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Lecture 6 Chapter 3
The Copernican Revolution
From the last lecture
Question
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•! If the Sun sets at 6pm,
when does a full Moon
rise?
•!
•!
6 pm. The side of the Moon we
see if facing the Sun, so when
the Sun is setting, the Moon is
rising.
Another way of looking at it:
•! The moon and Sun rising
times are 12 hrs apart. Sun
rose at 6 am ! Moon at
6pm.
chapter 2
Learning Goals
1 Describe how some ancient civilizations attempted
to explain the heavens in terms of Earth-centered models
of the universe.
2. Explain how the observed motions of the planets led to our
modern view of a Sun-centered solar system.
3. Describe the major contributions of Galileo and Kepler to
our understanding of the solar system.
4. State Kepler's laws of planetary motion.
5. Explain how astronomers have measured the true size of the solar
system.
6. Explain how the law of gravitation enables us to measure the masses
of astronomical bodies.
chapter 2
Goal 1
Learning Goals
1 Describe how some ancient civilizations attempted
to explain the heavens in terms of Earth-centered models
of the universe.
2. Explain how the observed motions of the planets led to our
modern view of a Sun-centered solar system.
3. Describe the major contributions of Galileo and Kepler to
our understanding of the solar system.
4. State Kepler's laws of planetary motion.
•  Ancient civilizations observed the skies
•  Many built structures to mark astronomical
events
Summer solstice
sunrise at
Stonehenge:
Alignment Astronomy
Egyptian pyramids.
•! Use circumpolar stars
(“Indestructibles”) to align the base of
the pyramids due north. This was
associated with eternity in the afterlife.
Stonehenge.
•! Main axis is aligned with the rising
of the Sun on the summer solstice.
Birth of Astronomy
•! Need to understand day, night, seasons (hunter-gatherers,
agriculture)
•! !"#$%&'()"%"*+&%(,-+-.*(!(/.0".+-.(-1(23"()&%".4&'
Birth of Astronomy
•! !"#$%$&'()*+,)-$.'*#)-"*(&+()
•! Celestial objects were considered divine, some events
like eclipses were believed to be omens announcing
the fate of countries and their rulers.)
Predictive Astronomy: Mayans
Mayans didn’t understand fractions, BUT measured the lunar cycle
and solar tropical year precisely
- (lunar cycle repeats every 149 new moons in 4400 days)
4400 days/149 = 29.5302 days
! less than 0.0004 difference with modern day value!
Solar tropical year:
365.2422
Mayan measurement:
365.2420!
The recognition and identification of events is
different from understanding their causes
This is not science
What Is Science?
“careful, disciplined, logical search for knowledge, obtained by
examination of the best available evidence and always subject to
correction and improvement upon discovery of better evidence”
1.! Unprejudiced
2.! Falsifiable
3.! Explain current observations and predict new ones.
Pseudo-science
1.! Non falsifiable (meaning the theory CANNOT be proved
right or wrong by available data) OR
2.! It doesn’t explain all observations, results are not
reproducible
ABOUT SCIENCE
Multiple hypothesis can equally well explain observations, how
do we choose?
1.! If we are lucky, predictions from one will prove it wrong, if
not
2.! Use Ockham’s Razor (“keep it simple”)
Ockham’s Razor
“entities should no be multiplied unnecessarily”
ABOUT SCIENCE
For example:
A.! Planets move in ellipses with the Sun in one focus because
of an attractive force between the Sun and the planets
B.! Planets move in ellipses with the Sun in one focus because
of an attractive force between the Sun and the planets
generated by powerful aliens
Which one will you choose?
ABOUT SCIENCE
Both explain the motion of the planets, but we choose A
A.! Planets move in ellipses with the Sun in one focus because
of an attractive force between the Sun and the planets
B.! Planets move in ellipses with the Sun in one focus because
of an attractive force between the Sun and the planets
generated by powerful aliens
WHY?
ABOUT SCIENCE
Ockham’s Razor: Keep it simple!
