On 2009 May 23, at 23:34 , Irv Bromberg wrote:
The Persian scheme, even though it is an astronomical calendar for the equinox, doesn't include any rule for progressively advancing which months have 31 days in parallel with the advance of perihelion, and the 6 longer months are not centered with respect to the present or recent past position of perihelion, in fact at present perihelion is nearly 3 months before the Persian New Year Day (Norouz).
Irv adds: Oops, my mistake. The longer months should be centered on aphelion, as Amos correctly pointed out.
In the present year, Sun will reach mean aphelion, at a solar longitude of about 103.1°, at about 02:54h Tehran standard time on the 14th of Tir (4th month) in the modern astronomical Persian calendar. So actually, aphelion is currently as well-centered as is possible with respect to the 31-day months of the year (first 6 months).
This reminds me of another oscillation problem for a calendar that is intended to keep the 31-day months centered with respect to aphelion: each time that there is a leap day and the position of aphelion is near the cutoff, that can cause the 31-day months to shift one way during the leap year, and then back during non-leap years. It seems to me that the rules of such a calendar ought to prevent any such short-term shifts.
-- Irv Bromberg, Toronto, Canada
