Lecture 3
Scientific Models of the Cosmos
(part 2, heliocentric)

Geometria una et aeterna est in mente Dei refulgens: cuius consortium hominibus tributum inter causas est, cur homo sit imago Dei.

-Kepler [*]

 

Note: This lecture and the previous follow the timeline from ancient Greece to the Renaissance. Study the timeline, which summarizes the major names and ideas presented in the first part of your textbook.

Note: These lectures-- like the book-- tend to be Greek-West centric. To treat every culture's historical development of astronomy (e.g., the Incan Quipu) would require another course itself.

Copernicus

Copernicus (picture) found Ptolemy's model "not sufficiently pleasing to the mind."
(esp., after he read Plato)

"De Revolutionibus" published year of his death.

Heliocentric model, with Sun at center of Cosmos. Planets orbit Sun with uniform circular motions.

 

Heliocentric model explains:

• Short-term daily motions of Sun and Celestial Sphere. Due to motion of Earth
  (rotating on axis).
• Long-term yearly motions of Sun and Celestial Sphere. Due to motion of Earth
  (revolving about Sun)
• Long-term retrograde motions of planets. Due to Earth passing by planet (Chaisson Fig2.9) -- no more eccentrics, deferents, epicycles needed (in principle*)
• Lack of stellar parallax. Due to outer celestial sphere of stars (firmament) being much farther away than any other distance in solar system

Nonetheless,

• still no more accurate in predictions than Ptolemy's model (still about 5° accuracy)
• does not explain why Earth seems at rest to us
• violates Aristotle's physics (e.g,. Earth element's nature)

And although your book does not highlight this fact: Copernicus' model also allows us to determine the relative sizes of all orbits in solar system (!) in terms of the fundamental length of 1 Astronomical Unit
(1 Astronomical Unit = 1 AU = radius of Earth's orbit).

Brahe

The first master of astronomical measurement (picture)

Famous for his observations of the Nova of 1572. (movie of crab nebula supernova remnant from 1054)

King of Denmark built him Castle/Observatory, filled with Tycho's Wounderous Machines capable of observing the sky to a resolution of 1 arc–minute.

 

Kepler

You don't have to memorize Kepler's mystical sounding books
( e.g., Mysterium Cosmographicum or Harmonices Mundi ) BUT...

You do have to know Kepler's 3 Laws of Planetary Motion (Chaisson section 2.5)

1. Ellipse law: The planetary orbits are ellipses with the Sun at one focus.
   Ellipse defined in Chaisson Fig2.16 and Chaisson MorePrecisely2-1
   The eccentricities for planets in our solar system.
2. Equal Areas law: A line from the planet to the Sun sweeps out equal areas in equal times.
   Chaisson Fig2.17
3. Harmonic law: P² = a³
   "P" is period of orbit and "a" is the semi-major axis of the ellipse.
   Chaisson table 2.1 and graph

 

Note: the planetary orbits are neither circular nor uniform.

Model predicts planetary motions to accuracy of 10-100x better than previous 5° accuracy of Ptolemy and Copernicus. (Exercise: what is this Keplerian accurracy in arc–minutes?)

 

Summary

Understand the comparison of Cosmological models according to Ptolemy, Copernicus and Kepler (Summaries 4-2 to 4-4 in Seeds p.72, or this table)

 

Reading

Chaisson: Chap 2.

The Galileo Project from Rice University is great source of information on early astronomers discussed here.

Wolfram Research hosts an online Scientific Biography.

The timeline shown in class.

 

Document URL: http://www.uh.edu/~jclarage/astr3131/lectures/3/3.html