•!
B is not discarded because:
–!
–!
–!
it sounds absurd
we don’t like it or
we don’t believe in the existence of alien beings
•!
B is discarded because the statement about aliens is
unnecessary to describe the observe motion of the planets.
•!
That planets move in elliptical orbits does not provide evidence
in favor or against the existence of powerful aliens.
Scientific Models
•! Physical model to explain the workings of nature
•! Models apply known laws of nature to explain observations
•! Key aspects of a scientific model
!! models explain what is seen
!! models predict observations accurately
!! simplify your understanding of nature
•! Validity of models is tested by checking how well
predictions fit the best & new observations
•! Scientific models are not static but evolve when new &
better observations become available
Scientific Models
•! Physical model to explain the workings of nature
•! Models apply known laws of nature to explain observ
•! Key aspects of a scientific model
!! models explain what is seen
!! models predict observations accurately
!! simplify your understanding of nature
•! Validity of models is tested by checking how well
predictions fit the best & new observations
•! Scientific models are not static but evolve when new
better observations become available
The Greeks and Astronomy had a major
role in the birth of modern science
Modeling the Cosmos: Early Greeks
•! Greeks enjoyed philosophy which to them meant the attempt to
understand all things in nature.
•! Tools: Direct observation, highly developed mathematical skills
(geometry & trigonometry), and logic.
•! Starting point: Idea of Earth as center was simple and reinforced
philosophical and religious systems that taught the unique role of
humans in the universe.
•! Any model of the cosmos will have to explain:
–!
–!
–!
–!
Motion of the Sun
Motion of the stars
Motion of the Moon
Motions of the 5 planets visible to the unaided eye: Mercury, Venus, Mars,
Jupiter & Saturn
•! Tools: Direct observation, highly developed mathematical skills
(geometry & trigonometry), and logic.
•! Starting point: Idea of Earth as center was simple and reinforced
philosophical and religious systems that taught the unique role of
humans in the universe.
•! Any model of the cosmos will have to explain:
–!
–!
–!
–!
Motion of the Sun
Motion of the stars
Motion of the Moon
Motions of the 5 planets visible to the unaided eye: Mercury, Venus, Mars,
Jupiter & Saturn
Ancient astronomers
observed:
Sun
Moon
Stars
Five planets: Mercury,
Venus, Mars, Jupiter,
Saturn
Greek science was preserved through the dark
ages by muslim astronomers
Naked Eye Planets
Mercury
•! Closest to the Sun
•! Fastest moving planet
God of commerce
Messenger to the Gods
Venus
•! “The evening star”
•! Brightest object in the sky
Goddess of love
Earth?
Sun and Moon
Mars has large variations on brightness
Mars
•! The red planet.
Mars, God of War
by Diego Rodriguez de Silva y Velazques
Jupiter
•! Largest planet
Abduction of Ganymede
by Rubens
Jupiter and Callisto
by Rubens
The rings were not known to the ancients
Saturn
•! Planet with the largest ring system
Saturn (ca. 18th century) - Arabic
illustration showing agricultural activities
under direction of Saturn, God of
agriculture?
Planets, Gods & Days of Week
•! English names for most of
the days of the week come
from names by Teutonictribes from Germany
•! Tuesday : Tiw - god of war
•! Wednesday: Woden - god
of day & night
•! Thursday: Thor - god of
thunder - head god
•! Friday: Fria - goddess of
spring
Aristotle & A Spherical Earth
•! Aristotle (384-322 B.C.) showed by
proof that the earth was spherical:
Painting of
Aristotle by
Rembrandt
1! He observed that the Earth’s shadow is
curved during a lunar eclipse
“The shapes that the Moon itself shows are
of every kind -straight, gibbous, and
concave - but in eclipses the outline is
always curved: and since it is the
interposition of the Earth that makes the
eclipse, the form of this line will be caused
by the form of the Earth’s surface which is
therefore spherical”
Aristotle’s treatise On the Heavens
Composite image of successive pictures taken during
a lunar eclipse showing the Earth shadow.
