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Kepler’s Laws

Kepler’s Laws. Why you can get there from here. Goals. Kepler: Astrologer turned Astronomer. Kepler’s Laws. Proof of Kepler’s Laws. Astrology to Astronomy.

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Kepler’s Laws

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  1. Kepler’s Laws Why you can get there from here.

  2. Goals • Kepler: Astrologer turned Astronomer. • Kepler’s Laws. • Proof of Kepler’s Laws.

  3. Astrology to Astronomy • On page 64 Carl says “Kepler stood on the cusp of history; the last scientific astrologer was the first astrophysicist.” What’s the difference between these two and what does it mean to make the transition from one to the other?

  4. Kepler’s Laws • Orbits are always ellipses. • Sweep out equal areas in equal times. • The period of orbit is related to average separation.

  5. units Gravity is the Force • Newton’s Law of Gravity: • So: • Becomes:

  6. Concept Test • Which of the following orbits is NOT allowed under Kepler’s First Law? a. b. c. d.

  7. Concept Test • Kepler’s Second Law says “a line joining a planet and the Sun sweeps out equal areas in equal amounts of time.” Which of the following statements means nearly the same thing? • Planets move fastest when they are moving toward the Sun. • Planets move farther in a given time when they are closer to the Sun. • Planets move equal distances throughout their orbit of the Sun. • Planets move slowest when they are moving away from the Sun. • Planets move the same speed at all points during their orbit of the Sun.

  8. Concept Test • You discover a new comet around our Sun: • Average distance from Sun = 4 AU. • What is the period? • 1 year • 4 years • 8 years • 64 years • Don’t have all the necessary information.

  9. Concept Test • Saturn takes about 30 years to make one orbit around the Sun. About how far away from the Sun is it? • 1 AU • 5 AU • 10 AU • 30 AU • 900 AU

  10. Concept Test • Aliens attack our Sun and reduce it to a tiny cinder only 1/16th its original mass. If the Earth stays at a distance of 1 AU from the Sun, how long will it now take to orbit the Sun? • 1 year • 4 years • 8 years • 16 years • 1/16 year

  11. Kepler’s Laws • Kepler’s First Law: • All planets orbit in an ellipse with the Sun at one focus. • A circle is a special case of an ellipse where both focii are at the same point.

  12. Orbital Mechanics Courtesy David Crisp and WFPC2 Science Team

  13. Mars: It Works Courtesy NASA/JPL/Cornell

  14. Courtesy NASA/JPL/Cornell It Works

  15. Spirit: View of Columbia Hills from floor of Gusev Crater

  16. Spirit: In the Columbia Hills.

  17. Cassini at Saturn

  18. Class Structure Investigate 3 Key Topics this semester: • Extrasolar Planets • A warm wet Mars • Planetary Perils: • Global Warming • Impact Hazards

  19. Class Structure • During each topic: • Pieces in a puzzle. • Many pieces in several topics • At the end of each topic: • See how pieces fit. • See how the scientific method is applied • What is the evidence • Have a test.

  20. Homework #4 • For Friday 12-Sept: Read B7.1, Do: • B3: Problems 33, 54 • B7: Problem 30

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