NavList:

Hello to all,

Further to my earlier "stand by" reply, and without adequate time yet to work it out entirely; partial reply only hereafter to this initial puzzle in which two questions were asked.

(1) - Moon UL or Moon LL ? (See top of attachment).

You cannot escape here using the local horizon and zenith.

Hence simply consider Sun (height, azimuth) and Moon (height, azimuth) as their (Lat, Long) and draw a GC from Moon Center to Sun center. Moon Departure angle immediately indicates which is the Limb to be used. (See top of attachment).

(2) - Sun Bad limb or not ? (See bottom of attachment).

Use a moving local grid centered in S1 onto the Sun bottom Limb (Upper Limb) and from 2 adequately separated times T(1) and T(2), draw the relative Moon center positions.

Work out everything as linear (i.e. relative Moon altitudes / Azimuths and Moon SD), ignore differential refraction in a first time - and check the times for which S1-Moon Center exactly equals Moon Semi-Diameter. Inside this time-frame, S1 is hidden the Moon, hence Sun LL cannot be used Outside such time frame Sun LL can be used.

Same approach for Sun UL.

That's not perfect, but does constitute a good and solid start up point.  (See bottom of attachment)

Note : If Moon SD greater than Sun SD, there is a possibility that both Sun UL and LL can be "obscured" at one same moment.

Time permitting, I will work out and publish this detailed example (Oct 14th, 2023 and suppose you're near 28.00° N, 90.00° W at noon time).

Kermit