Aristotle & A Spherical Earth
2! Aristotle learned from travelers that the
height of the Pole star above the horizon
varies as you travel from North to South
•! Going North: Polaris gets higher with respect
to the horizon
•! Going South: Polaris gets lower with respect
to the horizon
•! Go far enough south -- Polaris no longer
visible
!!Earth must be spherical!
Flat Earth
Spherical Earth
Aristotle & Geocentric Model
•! He pointed out that the motions in the sky could be explained
–! by a rotating celestial sphere or
–! a rotating Earth, but he rejected the idea of a moving Earth
It is surrounded by ten concentric spheres made of a perfectly transparent substance known as "quintessence."!
four is the Sun ("Solis"), five is Mars ("Martis"), six is Jupiter ("Iovis"), s
These spheres revolve around the earth, carrying the other celestial bodies.!
As you can see, one is the sphere "of the Moon" ("Lunae"), two is Mercury ("Mercurii"), three is Venus ("Veneris"),
and spheres eight, nine and ten hold the "fixed stars" (so-called because th
four is the Sun ("Solis"), five is Mars ("Martis"), six is Jupiter ("Iovis"), seven is Saturn ("Saturni"),
and spheres eight, nine and ten hold the "fixed stars" (so-called because they do not move relative to each other, unlike the planets,
which
move
among
the
other
stars).!
(The
symbols
by
the
names
of
the
pla
which move among the other stars).! (The symbols by the names of the planets are the traditional astrological symbols for them.!
The symbols in spheres eight, nine and ten are for the twelve astrological constellations, Gemini, Ares, etc.)!
The symbols in spheres eight, nine and ten are for the twelve astrological c
Beyond the tenth sphere is, as the words in the periphery say in Latin,
Beyond the tenth sphere is, as the words in the periphery say in Latin,
"The Kingdom of Heaven, the Abode of God and of the Elect."!
"The Kingdom of Heaven, the Abode of God and of the Elect."!
Question
•! Imagine you lived at the time of Aristotle. What observations
or evidence could you offer to support the idea of a stationary
earth?
–!We do not feel the earth moving
–!If earth moved then objects thrown upward would not
drop back to their point of departure
Question
•! Imagine you lived at the time of Aristotle. What observations
or evidence could you offer to support the idea of a stationary
earth?
–!We do not feel the earth moving
–!If earth rotated then objects thrown upward would not
drop back to their point of departure
–!If earth moved about the Sun, then one should observe
change in the apparent positions of the stars, stellar
parallax
Stellar Parallax
•! Apparent shift in the position of the stars because of the
motion of the observer.
Hipparchus (c. 150 B.C.)
•! Erected an observatory on Rhodes
•! compiled catalog of stellar coordinates - 850
entries
•! determined length of year to within 6 minutes
•! predicted lunar eclipses to within 1 hour
•! predicted the paths of totality for solar eclipses
•! Developed a geometrical, geocentric model of
the universe
Hipparchus
•! Deferent & Epicycle
–! Deferent - a large circle, either centered on Earth or
offset from Earth (eccentric)
–! Epicycle - smaller circle, centered on the circumference
of the deferent
–! Combination of Epicycle & Deferent explained
retrograde motion:
•! Planets fixed to the epicycle
•! Planets moved around epicycle which in turn moved
around the deferent
Run animation: geocentric model
Ptolemy (90- 168 A.D.)
•! Added geometrical devices to the basic
Hipparchus model to better explain the
motions of the planets
–! Epicycle, Deferent, Eccentric &
Equant
Eccentric:
Ptolemy made the deferent an
eccentric (not centered on
Earth)
Ptolemy
Equant:
Center of epicycle moves at a constant
distance from the eccentric, but at a
uniform angular rate from the equant.
•! Ptolemy never claimed his model described reality. It was a
mathematical representation to predict the positions of the
planets.
