Transcript Lecture 1

Lecture 7
ASTR 111 – Section 002
Reading
• Chapter 4.4 and 4.5
Outline
1. Exam 1 Discussion
2. Finish material in last lecture
3. Kepler’s laws
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=7
If it were an ellipse, this would
always be true
2
2
x
y


1
2
2
7
2
If it were an ellipse, this would
always be true
?
6 1


1
2
2
7 2
36 1
  0.98
49 4
2
2
Is this an ellipse?
?
10
Kepler’s First Law
Planets orbit the Sun in an ellipse
b
=a
Kepler’s Second Law
Kepler’s Third Law
Sidereal Review
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
• 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 tow 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
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