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EARLY COSMOLOGY TUTORIAL TOPICS Dr. Brian Monson has created this group of pages as a supplement for the unit on early astronomy that is taught in most college astronomy courses and has graciously granted ScienceMaster permission to republish them. It is by no means a complete discussion of this topic. To explore more work by Dr. Monson please visit his Planetary Conjunctions page.

CONTENTS Motions of the Celestial Bodies Geocentric Models First Iteration Second Iteration Heliocentric Models First Iteration Second Iteration Third Iteration Fourth Iteration

Johannes Kepler (1571 - 1630)

Kepler was the beneficiary of some very accurate data on the positions of the planets recorded by Tycho Brahe. The measurement uncertainty of this data was about 2 arc min. Copernicus' model could make predictions that were only accurate to about 5°. So Copernicus' model was 150 times less accurate than the best measurements of the era. This bothered Kepler. He felt that a truly successful model should make predictions as accurate as the measuring instruments used to test it and he set out to improve Copernicus' model to meet this goal. He kept the basic Copernican model intact except for two important changes:

1. He used elliptical orbits instead of circles.
2. He put each planet in a separate plane. In Copernicus' model all the planets are coplanar.

He made these discoveries through an exhaustive process of trial and error. The work was made more difficult because he had to decipher the motion of a planet around the sun from the moving earth. In other words, he had to distinguish between the part of the planet's motion due to its path around the sun and the part due to our motion around the sun. He did all these tedious and difficult calculations without even the aid of a slide rule. In the process, he formulated what are now called Kepler's Three Laws of Planetary Motion.

1. Planetary orbits are ellipses with the sun at one focus. Figure 1 shows the shape and features of an ellipse. Planetary orbits are not as eccentric as the one drawn here, however.
2. The line joining a planet to the sun sweeps out equal amounts of area in equal amounts of time. Figure 2 shows this area. If the time interval is equal on both sides, the green area will equal the blue area.
3. The period of the orbit to the second power is equal to the semi-major axis to the third. The period must be in years and the semi-major axis in astronomical units for this formula to work.

Kepler's second and third laws can be stated in ordinary language as:

• Planets move faster near perihelion than near aphelion
• Planets that are close to the sun orbit faster than more distant planets.

Kepler used these laws and Tycho's data to calculate the Rudolphine Tables in 1627. Their accuracy in predicting the positions of the planets and the fact that they remained accurate for many years helped lead to widespread acceptance of the heliocentric model.

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