•! The model successfully predicted the observed motions of
planets and was the absolute authority until the 17th century.
Ptolemy
Equant
this can be used to give a very accurate description of
motion in an ellipse
Earliest models had Earth at center of solar
system
Needed lots of
complications to
accurately track
planetary motions
For clarity only the tracks of Venus and
Jupiter are shown
The predictions of the Ptolemaic system were
excellent
It needed better observations to bring about the downfall
1 Describe
chapter
2 how some ancient civilizations attempted
to explain the heavens in terms of Earth-centered models
Goal 2
of the universe.
Learning
Goals
Explain how
observed
of theattempted
planets led to our
12.Describe
how the
some
ancientmotions
civilizations
of a Sun-centered
solar
system.
tomodern
explainview
the heavens
in terms of
Earth-centered
models
of the universe.
3. Describe the major contributions of Galileo and Kepler to
understanding
of the solar
system.
2.our
Explain
how
the
observed
motions
of
the
planets
led
to
our
Goal 3
modern view of a Sun-centered solar system.
4. State Kepler's laws of planetary motion.
3. Describe the major contributions of Galileo and Kepler to
5. Explain
how astronomers
measured the true size of the
our
understanding
of the solarhave
system.
system.
4. State Kepler's laws of planetary motion.
6. Explain how the law of gravitation enables us to measure the
astronomical
bodies.
5.ofExplain
how astronomers
have measured the true size of the
system.
Copernicus (1473 – 1543)
•! Polish
•! Studied medicine and law
•! Wrote “De Revolutionibus” explaining his
Heliocentric model.
Heliocentric Model
the Copernican Revolution
Copernicus
1.  Earth is not at the center of everything.
2.  Center of Earth is the center of Moon’s orbit.
•!EAll
arthplanets
is one ofrevolve
six (thenaround
known)the
planets
3. 
Sun.that revolve about the
Sun.
4.  The stars are very much farther away than the
•!HSun.
e placed the planets in the correct order: Mercury, Venus,
Earth, Mars, Jupiter, and Saturn.
5.  The apparent movement of the stars around the
•!The nearer a planet is to the Sun, the greater its orbital speed.
Earth is due to the Earth’s rotation.
•!Correct scale of the solar system.
6.  The apparent movement of the Sun around the
•!The Universe is bigger than thought at the time since parallax is
Earth is due to the Earth’s rotation.
not observed.
7. 
motion
of planets
duetoto
Earth’s
•!SRetrograde
ince he retained
circular
orbits, heishad
use
a complicated
motion
around
Sun.motion of planets.
model
to be
able tothe
predict
•!Predicted observations as well as Ptolemaic system.
but not better!
Reaction to Copernicus
•!The book was an exercise in mathematical astronomy and not
very popular.
•!It didn’t improve predictions.
•!Almost all astronomers rejected the idea of a moving Earth.
•!The church remained silent, since nobody paid attention to the
book, it was easy to ignore.
Copernicus dedicated the book to Pope Paul III and addressed
the book only to astronomers. He delayed the publication of
the book until his final days.
2.2 The Geocentric Universe
Sun, Moon, and stars all have simple
movements in the sky
Planets:
•  Move with respect to
fixed stars
•  Change in brightness
•  Change speed
•  Undergo retrograde
motion
Text
2.3 The Heliocentric Model of the
Solar System
Sun is at center of solar system. Only Moon
orbits around Earth; planets orbit around Sun.
This figure
shows
retrograde
motion of
Mars.
Model also accounts for change in brightness
to explain the heavens in terms of Earth-centered models
of the universe.
Goal
3 how the observed motions of the planets led to our
2.
Explain
modern view of a Sun-centered solar system.
3. Describe the major contributions of Galileo and Kepler to
our understanding of the solar system.
4. State Kepler's laws of planetary motion.
5. Explain how astronomers have measured the true size of the
system.
6. Explain how the law of gravitation enables us to measure the
of astronomical bodies.
