1 / 26

Lecture 7

This lecture covers Kepler's laws of planetary motion, including orbits, speed variations, and orbital periods. The outline also includes a discussion of Exam 1 and finishing up the material from the last lecture. The exam will be administered via the Blackboard system in the Testing and Tutoring Center. You have 75 minutes to complete the exam. Non-scientific calculators are allowed.

amejia
Download Presentation

Lecture 7

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 7 ASTR 111 – Section 002

  2. Reading • Chapter 4.4 and 4.5

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

  4. 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

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

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

  7. 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

  8. Text these numbers

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

  10. Equation for a circle

  11. Equation for an ellipse

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

  13. How would you convince someone that this is an ellipse? b=2 a=7

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

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

  16. Is this an ellipse? ? 10

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

  18. Kepler’s Second Law

  19. Kepler’s Third Law

  20. Sidereal Review

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

  22. 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

  23. 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 tow time intervals for which you sketched the triangular areas in Questions 3 and 4 would the planetbe traveling faster? Explain your reasoning!

  24. C D B E A F G H I

  25. 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.

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

More Related