2. Chapter 1
Kepler’s Laws
Charles Hakes
Fort Lewis College 2

3. Outline Logistics Review Kepler’s Laws Charles Hakes
Fort Lewis College 3

4. Logistics http://faculty.fortlewis.edu/hakes_c/
Read about Newton (1.4).
Charles Hakes
Fort Lewis College 4

5. I read the section on Kepler’s laws.
A) True B) False
Charles Hakes
Fort Lewis College 5

6. Planetary orbits are A) Circular. B) Parabolic. C) Elliptical.
D) Hyperbolic.
Charles Hakes
Fort Lewis College 6

7. Planetary orbits are A) Circular. B) Parabolic. C) Elliptical.
D) Hyperbolic.
Charles Hakes
Fort Lewis College 7

8. Two planets have orbits with the same periods. Which is true?
A) Their velocities must be the same.
B) They must have the same eccentricity.
C) They must have the same semi-major axis.
D) Their orbits must be identical.
Charles Hakes
Fort Lewis College 8

9. Two planets have orbits with the same periods. Which is true?
A) Their velocities must be the same.
B) They must have the same eccentricity.
C) They must have the same semi-major axis.
D) Their orbits must be identical.
Charles Hakes
Fort Lewis College 9

10. Figure 1.15 Johannes Kepler (1571-1630)
Charles Hakes
Fort Lewis College 10

11. Kepler Overview Theoretician Used observations of Tycho Brahe
Wanted a unifying principle to explain the motions of the planets without epicycles.
Took ~29 years, but he did it.
Charles Hakes
Fort Lewis College 11

12. Figure 1.16 Tycho Brahe
Charles Hakes
Fort Lewis College 12

13. Kepler’s “Laws” http://faculty.fortlewis.edu/hakes_c/
Allow pop-up windows!
Charles Hakes
Fort Lewis College 13

14. Kepler’s “Laws” That “shape” law
Orbits are elliptical, with the Sun at one focus.
Charles Hakes
Fort Lewis College 14

15. Kepler’s “Laws” That “shape” law That “speed” law
Orbits are elliptical, with the Sun at one focus.
That “speed” law
(A line between the Sun and a)Planet sweeps out (in the ellipse) equal areas in equal times.
Charles Hakes
Fort Lewis College 15

16. P2 (years) = a3 (astronomical units)
Kepler’s “Laws”
That “shape” law
Orbits are elliptical, with the Sun at one focus.
That “speed” law
(A line between the Sun and a)Planet sweeps out equal areas (of the ellipse) in equal times.
That “math” law
P2 (years) = a3 (astronomical units)
Charles Hakes
Fort Lewis College 16

17. A planet orbit could be circular.
A) True
B) False
Charles Hakes
Fort Lewis College 17

18. A planet orbit could be circular.
A) True
B) False
Charles Hakes
Fort Lewis College 18

19. Two planets have orbits with the same sized semi-major axis
Two planets have orbits with the same sized semi-major axis. Which is true?
A) The planet with the most eccentric orbit moves faster all the time.
B) The planet with the most eccentric orbit moves faster some of the time.
C) The planet with the most eccentric orbit never moves faster.
D) Not enough information to answer.
Charles Hakes
Fort Lewis College 19

20. Two planets have orbits with the same sized semi-major axis
Two planets have orbits with the same sized semi-major axis. Which is true?
A) The planet with the most eccentric orbit moves faster all the time.
B) The planet with the most eccentric orbit moves faster some of the time.
C) The planet with the most eccentric orbit never moves faster.
D) Not enough information to answer.
Charles Hakes
Fort Lewis College 20

21. Assume a planet orbits exactly twice as far from the Sun as the Earth does.
A) It’s period is 2 years exactly.
B) It’s period is between 2 and 3 years
C) It’s period is between 3 and 4 years
D) It’s period is 4 years exactly.
Charles Hakes
Fort Lewis College 21

22. Assume a planet orbits exactly twice as far from the Sun as the Earth does.
A) It’s period is 2 years exactly.
B) It’s period is between 2 and 3 years
C) It’s period is between 3 and 4 years
D) It’s period is 4 years exactly.
Charles Hakes
Fort Lewis College 22

23. Three Minute Paper Write 1-3 sentences.
What was the most important thing you learned today?
What questions do you still have about today’s topics?
Charles Hakes
Fort Lewis College 23

24. Three Minute Paper Answer this question (without discussion):
What is the air-speed velocity of an unladen swallow?
Charles Hakes
Fort Lewis College 24