: review
Write down one important idea or contribution
for each of the following people. One
sentence each. Give approximate date as
well.
1. Aristotle
2. Plato
3. Brahe
4. Copernicus
5. Galileo
6. Kepler
7. Ptolemy
Important terms—define in one or
two sentences
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Parallax shift
Sidereal day and month
Epicycle
Geocentric
Heliocentric
Precession cycle (include period)
Retrograde motion
Centripetal acceleration
Kepler’s laws
Phases of Venus