Solar noon or clock noon? What happens if the full moon is on Tuesday? Will that Tuesday count towards the third? Even if the full moon is at 23:59 (23:59 in which timezone)? Do you use solar equinox, or the Julian equinox, or the Gregorian equinox?
I wonder what the downsides would be in a time model that is indicated by a normalized global value for the current longitude where the sun is at meridian.
I think you need to be more specific here.