5 minute break
chapter 2
Learning Goals
1 Describe how some ancient civilizations attempted
to explain the heavens in terms of Earth-centered models
3
ofGoal
the universe.
2. Explain how the observed motions of the planets led to our
modern view of a Sun-centered solar system.
3. Describe the major contributions of Galileo and Kepler to
our understanding of the solar system.
4. State Kepler's laws of planetary motion.
5. Explain how astronomers have measured the true size of the
system.
Galileo Galilei (1564 - 1642)
•! Italian mathematician. Professor of
mathematics and astronomy.
•! He accepted the Copernican model of the
solar system.
•! 1609 he heard of the telescope and
constructed his own, he run many tests to
make sure the image seen by the telescope
was accurate.
•! Used the telescope to observe the sky.
•! 1610 published “The Sidereal Messenger”
with his discoveries.
2.4 The Birth of Modern Astronomy
Telescope invented around
1600
Galileo built his own, made
observations:
•  Moon has mountains and
valleys
•  Sun has sunspots, and
rotates
•  Jupiter has moons (shown)
•  Venus has phases
Geocentric vs. Heliocentric Model
How can we distinguish between the models?
Heliocentric: We should be able to observe phases on inferior
planets, similar to the phases of the moon.
2.4 The Birth of Modern Astronomy
Phases of
Venus cannot
be explained by
geocentric
model
Galileo
•! Jupiter has 4 moons revolving about it
with different periods.
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Galileo & A New Physics
•! Galileo realized the need to develop a new
physics to replace that of Aristotle.
•! Objections to Heliocentric Model
1.! Moving Earth ! objects on Earth (clouds,
stones, etc would be left behind)
2.! An ellipse is not a perfect shape, the heavens are
perfect and unchanging
3.! No stellar parallax
Describing Motion
•! speed – rate at which an object moves, i.e. the
distance traveled per unit time [m/s; mi/hr]
•! velocity – an object’s speed in a certain direction,
e.g. “10 m/s moving east”
•! acceleration – a change in an object’s velocity,
i.e. a change in either speed or direction is an
acceleration [m/s2]
The Acceleration of Gravity
•! As objects fall, they
accelerate.
•! The acceleration due
to Earth’s gravity is
10 m/s each second,
or g = 10 m/s2.
•! The higher you drop
the ball, the greater
its velocity will be at
impact.
If the initial velocity is zero then
s = (1/2) g t^2
s is the distance traveled in time t
g is the acceleration due to gravity
On Earth g is about 9.8 meter/second^2
Describing Motion
•! momentum – object’s mass ! object’s velocity ! m ! v
•! force – causes a change in an object’s momentum
•! If object’s mass does not change, a force causes change
in velocity…
Is Mass the Same Thing as Weight?
•! mass – the amount of matter in an object
•! weight – a measurement of the gravitational
force that acts upon an object.
•! Gravitational force “downward” is balanced by
“upward” force of the ground—the downward
force pressing you against the ground is what
you call your weight!
Galileo & A New Physics
•! Objections to Heliocentric Model
1.! Moving Earth ! objects on Earth (clouds,
stones, etc would be left behind)
horizontal motion is natural , with no forces, objects
would continue to move in a uniform way – INERTIA
Inertia
•! Inertia is defined as the tendency of a
body to oppose changes in velocity.
•! Galileo experimented with balls and
incline planes to study inertia
Gravity
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Galileo & A New Physics
•! Objections to Heliocentric Model
2. An ellipse is not a perfect shape, the heavens are
perfect and unchanging
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Galileo & A New Physics
•! Objections to Heliocentric Model
3. No stellar parallax
–! Milky Way made out of stars, stars farther than
expected ! parallax too small to be measured
Galileo & the Inquisition
•! Warned to stop teaching the Copernican model in 1616
•! Publishes “Two Chief World Systems” with approval of Church in
1632 - Comparison of Geocentric & Heliocentric models
The Dialogue
•! Dialogue: takes form of a conversation between 3
philosophers:
–!Salviati: brilliant philosopher
who argues for the Copernican
system
–!Simplicio: a good humored
fool who defends Geocentric
model using the Pope’s favorite
arguments
–!Sagredo: 3rd philosopher,
intelligent but uninformed.
