A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2017 Apr 29, 07:39 -0700
Herbert Prinz, you wrote:
"between 1800 and 2050, I find the extreme durations of the moon phases (quarters) to be 6.58d and 8.24d."
Thank you for checking the real statistics. I tried to come up with a believable analytic approximation while driving to Massachusetts yesterday but gave up after a while. Given these numbers, I can now see one that works:
T = (1 +/- 2e)T0
where T is the shortest/longest lunar "week", T0 is the mean lunar "week" (about 7.4 days), and e is the mean eccentricity of the Moon's orbit which is about 0.056. My first guess was that the up/down percentage would be just e. I leave it as an exercise to the reader to decide why it's 2e.
By the way, if the long lunar week is 8.24 days, that could be compatible with the original claim of 9 days if we consider calendar dates. If the New Moon falls anytime after 6:15pm on, e.g., April 10, then when we add 8.24 days to this, the event occurs just after midnight on April 19.