Tuesday May 31st 2011 is our periodic 5th Tuesday Math and Astronomy program by Bob Roeth. This will be our last meeting at the Sports Pavilion, as we will move to Regis Hall at St. Ignatius in early June (we’ll provide details later for the new venue). The Math program will start at 7:30, as usual.
Bob Roeth’s comments follow:
Having a scientific calculator will be helpful in the first part of the evening. Included will be some calculations based on an [approx] ellipse made by the string and pins method and then on the Earth orbit.
After that, I will try to show how Ptolemy’s epicycles and equants combined could produce a very close approximation to the picture according to Kepler. This involves:
Showing how an epicycle can be made to produce a shape that satisfies the mathematicians’ standard formula for an ellipse, and
showing that the planets in our solar system have small enough eccentricities that the unoccupied focus has properties very close to what Ptolemy wanted for his equant. His positioning of his equants was by mere trial and error and he was so good at it that his results added greatly to the difficulties the Copernicans already had in trying to establish the Sun as central in what we call the Solar System.
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