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Astronomy 101: 9/23/2008
Announcements
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PRS question. We are made from a variety of
elements; carbon is a particularly important
example.
True or false: most of the atoms from which
we are made were once deep inside the Sun.
1. TRUE
PRS question. As soon as the professor fires
gun, the monkey will hear the gunshot and drop
from the tree.
In order to hit the monkey with the bullet,
the professor should:
1. Aim slightly below the monkey.
This will “lead” the monkey’s fall,
i.e., by aiming low, he’ll compensate
for the distance the monkey falls
before the bullet gets there.
2. Aim directly at the monkey.
Ancient astronomers:
Why did they do it?
Orientation of the waxing crescent moon in Central
Africa during the course of the year: long used to
predict the arrival of the rainy season.
2. FALSE
Yes, the Sun creates heavier elements in its interior.
However, those elements remain stuck deep inside.
Something must happen to the Sun to get the stuff out!
Why did they do it?
How is the week connected to the planets??
Consider the planet names used by Teutonic tribes (Germany):
• Archeologists & anthropologists surmise:
– to keep time
– for agricultural and navigation purposes
– for religious purposes
• As far as we can tell, none of these ancient
cultures tried to build a physical model based on
their observations.
• Instead, they created myths to explain the motions
of the objects in the sky.
Object
Sun
Moon
Mars
Mercury
Jupiter
Venus
Saturn
Teutonic Name
Sun
Moon
Tiw
Woden
Thor
Fria
Saturn
English day
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Stonehenge
(completed 1550 BC)
Stonehenge
This famous structure in England was used as an observatory.
• If you stand in the middle:
– the directions of sunrise &
sunset on the solstices is
marked.
– the directions of extreme
moon rise & set are marked.
• The Aubrey holes are believed to
be an analog eclipse computer.
Mayans (fl. A.D. 400 – 1200)
• Accurately predicted eclipses
• Venus was very important
• Mayan mathematics
the Observatory at Chichén Itzá
Anasazi (ca. A.D. 1000)
• lived in “four corners”
area of SW USA
• built structures to mark
solstices and equinoxes
– invented the concept of “zero”
– base 20 counting system
Sun Dagger at Fajada Butte
Plains Tribes of N. America
• star maps and sighting
circles were drawn on
the ground to mark:
– solstice rising points
of Sun
– rising points of stars
Big Horn Medicine Wheel, WY
Greek astronomy and the
beginnings of science
Greek astronomers:
• Carefully observed the sky
• Applied logic and math to formulate
hypotheses, make predictions, and then
test them with additional observations
• But, they were also swayed by, e.g.,
aesthetics
Plato (428 - 348 BC)
Aristotle (384 -322 BC)
• Scientific approach
• Earth’s shadow on the
Moon during a lunar
eclipse is round.
Therefore the earth is
round!
• Observers see different
stars at different locations
on the Earth. Also favors
round shape.
• All natural
motion is circular
• Reason is more
important than
observation
Eratosthenes (276 - 195 BC)
• Measured the circumference of the Earth as follows:
• The Sun is at the zenith in the city of Syene at noon on the
summer solstice.
•But at the same time in Alexandria, it is 7° from the zenith.
The Wanderers
Since ancient times, people have noticed 5 bright
“stars” that seem to wander among the fixed stars.
“Planet” means wanderer.
The planets normally
move eastward relative to
the stars like the Sun &
Moon (direct motion), but
sometimes they switch
around and move
westward (retrograde
motion)
• Eratosthenes inferred that
Alexandria was 7° of latitude
north of Syene.
• The distance between the
two cities is 7/360 times the
Earth’s circumference.
• His result of 42,000 km is
very close to the right number:
40,000 km.
16
The Greek Model of the
Solar System
Geocentric model (because the Earth is at the center)
Serious flaw: had difficulty explaining retrograde motion!
Aristarchus (310-230 BC)
• From Earth’s shadow during
lunar eclipse, deduced that
the Moon has 1/3 the
diameter of the Earth
• Then used geometry to argue
that the Sun is much bigger
than the Earth! Also,
concluded that the Sun is
much farther than the Moon.
Proposed a heliocentric model!
Why did the ancient Greeks reject
the notion that the Earth orbits the
sun?
Parallax
Apparent shift of an object’s position due to
viewing it against a distant background
from two different points.
• It ran contrary to their senses.
• If the Earth rotated, then there should be a
“great wind” as we moved through the air.
• Greeks knew that we should see stellar
parallax if we orbited the Sun – but they
could not detect it.
Stellar Parallax
Apparent shift of a star’s position due to the
Earth’s orbiting of the Sun
Why Parallax Wasn’t Seen
Apparent shift of a star’s position due to the
Earth’s orbiting of the Sun
The nearest stars are
much farther away than
the Greeks thought.
So the parallax angles of
the star are so small, that
you need a telescope to
observe them.
As distance increases, the
parallax angle becomes smaller
Measuring Distance with
Parallax
Apparent shift of a star’s position due to the
Earth’s orbiting of the Sun
By measuring the
parallax angle p,
we can
measure the
distance to the
nearby star!
