Transcript Lecture 1

Lecture 7
ASTR 111 – Section 002
• There is a famous song by Pink Floyd with
the lyrics "See you on the
dark side of the moon". Does this make
sense? http://www.youtube.com/watch?v=WsuhJUqAtis
The Moon’s
rotation always
keeps the same
face toward the
Earth due to
synchronous
rotation.
Is one side
always dark?
Reading
• Chapter 4.4 and 4.5
Outline
1. Exam 1 Discussion
2. Finish material in last lecture
3. Kepler’s laws
To help you prepare for the exam,
I will post a quiz in a few hours. It
will cover the material discussed
Tuesday and today. It is due on
9/29 at 9 am.
First Exam
• 9/29 (Tuesday).
• Based on lecture notes, problems worked in
lecture, and quizzes. (Chapters 1 through 4.5
have more details on these subjects.)
• Approximately 50 questions.
• In the Testing and Tutoring Center in Sub II
(Student Union Building II)
• Exam will be administered via Blackboard
system.
• You may bring a non-scientific calculator!
• You have 75 minutes to complete the exam.
Outline
1. Exam 1 Discussion
2. Finish material in last lecture
3. Kepler’s laws
Outline
1. Exam 1 Discussion
2. Finish material in last lecture
3. Kepler’s laws
Kepler proposed elliptical paths for the
planets about the Sun
Using data collected by
Brahe, Kepler deduced
three laws of planetary
motion:
1. the orbits are ellipses
2. a planet’s speed varies
as it moves around its
elliptical orbit
3. the orbital period of a
planet is related to the
size of its orbit
Text these numbers
Abbreviation
Circle with radius 1.0
x goes from -1.0 to 1.0 in
steps of 0.1.
Compute y using
2
2
x
y


1
2
2
r
r
Equation for a circle
2
2
x
y


1
2
2
r
r
Equation for an ellipse
2
2
x
y


1
2
2
a
b
How would you convince someone
that this is an ellipse?
How would you convince someone
that this is an ellipse?
b=2
a=8
If it were an ellipse, this would
always be true
2
2
x
y


