The Science of Astronomy Copernicus, Tycho, and Kepler
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Today’s Topics
• Ancient Astronomy
• Greek Astronomy
• Models & Theories
• Ptolemaic (Earth-centered) model of solar system
• Copernicus, Tycho, & Kepler
• Problems with Ptolemaic system
• Copernican (Sun-centered) solar system
• Tycho & Kepler
• Kepler’s Laws of Orbits
Ancient Astronomy
• Astronomy is the oldest science,
stretching thousands of years into
prehistory
• All humans are scientific thinkers
• Choosing apples in the store
• Astronomy was important to ancient
people
• Determining time of day
• Predicting seasons & rainfall patterns
• Important for development of agriculture
• At right are Stonehenge (constructed
between 3100-1550 BCE) and Templo
Mayor (Aztec temple, built between
1325-1519) both of which can be used
to mark the equinoxes
Greek Astronomy
• Greeks were the first to create models
or theories of nature
• Models (or theories) are conceptual
representations which can explain
and predict observable phenomena
• Theories can never be proven - only
disproven
• A successful theory incorporates many
observations and can predict testable
observations correctly
• Examples of successful theories
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Plate tectonics
Special and General Relativity
Biological Evolution by Natural Selection
Genetics and Heredity (DNA)
Sun-centered Solar System (Kepler)
Earth-centered model of
the Solar System (c. 400 BCE)
Ptolemy (c. 100-170 CE)
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Ptolemy was a Greek astronomer who
created an Earth-centered model
The model correctly predicted the
positions of the Sun and planets to the
accuracy of the time (a few degrees the width of your hand at arms length)
The theory explained retrograde
motion (the apparent “backtracking”
of planets) using epicycles (circles on
circles) - Interactive Figure 3.15
This theory was far and away the best
of its day and lasted 1500 years (until
better observations came along)
Copernicus, Tycho, & Kepler
• By the time of Copernicus (1473-1543),
the predictions of the Ptolemaic model
were noticeably inaccurate
• Copernicus argued for a Sun-centered
system, based on a more natural
explanation of retrograde motion (when
you pass a car on the inside of a track, it
seems to be going backwards)
• However, he kept the idea of circular
orbits (which is incorrect), so his model
also required epicycles and was no more
simple or accurate than Ptolemy’s
• Many supporters preferred the aesthetic
advantages of the Copernican model
Tycho Brahe
• Born in 1546 to Danish noble
family
• Flamboyant and arrogant
• When 20 yrs old, had duel over
who was the best mathematician
and lost part of his nose, which
he replaced with a gold nose!
• Over 35 years he made
astronomical observations using
instruments of his own design
• He measured the positions of
objects with unprecedented
accuracy (less than 1/60th of a
degree; the width of a fingernail
at arm’s length)
Johannes Kepler
• Kepler was born in 1571 in
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southwest Germany
Had a religious training leading
him to a mystical view of the
Universe
In 1595 he was a high school math
teacher in Austria and had a
revelation – there were 6 known
planets and five perfect “Platonic”
solids
Maybe he could explain the orbits
of the planets!
He entitled his theory “The Sacred
Mystery of the Cosmos”
Tycho and Kepler together
• Problem – his beautiful theory
didn’t fit the observations!
• However, the observations (before
Tycho) weren’t that good, so he
doubted the observations
• In 1600, Kepler joined Tycho in
Prague (Tycho had left Denmark
due to quarrels with the King)
• Tycho died in 1601 and
bequeathed his data to Kepler
Triumph of Observation over Theory
• 8 years and 900 pages of calculations
later, Kepler had solved the problem
• “If you are wearied by this tedious
procedure, take pity on me…”
• Kepler tried seventy circular orbits to
try to explain the motion of Mars!
• Kepler’s genius is that he gave up
his cherished theory for the correct
description of Nature
Kepler’s Laws
• 1st Law - The Planets move in
elliptical orbits with the Sun at one
focus
• 2nd Law - Orbits sweep out equal
areas in equal times
• 3rd Law - More distant planets
orbit at slower average speeds,
obeying a simple mathematical
relationship
p2 ∝ a3
where p is the period of an orbit,
and a is the average distance of
the planet from the Sun
Ellipses
• An ellipse is a special type of oval that can be constructed using a
pencil, a string, and two tacks (Interactive Figure 3.18a)
• The eccentricity is a measure of how “squashed” the ellipse is
• A circle has an eccentricity of zero, and a very flat ellipse has an
eccentricity that approaches one
• The size of an ellipse is measured by its semi-major axis
(Interactive Figure - Eccentricity and semi-major axis of an ellipse)
Kepler’s 2nd Law
“Equal areas in equal times”
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In a given time, a line connecting the Sun to the planet will sweep out an area that
is the same in all parts of the orbit (Int. Fig. 3.20)
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Thus, the planet moves faster when it is closer to the Sun (Int. Fig. Kepler II)
Kepler’s 2nd Law
B
A
C
D
E
Lecture Tutorials
1.
