A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2018 May 28, 13:46 -0700
Peter, you wrote:
"Is there an interval around full moon when it's acceptable to use either the east or west limb for distance measurements, in the sense that the illumination on both limbs is close to ideal?"
Yes, it seems that approximately a full 24-hour period centered on the actual time of Full Moon should be relatively safe. With a simple model of the Moon's illumination, the fraction illuminated, f, is given by f=(1-cos(LD))/2 where LD is the lunar distance from the Sun. We can calculate the deficit from full diameter on the "wrong" limb as 31·(1-f) assuming 31' for a mean diameter of the Moon. If the LD is greater than about 174°, which it would be for about a day centered on the exact time of Full Moon, then the error from using the wrong limb would be about a tenth of a minute of arc or less. This assumes that the other body, planet or star, is relatively near the ecliptic. An interesting risk here: if we know that both limbs are "safe", but then shoot the Near Limb and record it as a Far Limb sight, we'll get a big error with no obvious cause.
Yes. Fun geometric complications there, especially if the other body is at some relatively large angle to the Moon's apparent motion across the sky. I leave this as an exercise for the reader. Heh. :)