1
2
2
8
2
If it were an ellipse, this would
always be true
?
7 1


1
2
2
8 2
49 1
  1.0156
64 4
2
2
Kepler’s First Law
Planets orbit the Sun in an ellipse
b
=a
Kepler’s Second Law
Sidereal Review
Mnemonic: Sidereal
period is real period, or
period with respect to the
stars.
A planet’s
synodic period
is measured
with respect to
the Earth and
the Sun (for
example, from
one opposition
to the next)
Sidereal Review
From the Greek word
“Synodikos”, meaning
conjunction
A planet’s
synodic period
is measured
with respect to
the Earth and
the Sun (for
example, from
one opposition
to the next)
Kepler’s Third Law
Kepler’s Third Law
This is a huge discovery!
Confucius says
“I hear and I forget. I see and I remember. I do and I
understand.”
http://www.thequoteblog.com/wp-content/uploads/2007/06/confucius.jpg
Kepler’s Laws
• Planet orbit is ellipse
• Equal area in equal time
• Farther away planets orbit slower
•
Suppose that you are
looking down on a solar
system with one planet
#9
orbiting a star. You take
a picture every 10 days.
1. Does this planet obey
Kepler’s laws? How do
#10
you know?
2. How would the speed of
this planet change?
How would you measure #11
the change in speed?
#8
#7
#6
#5
#4
#3
#12
#2
#1
Based on Lecture-Tutorials for Introductory Astronomy
2nd
ed., Prather et. al, page 21
•
1.
2.
Suppose that you are looking
down on a solar system with one
planet orbiting a star. You take a
picture every 10 days.
#9
Does this planet obey Kepler’s
laws? How do you know? (1)
Orbit is a circle (a special type of
ellipse where a=b). (2) Equal
areas are swept out in equal
time. (3) Always same distance,
but can’t tell without distance
being known. Synodic period is #10
120 days = 120/365 years.
How would the speed of this
planet change? How would you
measure the change in speed?
Speed does not change. I would #11
measure distance between dots.
Speed = distance/time and time
is 10 days, so if distance does
not change, speed does not
change.
Based on Lecture-Tutorials for Introductory Astronomy
2nd
#8
#7
#6
#5
#4
#3
#12
ed., Prather et. al, page 21
#2
#1
1. Does this planet obey Kepler’s laws? How do
you know?
1. (Law 1) Orbit is a circle (a special type
of ellipse where a=b).
2. (Law 2) Equal areas are swept out in
equal time.
3. (Law 3) Always same distance but can’t
tell without distance being known.
Synodic period is 120 days = 120/365
Earth years.
2. How would the speed of this planet
change? How would you measure the
change in speed?
• Speed does not change.
• I would measure distance between
dots. Speed = distance/time and
time is 10 days, so if distance does
not change, speed does not
change.
• The following planet obeys Kepler’s second law.
3. Draw two lines: one connecting the planet at Position A to the star and a
second line connecting the planet at Position B to the star. Shade in the
triangular area swept out by the planet when traveling from A to B.
4. Which other two planet positions, out of C-I, could be used together to
construct a second swept-out triangular area that would have
approximately the same area as the one you shaded in for Question 3?
Shade in the second swept-out area using the planet positions that you
chose. Note: Your triangular area needs to be only roughly the same size;
no calculations are required.
5. How would the time it takes the planet to travel from A to B compare to the
time it takes to travel between the two positions you selected in the
previous questions? Explain your reasoning!
6. During which of the two time intervals for which you sketched the triangular
areas in questions 3 and 4 is the distance traveled by the planet greater?
7. During which of the two time intervals for which you sketched the triangular
areas in Questions 3 and 4 would the planet be traveling faster? Explain
your reasoning!
C
D
B
E
A
F
G
H
I
• The following planet obeys Kepler’s second law.
3. Draw two lines: one connecting the planet at Position A to the star and a
second line connecting the planet at Position B to the star. Shade in the
triangular area swept out by the planet when traveling from A to B.
4. Which other two planet positions, out of C-I, could be used together to
construct a second swept-out triangular area that would have approximately
the same area as the one you shaded in for Question 3? Shade in the
second swept-out area using the planet positions that you chose. Note:
Your triangular area needs to be only roughly the same size; no
calculations are required.
C-H
5. How would the time it takes the planet to travel from A to B compare to the
time it takes to travel between the two positions you selected in the previous
questions? Explain your reasoning! Same.
Equal area =
equal time.
6. During which of the two time intervals for which you sketched the triangular
areas in questions 3 and 4 is the distance traveled by the planet greater?
C-H
7. During which of the tw0 time intervals for which you sketched the triangular
areas in Questions 3 and 4 would the planet be traveling faster? Explain
C-H because longer distance in same
time means faster speed.
your reasoning!
C
D
B
E
A
131 squares here
F
G
H
I
C
D
B
E
A
131 squares here
F
H
G
I
A better strategy …
C
D
B
E
A
F
G
H
I
8. The drawing on the following slide shows another
planet. In this case, the twelve positions are exactly
one month apart. As before, the plane obeys Kepler’s
second law.
9. Does the planet appear to be traveling the same
distance each month?
10. At which position would the planet have been traveling
the fastest? The slowest? Explain your reasoning.
11. At position D, is the speed of the planet increasing or
decreasing? Explain.
12. Provide a concise statement that describes the
relationship that exists between a planet’s orbital speed
and the planet’s distance from its companion star.
E
D
F
C
B
G
A
L
H
K
I
J
8.
9.
The drawing on the following slide shows another planet. In this case, the
twelve positions are exactly one month apart. As before, the planet obeys
Kepler’s second law.
Does the planet appear to be traveling the same distance each month?
No
10. At which position would the planet have been traveling the fastest?
G.
The slowest? A. Explain your reasoning.
11. At position D, is the speed of the planet increasing or decreasing?
Explain. Increasing
12. Provide a concise statement that describes the relationship that exists
between a planet’s orbital speed and the planet’s distance from its
companion star. Increases with decreasing distance
from the planet. Decreases with increasing
distance from planet.