NavList:

Frank, I'm glad you posed this latest scenario, because now I can compare (using *FLAT* Pythagoras code) to 'proper' online Eclipse Calculators.

To find the time when the Moon 'touched' the LL of the sun, I used (flat Pythagoras) code to find when does an x,y coordinate fit inside a circle (the Moon).

By extension, using the same approach, when do two circles first touch? (start of eclipse).

My "test" is now:

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delta_az = (sun_az - moon_az) * cos(((sun_alt+moon_alt)/2.0) * PI / 180.0);

distance = sqrt( pow( (delta_az), 2 ) + pow( (sun_alt - moon_alt), 2 ) );

if( distance <= (moon_radius + sun_radius) )   // Overlap of circles

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Using the JPL Horizons Ephemeris as the source for the position of the Sun and Moon, I found the first and last contact points for the suggested coordinates of (N 28.0 W 90.0) to be:

2023-Oct-14 18:51:08.5 (UT) = Last touch of Moon with the Sun.

Note: The smallest increments you can ask for in JPL Horizons = 0.5 seconds (of time).

Now to compare with other sources (in order of closeness to my results)

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XJubier Prediction of Eclipse

( ΔT=69.2s)

Start 15:36:09.9

End 18:51:09.5

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USNO Calculator

Delta T: 72.5s

Eclipse Begins 15:36:06.7

Eclipse Ends 18:51:04.0

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So there are lots of different times to choose from - according to ones predilection ;-) 

More to come later, after I have gone and voted in our New Zealand General Election!

Regards, Geoff Hitchcox, Christchurch, New Zealand.