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I haven't the maths skills like many have in this forum, however I thought I would have a go at the problem from using the simple code of "is a point inside a circle".

I used the JPL Horizons ephemeris to generate the refracted positions of the Sun and Moon at one second (of time) intervals.

My results do not agree with Lars Bergman - so I assume I have done something wrong in my code.

Here is my test for "blocking" the Suns LL.

===================== 

distance = sqrt( pow( (sunLL_az - moon_az), 2 ) + pow( (sunLL_alt - moon_alt), 2 ) );

fprintf (fresults,"%s ",sundate);

if(distance < radius_of_moon) fprintf(fresults,"Sun LL is covered by the Moon\n");  

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Assumed position = 28.00° N, 90.00° W.

First contact of the Moon with the LL of the Sun

Date__(UT)__HR:MN:SC.fff, , ,Azi_(r-app), Elev_(r-app),  Ang-diam (arc seconds)

2023-Oct-14 17:10:46.000,*,m, 165.487045,    52.792602,  1924.134, SUN

2023-Oct-14 17:10:46.000,*,m, 165.600626,    52.752441,  1828.310, MOON

Local Solar Noon (Moon still covering the Sun's LL)

Date__(UT)__HR:MN:SC.fff, , ,Azi_(r-app), Elev_(r-app),  Ang-diam (arc seconds)

2023-Oct-14 17:46:00.000,*,m, 179.999893,    53.770933,  1924.148, SUN

Last contact of the Moon with the LL of the Sun

Date__(UT)__HR:MN:SC.fff, , ,Azi_(r-app), Elev_(r-app),  Ang-diam (arc seconds)

2023-Oct-14 18:02:29.000,*,m, 186.873826,    53.548351,  1924.154, SUN

2023-Oct-14 18:02:29.000,*,m, 186.622021,    53.313648,  1828.988, MOON

Regards, Geoff Hitchcox, Christchurch, New Zealand