Get right to work! You typically have 10-15 minutes to complete
these activities. That is plenty of time, if you don’t mess around.
2.
The questions go from easier to harder. Don’t spend a long time
agonizing over the early questions; they are generally pretty
straightforward. If there is a very simple answer that makes sense,
that is probably correct.
3.
Most of the questions on the exams are like those in the Lecture
Tutorials, so you are writing your own textbook! If you don’t
write complete clear explanations of your answers now, you are
going to be mad at the author of your textbook (yourself!) when
you go to study for the exam! :)
4.
If you feel pressured for time, at least write enough so that you can
go back later to write a more detailed explanation (aka, leaving
bread crumbs) – don’t write nothing!
5.
It is OK to change groups around to find people you work well with
Lecture Tutorial: Kepler’s 2nd Law
pp. 21-24
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Work with one or more partners - not alone!
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Get right to work - you have 15 minutes
•
Read the instructions and questions carefully.
•
Discuss the concepts and your answers with one another.
Take time to understand it now!!!!
•
Come to a consensus answer you all agree on.
•
Write clear explanations for your answers.
•
If you get stuck or are not sure of your answer, ask another
group.
•
If you get really stuck or don’t understand what the Lecture
Tutorial is asking, ask me for help.
Kepler’s 2nd Law Quiz I
The planet shown in the drawing obeys Kepler’s
Second Law. At which lettered position is the planet
speeding up?
B
A
C
D
E
Kepler’s 2nd Law Quiz II
The planet shown in the drawing obeys Kepler’s
Second Law. Each lettered position represents a
particular day during the year. During which day (at
which lettered position) will the planet move the
shortest distance?
B
A
C
D
E
Kepler’s 2nd Law Quiz III
Which of the three planet orbits shown below (a, b or c)
would you say most closely matches the shape of
Earth’s orbit around the Sun?
a
b
c
Kepler’s 3rd Law
• Kepler’s 3rd Law concerns the
relationship between the average
distance of a planet from the Sun
and its orbital period
• The closer a planet is to the Sun, the
shorter its period
• This is both because the distance
travelled each period is shorter and
because the closer planets move
faster (Interactive Figure 7.1)
• Kepler’s 3rd Law can be expressed
mathematically as
Period 2 ∝ Distance3
• Note that the period (and speed) do
not depend on the planet’s mass
Kepler’s 3nd Law
Period 2 ∝ Distance3
Planetary Data (including Eris)
Name
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Eris
Orbital Elements
Semimajor Axis
(AU)
Eccentricity
0.3870989
0.72333199
1.0000001
1.5236623
5.2033630
9.5370703
19.191264
30.068963
39.481687
67.5
0.206
0.007
0.017
0.093
0.048
0.054
0.047
0.0086
0.249
0.437
Orbital Period
p2/a3
(years)
(yr2/AU3)
0.2408467
0.61519726
1.0000174
1.8808476
11.862615
29.447498
84.016846
164.79132
247.92065
560
0.9996
1.0002
1.0000
1.0000
0.9988
0.9996
0.9987
0.9989
0.9987
1.0197
Note that if a is measured in astronomical units (AU), and p
is measured in years, then Kepler’s 3rd Law can be written
p2 = a3
Lecture Tutorial: Kepler’s 3rd Law
pp. 25-28
•
Work with one or more partners - not alone!
•
Get right to work - you have 15 minutes
•
Read the instructions and questions carefully.
•
Discuss the concepts and your answers with one another.
Take time to understand it now!!!!
•
Come to a consensus answer you all agree on.
•
Write clear explanations for your answers.
•
If you get stuck or are not sure of your answer, ask another
group.
•
If you get really stuck or don’t understand what the Lecture
Tutorial is asking, ask me for help.
Homework
•
For homework
• Complete the Lecture Tutorials Kepler’s 2nd Law
and Kepler’s 3rd Law (if necessary)
• Complete the ranking tasks, Kepler Orbital
Motion #1, 2, 5 (download from class website)
Kepler’s 3rd Law Quiz I
If a small chunk of rock and the large International
Space Station are orbiting Earth at the same altitude
above Earth’s surface, which object takes longer to
orbit once around Earth?
a) the large space station
b) the small chunk of rock
c) they would take the same amount of time
Kepler’s 3rd Law Quiz II
Consider a planet orbiting the Sun. If the orbital
distance of the planet doubled, then the planet would take
a) More than twice as long to orbit the Sun
b) Exactly twice as long to orbit the Sun
c) The same amount of time to orbit the Sun
d) Exactly half as long to orbit the Sun
e) Less than half as long to orbit the Sun