Re: Find Solar Calendar Seasons spreadsheet posted

The chart shows ±48 hours on the primary y-axis.  With a small step size it is worth reducing the y-axis range accordingly.  For example, with the 178-year cycle, 100-year step size and middle year 2000, try changing the primary y-axis to ±16 hours, with 2 as the major unit.  The curves for years prior to 2000 are then plotted with thin lines, indicating that they don't cross the baseline year, to be expected because prior to the present era there is no point in the solar cycle that has such a short mean year.  The curves for years after 2000 are all medium-thick, indicating that they do cross the baseline year.  Thus I classify this as a stable calendar season starting in the present era at aphelion.

Irv adds:  OK, I've added an "Automatically Scale" checkbox option to the "Setup" page.  It uses the list of axis scale settings that appear on the "Scale" worksheet.  If the checkbox is unchecked then the macro leaves the primary y-axis scale alone.

This revealed an anomaly that I hadn't noticed before -- there are marked lunar oscillations when the step size is small and the y-axis scale is automatically reduced accordingly!

These oscillations cause the calendar season crossovers to appear rather erratic.

I tried eliminating the lunar oscillations by removing nutation from the solar longitude calculation -- no effect.  One would need to remove all lunar terms, but it would be better to have an algorithm specifically designed for the Earth-Moon barycenter.  SOLEX can do that in the "planets only" mode, but that doesn't help me much, except possibly to develop such an algorithm.  The mean solar longitude is needed instead of the actual solar longitude.

It turns out that there is a satisfactory workaround -- use a step size that is a reasonable multiple of the mean synodic month!  Even a number like 19 works well!  So do multiples of 19 and so on -- I have provided a list on the "Setup" page.