Dear Calendarists:
There is a fascinating essay being developed by Richard Fitzpatrick, Professor of Physics at the University of Texas at Austin, concerning methods to improve upon Ptolemy's celestial mechanics algorithms while retaining the geocentric apparent astronomical viewpoint. He identifies specific errors made by Ptolemy and how to correct them, very interesting. He explains the physical relevance of the main cycle and the epicycle, why these differ for inner vs. outer planets, and why there is no need to have epicycles upon epicycles (which is actually a post-Ptolemaic "enhancement").
On the other hand he himself introduces several unnecessary simplifications that restrict the range of time over which his improved algorithms will be valid: he assumed that the planetary orbital inclinations and eccentricity are constant, that Earth's axial tilt is constant, that Earth's celestial poles are unaffected by diurnal motion, and that the precession rate is uniform, and apparently he makes no correction for the tidal slowing of the Earth rotation rate. These assumptions and simplifications limit his algorithm validity to perhaps a range of plus or minus a few centuries relative to the present era.
Here is the web site:
http://farside.ph.utexas.edu/
From there there is a link to his work on improving Ptolemy's algorithms:
http://farside.ph.utexas.edu/syntaxis.html
...which are available as a PDF file here:
http://farside.ph.utexas.edu/syntaxis/Almagest.pdf
It seems that his Ptolemaic work is either a hobby or a work-in-progress, because he hasn't formally published anything about celestial mechanics. Most of his papers are about fusion for energy production.
I haven't corresponded with him to suggest any improvements yet.
-- Irv Bromberg, Toronto, Canada