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•!
•!
•!
•!
•! Church publicly
forgave Galileo’s
“crimes” in 1992!!!
2. Explain how the observed motions of the pl
modern view of a Sun-centered solar system.
3.
Describe
the major contributions of Galileo
Goal
4
our understanding of the solar system.
4. State Kepler's laws of planetary motion.
5. Explain how astronomers have measured th
system.
6. Explain how the law of gravitation enables u
of astronomical bodies.
2.5 The Laws of Planetary Motion
Kepler’s laws were
derived using
observations made by
Tycho Brahe
Tycho Brahe (1546 – 1601)
•!Danish nobleman
•!New improved observations were
needed to renovate astronomy.
•!Observed the sky for 20 years.
•!1572 “new transient star”: supernova
! He didn’t know what it was, but showed the new star was beyond the
orbit of the moon and implied a change in the heavens.
•!1577 “great comet” was also beyond the orbit of the moon and its
path carried it across the crystalline celestial spheres
! there were no crystalline spheres.
Johanes Kepler (1571 – 1630)
•!Tycho’s assistant and convinced
Copernican (Heliocentric).
•!He used Tychos observations to find
the true motion of the planets.
Asteroids and
Trojans
The
eccentric orbit of Mars
Had a key role in the development of Kepler’s theories
2.5 The Laws of Planetary Motion
1. Planetary orbits are ellipses, Sun at one focus
More Precisely 2-1: Some
Properties of Planetary Orbits
Semimajor axis and eccentricity of orbit
completely describe it
Perihelion: closest approach to Sun
Aphelion: farthest
distance from Sun
Each planet moves in an ellipse with the Sun at one focus. The length of a line drawn from the
Sun, to a planet and then to the empty focus, denoted by the dashed line, is always 2a, or twice
the semi-major axis, a. The eccentricity, or elongation, of the planetary ellipse has been greatly
overdone in this figure; planetary orbits look much more like a circle.
2.5 The Laws of Planetary Motion
2. Imaginary line connecting Sun and planet
sweeps out equal areas in equal times
Areas A, B and C are equal
2.5 The Laws of Planetary Motion
3. Square of period of planet’s orbital motion
is proportional to cube of semimajor axis
Kepler’s Three Laws of Planetary Motion
Law #1: Tells us the shape of a planet’s orbit
(ellipse, with Sun at one focus)
Law #2: Tells us how the planet’s speed depends on
where it is in the orbit
(planet moves faster as it nears the Sun)
Law #3: Tells us how the planet’s average speed depends
on the size of the orbit
(for bigger orbits, planets move more slowly)
2. Explain how the observed motions of the planets led to our
modern view of a Sun-centered solar system.
3. Describe the major contributions of Galileo and Kepler to
our understanding of the solar system.
4. State Kepler's laws of planetary motion.
5. Explain how astronomers have measured the true size of the solar
system.
6. Explain how the law of gravitation enables us to measure the masse
of astronomical bodies.
2.6 The Dimensions of the Solar System
Astronomical unit: mean distance from
Earth to Sun
First measured during transits of Mercury
and Venus, using triangulation
2.6 The Dimensions of the Solar System
Now measured using radar:
Ratio of mean
radius of Venus’s
orbit to that of
Earth is very well
known
modern view of a Sun-centered solar system.
3. Describe the major contributions of Galileo and Kepler to
our understanding of the solar system.
4. State Kepler's laws of planetary motion.
6 how astronomers have measured the true size of the solar
5.Goal
Explain
system.
6. Explain how the law of gravitation enables us to measure the masses
of astronomical bodies.
2.7 Newton’s Laws
Newton’s laws of
motion explain how
objects interact with
the world and with
each other.