Kepler's Laws of Planetary Motion in Lecture 7

1. Lecture 7 ASTR 111 – Section 002

2. There is a famous song by Pink Floyd with the lyrics "See you on thedark side of the moon".  Does this make sense? http://www.youtube.com/watch?v=WsuhJUqAtis

3. The Moon’s rotation always keeps the same face toward the Earth due to synchronous rotation.Is one side always dark?

4. Reading • Chapter 4.4 and 4.5

5. Outline • Exam 1 Discussion • Finish material in last lecture • 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.

6. 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. First Exam

7. Outline • Exam 1 Discussion • Finish material in last lecture • Kepler’s laws

9. Outline • Exam 1 Discussion • Finish material in last lecture • Kepler’s laws

10. Kepler proposed elliptical paths for the planets about the Sun Using data collected by Brahe, Kepler deduced three laws of planetary motion: • the orbits are ellipses • a planet’s speed varies as it moves around its elliptical orbit • the orbital period of a planet is related to the size of its orbit

11. Text these numbers

12. Abbreviation Circle with radius 1.0 x goes from -1.0 to 1.0 in steps of 0.1. Compute y using

13. Equation for a circle

14. Equation for an ellipse

15. How would you convince someone that this is an ellipse?

16. How would you convince someone that this is an ellipse? b=2 a=8

17. If it were an ellipse, this would always be true

18. If it were an ellipse, this would always be true

19. Kepler’s First Law Planets orbit the Sun in an ellipse b = a

20. Kepler’s Second Law

21. Sidereal Review A planet’s synodic period is measured with respect to the Earth and the Sun (for example, from one opposition to the next) Mnemonic: Sidereal period is real period, or period with respect to the stars.

22. Sidereal Review A planet’s synodic period is measured with respect to the Earth and the Sun (for example, from one opposition to the next) From the Greek word “Synodikos”, meaning conjunction

23. Kepler’s Third Law

24. Kepler’s Third Law This is a huge discovery!

25. 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

26. Kepler’s Laws • Planet orbit is ellipse • Equal area in equal time • Farther away planets orbit slower

27. Suppose that you are looking down on a solar system with one planet orbiting a star. You take a picture every 10 days. Does this planet obey Kepler’s laws? How do you know? How would the speed of this planet change? How would you measure the change in speed? #7 #8 #6 #9 #5 #4 #10 #11 #3 #12 #2 #1 Based on Lecture-Tutorials for Introductory Astronomy 2nd ed., Prather et. al, page 21

28. Suppose that you are looking down on a solar system with one planet orbiting a star. You take a picture every 10 days. 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 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 measure distance between dots. Speed = distance/time and time is 10 days, so if distance does not change, speed does not change. #7 #8 #6 #9 #5 #4 #10 #11 #3 #12 #2 #1 Based on Lecture-Tutorials for Introductory Astronomy 2nd ed., Prather et. al, page 21

29. Does this planet obey Kepler’s laws? How do you know? (Law 1) Orbit is a circle (a special type of ellipse where a=b). (Law 2) Equal areas are swept out in equal time. (Law 3) Always same distance but can’t tell without distance being known. Synodic period is 120 days = 120/365 Earth years.

30. 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.

31. The following planet obeys Kepler’s second law. 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. 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. 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! 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? During which of the two time intervals for which you sketched the triangular areas in Questions 3 and 4 would the planetbe traveling faster? Explain your reasoning!

32. C D B E A F G H I

33. The following planet obeys Kepler’s second law. 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. 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 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. 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 During which of the tw0 time intervals for which you sketched the triangular areas in Questions 3 and 4 would the planetbe traveling faster? Explain your reasoning!C-H because longer distance in same time means faster speed.

34. C D B E A 131 squares here F G H I

35. C D B E A 131 squares here F H G I

36. A better strategy … C D B E A F G H I

37. 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. • Does the planet appear to be traveling the same distance each month? • At which position would the planet have been traveling the fastest? The slowest? Explain your reasoning. • At position D, is the speed of the planet increasing or decreasing? Explain. • 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.

38. E D F C B G A L H K J I

39. 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 • At which position would the planet have been traveling the fastest? G. The slowest? A. Explain your reasoning. • At position D, is the speed of the planet increasing or decreasing? Explain. Increasing • 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.