Most sophisticated geocentric model
developed by Claudius Ptolemy
Epicycle idea: each planet follows a smaller circular
orbit that, in turn, follows the bigger circular orbit.
What changed?
• Like a wheel attached to a
wheel.
• Predicted future positions
of planets relatively
accurately
• Model remained favored
and in use for 1500 years!
1. Nicolaus Copernicus (1473-
How did people
overcome the nutty Greek
model?
Morning and Evening “Stars”
We see Mercury and
Venus follow the Sun
around in the sky. They
may go down after, or
come up before it. If they
go down after, we see
Light in
gray
= Mercury
them
the
evening.orbit
1543)
• Favored heliocentric
model because of
retrograde motion
• Yet he believed in
circular motion
De Revolutionibus
Orbium Coelestium
Yellow = Venus orbit
Ultimately, Copernicus was force to use epicycles too!!
Using simple geometry and angle
measurements, Copernicus estimated the
distances from the Sun to the planets
Inner planet (e.g., Venus)
Outer planet (e.g., Jupiter)
This is because they have orbits
inward of ours. That means they can
only be seen to a certain maximum
angle away from the Sun.
Planet distances calculated by Copernicus
Astronomical unit (AU): average distance between Earth and Sun
Planet
Distance
(Copernicus)
Mercury
Venus
Earth
Mars
Jupiter
Saturn
0.38 AU
0.72 AU
1.00 AU
1.52 AU
5.22 AU
9.17 AU
Distance
(today)
0.39 AU
0.72 AU
1.00 AU
1.52 AU
5.20 AU
9.54 AU
•
2. Tycho Brahe (15461601)
Great observer, but
before invention of
telescopes!
• Charted accurate
positions of planets
• Observed a “nova”
in 1572; also
discovered a comet
in 1577
Brahe’s island: Hven,
Denmark
• Hired
Johannes
Kepler in
1600
Tycho Brahe’s “telescope”
Brahe measured angles with impressive precision, and mapped
out the sky in unprecedented detail.
Johannes Kepler (1571-1630)
• Greatest theorist of his
day
• Struggled to explain
Brahe’s observations
with circular orbits
and failed, particularly
in the case of Mars
• With elliptical orbits,
• Finally realized that
all planetary motions
the circular orbits
could be explained and
were the problem!
predicted precisely!
Brahe’s observatory: Uraniborg
An ellipse is a special type
of oval...
A circle is defined by its center and its radius.
An ellipse is defined by its foci and its
major/minor axes.
A circle is a special type of
ellipse...
Consider an ellipse with two foci. If we move the foci
closer and closer together, they will eventually meet
and will both be located at the same spot. This spot is
the center of a circle!
Kepler’s First Law
1. Each planet’s orbit around the Sun is an
ellipse, with the Sun at one focus.
Kepler’s Second Law
2. A planet’s orbital speed varies so that a line
from the planet to the Sun sweeps out equal
areas in equal intervals of time.
perihelion: closest point to Sun
aphelion: most distant
point from Sun
PRS Question
Kepler’s Third Law
3. The ratio of the cube of a planet’s average
distance from the Sun to the square of its orbital
period is the same for each planet.
At aphelion, does a planet move faster,
slower, or the same speed as it does at
perihelion?
1. Faster
2. Slower
3. The same
speed
a3 / P2 = 1
a3 = P2
(a must be in AU and
P in years)
First correct mathematical formulas in astronomy!
Most asteroids are located between Mars
and Jupiter. If an asteroid has an average
distance of 3AU from the Sun, how long
does that asteroid take to orbit the Sun
(approximately)?
1.
2.
3.
4.
5.
0.5 years
1 year
2 years
5 years
50 years
Kepler’s 3rd law: P2 = a3
•
•
•
•
•
a = 3 AU
a3 = 3 x 3 x 3 = 27
P2 = 27, so P = square root (27) = √27
√27 is roughly equal to √25
√25 = 5 years
Asteroids are interesting
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
After Kepler, philosophers still adhered
to the Greek model for 3 reasons:
1. Falling objects should be left behind if the
Earth moves
2. The heavens must be perfect and
unchanging
3. Stellar parallax
Final key scientist in this story:
Galileo Galilei
Galileo’s arguments against the
Greek objections:
1.
2.
3.
Galileo’s Observations
• Galileo saw shadows
cast by the mountains
on the Moon.
• Observed craters.
• The Moon had a
landscape; it was a
“place”, not a perfect
heavenly body.
Used experiments to show that objects in motion tend to
remain in motion
Many observations (with the new-fangled invention
called the telescope showed that the heavens are far
from perfect (e.g., spots on the Sun, jagged mountains
and valleys on the Moon)
The Milky Way indicated that stars are far more
numerous than thought, and probably much more
distant than appreciated
Galileo’s Observations
• Galileo discovered
that Jupiter had four
moons of its own.
• Jupiter was the
center of its own
system.
• Heavenly bodies
existed which did
not orbit the earth.
Galileo’s observation of the phases of Venus was
the final evidence which buried the geocentric
model.
Geocentric
No gibbous or full phases!
Heliocentric
All phases are seen!
Galileo observed all phases!
Recent Observations (2004)
of Phases of Venus
Galileo nearly paid dearly
for his scientific research...