Download Powerpoint 2003

The Copernican
Revolution
Figure 2-1
Stonehenge
Figure 2-2
Observatories in the Americas
The Greek Frame of Mind
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Much of the Greek method of thinking
revolved around philosophy instead of
scientific reasoning
Greeks valued perfection and therefore
any model of the universe should involve
the perfect shape, the circle
Greek also had no reason to believe that
the Earth was not the center of the
universe. Egotistical, yes - but
completely reasonable at the time
The only 'scientific' data they had
available to them was the motion of the
Sun, Moon, and planets, which were
monitored heavily at the time
Ptolemy ~140 AD
What is this?
Retrograde Motion within a Planetarium Ceiling – We will do this!
The Motion of the Planets
Retrograde Motion
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A model of the universe
would be very simple except
for the fact that the planets
undergo a looping motion in
their orbits
Retrograde Motion
Remember, in one night, all
planets still rise in the east
and set in the west
However, if you keep track
of the planet's position
versus the background stars
night to night, you will see
the planet 'move'
The word 'planet' means
wanderer in Greek
Jupiter and Saturn (6/2000 - 5/2001)
Figure 2-5
Inferior and Superior Orbits
Ptolemaic Model
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In order to produce the
retrograde motion of the
planets, Ptolemy created a
model with epicycles
All the planets orbited the Earth
in a perfect circle
The planet itself made a smaller
orbit centered upon the larger
orbit around the Earth
With the right timing, this
model can reproduce the
retrograde motion seen from
Earth
Deferent = larger circular orbit around Earth
Epicycle = smaller circular orbit around the deferent
Ptolemaic Model
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In Ptolemy's complete
model, each planet had its
own orbit around the Earth
with its own epicycle
• By changing the period of the
orbit and the epicycle, the
model could match
observations relatively well
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The Sun and the Moon
traveled around the Earth
in perfect circles
The entire model was
composed of more than 80
circles and was very
complicated
Simplified Ptolemaic Model
The Ptolemaic Model Survives
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Since the Ptolemaic model matched observations sufficiently
and no contrary evidence was produced, it was supported for
nearly 1,500 years!
After all, if the Earth was moving, shouldn't we feel it?
Also, the Greeks were smart enough to realize that if the Earth
was orbiting the Sun, it would produce stellar parallax
• The Greeks didn't believe it existed because they didn't have
telescopes to observe such small variations in a star's
position
On top of all this, the Dark Ages provided relatively little
advance in any sciences for Europe
The Copernican Revolution
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At the end of the Dark Ages, a
Polish cleric name Copernicus
devised a new model of the
universe where the Earth was no
longer at the center
The heliocentric (Sun centered)
model placed the Earth out of its
central position, yet still
maintained many of the
observations we see
The beauty in his model was its
simplicity over the Ptolemaic
• Occam's Razor
The simplest solution is the
best
Nicolaus Copernicus (1473-1543)
The Copernican Model
In the Copernican model, retrograde motion is an
apparent effect caused by the Earth 'overtaking' an
outer planet in its orbit
The Copernican Revolution
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Despite the fact that the Copernican model was a
better representation of the solar system, it was not
widely accepted
While it did provide a much simpler description
compared to Ptolemy, it did not necessarily improve
the predictive power of the model
The religious dogma of the time insisted upon Earth
being the center of the universe
Copernicus published his works in Latin, which was
unreadable by the common public
Galileo - The Observer
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A century after Copernicus'
work, other scientists began to
make strides toward
popularizing the heliocentric
model
Galileo was the first to use a
telescope to make detailed
observations of the sky
Though he did not invent the
telescope, he made many
working prototypes and trained
them on a variety of celestial
bodies
Galileo Galilei (1564-1642)
Galileo's Observations - I
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Galileo used his telescopes to
make observations of many
heavenly objects
The sketch to the right shows
Galileo's observations of the
moons of Jupiter
He noticed that the position of
these four moons changed night
to night, as if they were rotating
around Jupiter
These moons now bear his name
• The Galilean moons are:
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Io
Europa
Ganymede
Callisto
Galileo's Observations - II
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Galileo also noticed that
Venus was not simply a
point of light, but
actually a disk
He watched Venus go
through complete
phases, just like the
Moon
This cycle of phases can
only be satisfied by the
heliocentric model, not
the geocentric
The phases of Venus
Galileo's Observations - III
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Galileo also pointed his
telescope toward the Sun
• NEVER DO THIS
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He discovered that the
disk of the Sun was not
perfect and was
occasionally dotted with
small black spots
By making daily sketches
of these spots, he was
able to determine that the
Sun itself was rotating
Galileo - Acceleration of Gravity
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Galileo discovered that the higher an object is
dropped, the greater its speed when it reaches
the ground
All falling objects near the surface of the Earth
have the same acceleration (9.8 m/s2)
The acceleration of gravity on the surface of
other solar-system bodies depends on their
mass and radius
• Mars and the Moon have a smaller acceleration of
gravity
• Saturn is about the same as Earth
• Jupiter is more than Earth
Astronaut Alan Bean
Performed Galileo’s experiment on the Moon
Galileo's Conclusion
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All of Galileo's observations were
pointing towards a heliocentric view of
the universe
Galileo published his observations and
conclusions in multiple works,
including some published in Italian to
appeal to a wider audience
Galileo was threatened with torture,
forced to deny his beliefs in the
heliocentric model, and sentenced to
house arrest for the rest of his life
The seeds of the Copernican
Revolution had been planted
You makin’ that up
!!!
