Natural Science - Year I
Unit 27: Brahe, Kepler, and Elliptical Orbits
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Science Lecture for Unit 27: Planets in Motion
Kepler Law's: the Elliptical Orbits of Planets
Now that we have inventoried the objects in the solar system, we need to look at how they move.
Read the explanation of Kepler's laws in Strobel's Introduction to the History and Philosophy of Western Astronomy. Strobel's entire book is worth looking at but we'll only read this page today. [One page with graphics and review questions.]
If you need more information to answer the questions below, you might also want to look at the diagrams of Kepler's three laws (1 page. If you want to view the movies and don't have "Sparkle", save the .mpg files and open them with any mpg reader, such as Quicktime).
Review the history reading as well and be sure that you can answer these questions:
- What is an ellipse?
- What are the foci (two focus points)?
- What is the major axis and the minor axis of the ellipse?
- What is eccentricity?
- What happens to the shape of the ellipse if the distance between the foci is zero?
- What happens to the shape of the ellipse if the distance between the foci is large compared to the size of the ellipse?
- Why did Kepler have such a hard time determining that the orbit of Mars was an ellipse?
- If a planetary orbit is an ellipse, what is at each focus?
- When is a planet moving the fastest, at aphelion or perihelion? Why?
- Kepler knew the periods of the five planets visible to the naked eye, and his law gives a proportionality between period and distance from the sun. Why couldn't he determine the exact distance to the sun?
- What is an empirical observation? Why doesn't it have the same force of authority as a "physical law"?
- What are Kepler's three laws of planetary motion?
- What is the difference between an empirical observation and a physical law?
- What conclusions can we draw from Kepler's laws of planetary motion about planets or their motions?
- How did Kepler's discovery of Mar's orbit advance Copernicus' claim that mathematics can be used to describe physical objects?
Further Study/On Your Own
- A good short review Conic Sections (ellipses, parabolas, and hyperbolas) is contained in this introduction to conics. Notice the general equation and how specific relationsships among the coefficients (the A, B, C, D, E, F factors) change the shape.
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