AST 1002: Outline for Topic B

[Sections Taught by Prof. H.L. Cohen]

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Last updated January 1, 2003

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Topic B: The New Astronomy (Motions of the Planets)

• Geocentric vs. Heliocentric (Ref. Table 4, Fig. 3)
  • Definition of geocentric & heliocentric (i.e., location of Sun and Earth in each model)
  • Principle developers and supporters of each world view; major contributions of each
  • (Geo: Aristotle, Ptolemy, Tycho; Helio: Aristarchus, Copernicus, Galileo)
  • Approximate time period for each person above (see Fig. 3)
  • Comparative features of Ptolemaic and Copernican models (see Table 4)
  • Tools or techniques ("enhancements") used in each model, and their functions including
    –Eccentric circles
    –Deferent/epicycles
    
  • How each model explained (see Table 4)
    –Phases of Moon
    –Nonuniform motion of Sun, Moon and planets
    –Retrograde motion
    –Greatest brilliancy of superior planet when in retrograde motion
    –Elongations of Mercury and Venus reach maximum values always less than 90 degrees
    
  • Meaning of inferior and superior planets (in terms of orbit positions)
    –For Geocentric models
    –For Heliocentric models
    
  • Which planets inferior; which superior
  • Why people might have preferred one model over the other
    –Was one a better predictor of planetary positions?
    –Was one simpler?, etc.
    
• Kepler's Laws (ref. Fig. 4)
  • Meaning of full title of Kepler's book, "The New Astronomy"
    –Why a "new astronomy" (two reasons)
    –Significance of using observations of Mars
    –Role of Tycho Brahe
    
  • When Laws 1 & 2 published
  • When Law 3 published
  • Alternate names for Laws 2 and 3
  • How Kepler's writings differ from Newton
  • What question(s) each law asks and answers
  • Why Kepler's Model (Laws) finally preferred (accepted) over other types (Ptolemaic, Copernican, etc.)
• Kepler's First Law (Ref. Fig. 4)
  • What questions First Law asks and answers
  • How to draw ellipse if given string length and eccentricity (see Example 1a)
  • Keplerian ellipse — know all parts, definitions and relations (see Fig. 4) including
    –Semimajor axis, mean distance (a), and eccentricity (e)
    –Perihelion and aphelion including dates for Earth
    –Where is planet if at mean distance from Sun
    –Alternate interpretations of eccentricity (percent Sun off-center; variation in distance to Sun)
    –Astronomical Unit (definition) and values of AU in kilometers and miles
    
  • Cause of Earth's seasons (effect of eccentricity on Earth's seasons; also Mars)
  • What is unusual about Pluto's orbit?
    –Year first inside Neptune's orbit; last time at perihelion; next date outside Neptune's orbit
    –Length of Pluto's orbit period and when discovered
    –Hence, how long Pluto inside Neptune's orbit
    
• Kepler's Second Law (Law of Areas)
  • What question Second Law asks and answers
  • Understand meaning of "equal area in equal times" (i.e., areas proportional to times)
  • Implication of Second Law on orbit speed
  • How Second Law used to predict a planet's position in its orbit
  • Simple methods to estimate areas
  • Effect of Second Law on Earth's seasons
    –How many days in each of the four seasons (count them!)
    –How many days different are N. Hemisphere summer and winter seasons
    
• Kepler's Third Law (Harmonic Law)
  • What question does The Third Law ask and answer (Ans. How is orbit period and size related?)
  • Mathematical form of Third Law (P² x a³)
  • Implication of Third Law on average orbit speed
  • How orbit period and mean distance depend on orbit eccentricity (they don't!)
  • How to use Third Law to calculate either P or a (see Examples 2a and 2b)
• Issac Newton's Contribution to Keplerian Motion
  • Difference between Kepler's and Newton's approach to problem
  • Definition of force (F proportional to mass x acceleration)
  • Mathematical form of Law of Gravitation (F proportional to m x M/d²)
  • How Newton's formulations of each of Kepler's Law different
  • Know names of the four conic sections
  • Mathematical form of Newton's Harmonic Law [(M+m) x P² = a³]
  • Reasoning that suggests Kepler's Harmonic Law "deficient"
  • Why Kepler did not discover missing mass factor in Harmonic Law
  • Importance of Newton's form of the Harmonic Law
  • How mass affects relation between P and a (see Study Guide, Quest. B47-50)
• Tentative List of Study Guide Questions To Omit for Topic B
  • Try to answer all questions for practice
  • Do not worry if you cannot do #32 — it is difficult for most students.
    (Exam #2 has no questions this challenging!)

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* This list is reasonably complete but students remain responsible for all material presented in class. Tables, figures, examples, etc., listed here refer to printed Study Guide items.

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For comments and suggestions contact Howard L. Cohen at cohen@astro.ufl.edu About this site (department disclaimer and recommended web browser) © Copyright 1999-2003 Howard L. Cohen