Tycho Brahe - An Observer
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Tycho Brahe was a
prominent scholar and
aristocrat in Denmark in
the mid-late 1500's
He made a huge number
of observations of the
stars and planets, all
with the naked eye
• Even without a telescope,
he was very accurate in his
measurements
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Also recorded the
appearance of comets
and supernovae
Tycho (1546-1601)
Brahe’s Model
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Geo-Heliocentric
Wanted to please the
church and his
observations
simultaneously.
Let Earth still be most
important with other
planets orbiting sun.
Johannes Kepler - A Theorist
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Shortly before his death,
Tycho began working
with another scientist
named Kepler
Kepler was put to the
task of creating a model
to fit all of Tycho's
planetary data
Kepler spent the
remainder of his life
formulating a set of laws
that explained the
motion of the planets
Kepler (1571 - 1630)
Kepler's First Law
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Kepler first noted that the
orbital path of a planet around
the Sun is an ellipse, not a
perfect circle
The Sun lies at one of the foci
of the ellipse
The eccentricity of an ellipse is
a measure of how 'squished'
from a circle the shape is
Focus
Focus
Most planets in the Solar
System are very close to a
perfect circle
• Eccentricity, e ~ 0 for a circle
Kepler's 1st Law: The orbital
paths of the planets are elliptical
with the Sun at one focus.
Kepler's First Law
=closest to the Sun
=farthest from the Sun
Kepler's Second Law
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Kepler also noticed that
the planets sweep out
equal areas in their orbit
over equal times
Notice that this means
the planet must speed up
and slow down at
different points
If it takes the same
amount of time to go
through A as it does C, at
what point is it moving
faster?
• C, when it is closest to
the Sun
Kepler's 2nd Law: An imaginary line
connecting the Sun to any planet
sweeps out equal areas of the
ellipse over equal intervals of time.
Kepler's Third Law
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Finally, Kepler noticed
that the period of
planet's orbit squared is
proportional to the cube
of its semi major axis
This law allowed the
orbits of all the planets
to be calculated
It also allowed for the
prediction of the
location of other
possible planets
Kepler's 3rd Law Simplified
T a
2
3
NOTE: In order to use the
equation as shown, you must be
talking about a planet in the Solar
System, T must be in years, and
a must be in A.U. !!!
Kepler's Third Law - Examples
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Suppose you found a new planet in the
Solar System with a semi major axis of
3.8 A.U.
T 2  a3
T 2  3.83  54.872
T  54.872
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1
2
 54.872  7.41 years
A planet with a semi major axis of 3.8
A.U. would have an orbital period of
7.41 years
Kepler's Third Law - Examples
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Suppose you want to know the semi
major axis of a comet with a period of
25 years
a3  T 2
a 3  252  625
a  625
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1
3
 3 625  8.55 A.U.
