Monday, February 29, 2016
The 132 AD Autumnal Equinox Assuming Ptolemy's Latitude for Alexandria
On p. 100 of Ptolemy, The Geography, Ptolemy lists the latitude of Alexandria a 31°. The smallest step in the table is 5 minutes of arc or 1/12th of a degree which corresponds to a round off error of 1/24th of a degree. If one assumes a spherical earth the latitude is the altitude of the pole at a particular location so it can be obtained by observation. I recomputed the 132 AD autumnal equinox using Ptolemy's latitude and got about 4 pm on Sep 23. Since the astronomical day starts at noon this would have been Sep 24 according to that calendar.
A 1/24th degree round off error might account for Ptolemy's value of 2 pm for the time of the equinox.
correction (Mar 1): the value for the day of year in the 1st image should read doyAE = 267.681. Forgot to change the value for the month in the function.