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Kepler’s Laws of Planetary Motion: Understanding the Orbits of Planets and Satellites

Learn about Kepler’s Laws of Planetary Motion and how they revolutionized our understanding of planetary orbits. Explore the concepts of ellipses, equal areas, and the relationship between a planet’s period and its distance from the Sun.

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Kepler’s Laws of Planetary Motion: Understanding the Orbits of Planets and Satellites

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  1. Kepler’s Laws

  2. Kepler’s Laws of Planetary Motion Kepler started as an assistant to Danish astronomer Tycho Brahe. Using instruments called quadrants, Brahe measured the positions of planets so accurately that his measurements are still valid today.

  3. Kepler’s Laws of Planetary Motion Tycho Video

  4. Kepler’s Laws of Planetary Motion Recall that: • Kepler expected circular orbits • a small discrepancy led him to ellipses… Johannes Kepler(1571-1630)

  5. Dr. Carl Sagan

  6. Kepler’s Laws of Planetary Motion What is an ellipse? An ellipse looks like an elongated circle

  7. Kepler’s Laws of Planetary Motion • Kepler’s First Law:All planets move in elliptical orbits, with the sun at one focus.

  8. Kepler’s Laws of Planetary Motion Kepler also found that the planets don’t go around the sun at a uniform speed but move faster when they are nearer the sun and more slowly when they are farther from the sun.

  9. Kepler’s Second Law: A line that connects a planet to the sun sweeps out equal areas in equal times.

  10. Kepler’s Laws of Planetary Motion Kepler’s Third Law After ten years of searching for a connection between the time it takes a planet to orbit the sun and its distance from the sun, Kepler discovered a third law.

  11. Kepler’s Third Law:The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. p2 = a3 p = orbital period in years a = avg. distance from Sun in AU This means more distant planets orbit the Sun at slower average speeds, planets closer to the Sun orbit at faster speeds.

  12. Kepler’s Laws of Planetary Motion The ratio is the same for all planets. If a planet’s period is known, its average orbital radial distance is easily calculated. Kepler’s laws apply not only to planets but also to moons or any satellite in orbit around any body.

  13. Graphical version of Kepler’s Third Law

  14. Kepler’s Laws of Planetary Motion Kepler was the first to coin the word satellite. He had no clear idea why the planets moved as he discovered. He lacked a conceptual model.

  15. Thought Question:An asteroid orbits the Sun at an average distance a = 4 AU. How long does it take to orbit the Sun? • 4 years • 8 years • 16 years • 64 years Hint: Remember that p2 = a3

  16. An asteroid orbits the Sun at an average distance a = 4 AU. How long does it take to orbit the Sun? • 4 years • 8 years • 16 years • 64 years We need to find p so that p2 = a3 Since a = 4, a3 = 43 = 64 Therefore p = 8, p2 = 82 = 64

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