A planet with an orbital period of 25
years would have a semi major axis of
8.55 A.U.
Isaac Newton
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Kepler's Laws were a
revolution in regards to
understanding planetary
motion, but there was no
explanation why they worked
That explanation would have
to wait until Isaac Newton
formulated his laws of motion
and the concept of gravity
Newton's discoveries were
important because they
applied to actions on Earth
and in space
Besides motion and gravity,
Newton also developed
calculus
Newton (1642-1727)
Newton and the Apple - Gravity
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After formulating his three
laws of motion, Newton
realized that there must
be some force governing
the motion of the planets
around the Sun
Amazingly, Newton was
able to connect the
motion of the planets to
motions here on Earth
through gravity
Gravity is the attractive
force two objects place
upon one another
Gravitational Force
•
•
The gravitational
force is always
attractive
The strength of the
attraction decreases
with increasing
distance
The Gravitational Force
Gm1m2
Fg 
r2
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G is the gravitational constant
• G = 6.67 x 10-11 N m2/kg2
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m1 and m2 are the masses of the two
bodies in question
r is the distance between the two bodies
Gravity - Examples
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Weight is the force you feel due to the gravitational
force between your body and the Earth
• We can calculate this force since we know all the variables
Gm1m2
Fg 

2
r
(6.67 10
11
N m
24
)(
72
kg
)(
5
.
97

10
kg)
2
kg
6
2
(6.378 10 m)
2
Fg  705 N
1 Newton is approximately 0.22 pounds
0.22lbs
Fg  705 N 
 155lbs
1N
Gravity - Examples
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If gravity works on any two bodies in the universe,
why don't we all cling to each other?
• Replace the from previous examples with two people and the
distance with 5 meters
Gm1m2
Fg 

2
r
(6.67 10
11
N m
)(72kg)(65kg)
2
kg
2
(5m)
2
8
Fg  0.0000000125N  1.25 10 N
1 Newton is approximately 0.22 pounds
0.22lbs
Fg  1.25 10 N 
 2.75 10 9 lbs
1N
8
Orbit of Earth around Sun
Orbits
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The law of universal
gravitation accounts
for planets not falling
into the Sun nor the
Moon crashing into
the Earth
Paths A, B, and C do
not have enough
horizontal velocity to
escape Earth’s surface
whereas Paths D, E,
and F do.
Path E is where the
horizontal velocity is
exactly what is
needed so its orbit
matches the circular
curve of the Earth
The same concept holds for planetary
orbits about the Sun
PTYS/ASTR 206
Keplers Laws and Gravity 2
1/27/09
Galilean Satellites and Kepler’s Laws
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Newton derived Kepler’s third law using
physics and his universal law of
gravitation. His form of Kepler’s 3rd law
for the orbits of the planets about the Sun
is:
The EARTH
Is just a tiny planet
The Earth
has a moon
The Earth and Moon together, as seen from the departing Galileo space probe
The Sun
Mass
2x1030 kg
Radius
7x105 km
Central temperature
15 million K
Surface temperature
5780 K
Composition
(by mass)
75% hydrogen
25% helium
Our Planet is Pretty Big
Planets are Pretty Big…..Right?
Our sun is Pretty Big
Our sun is Pretty Big … Right?
Our sun is Pretty Big … Right?
…and our star is one of
200,000,000,000 in this…
Which Looks Like This:
…which is one of these…
…and there are about 40
billion other galaxies in the
universe.
How are we going to get a
handle on this BIG Universe of
ours???
Units of Distance
Astronomers use (and mix
together) units of distance.
Metric:
1 meter = 1 m
1 centimeter = 1cm
1 kilometer = 1 km
Astronomical Unit (AU) – Earth-Sun distance
= 1.496 x 1011 m
Light Year – Distance light travels in 1 year
= 9.46 x 1012 km
Parsec (pc) = = 3.08 x 1016 m
….kiloparsec (kpc), megaparsec (Mpc)
So…how big is IT anyway?
(the Universe that is….)
…about 10 billion-billion-billion centimeters in diameter
or
10,000,000,000,000,000,000,000,000,000 cm
or
1028 cm
or
10 billion l-y
or
6000 Mpc
Where is the Shuttle?
Where is the Shuttle?
Where is the Shuttle?
=
10 cm
12,800 km
Scale of the Universe
1) The Earth is the Size of a clenched fist
-
or…. 12,800 km = 10 cm
2) The Moon is 3500 km in Diameter
-
or….the size of the tip of your THUMB
3) The Moon is 384,000 km away
-
or…. 3 meters from the fist
4) The Sun is 1,400,000 km in diameter
-
or…. 11 meters in diameter
5) The Sun is 150,000,000 km away
-
or…. 1.2 km from the fist
The Earth and the Sun
Earth
Sun
Diameter
12800 km
1.5 million km (117x Earth)
Mass
6x1024 kg
2x1030 kg (333,000x Earth)
Composition
rocks
gas
(75% hydrogen
25% helium)
Rotation period
=1 day
~25 days