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Corrected Version:

For 17:07:33 and not 17:07:03,

Hello to all,

At 17:07:33 Sep 21st, 2016, with deltaT=+69,9s, Sun Coordinates are: GHA 078°41.1' W , DEC = 00°20'65 N and Geocentric SD=15.93' .

Ignoring refraction, parallax and semidiameter augmentation (because of the Sun is so close to Zenith and because of the very important distance of the Sun in units of Earth radius), the SunLL height correction boils down to only SD, hence the actual distance from Observer to the Sun "Vertical" Projection (SVPOE) on Earth is 90° - (89°14.8' + 0°15.9') = 29.3' .

So close from Equator and with such a small distance involved (29.3 NM), the Great Circle Azimuths should not change much ... let us try the following:

1 - From SVPOE ( 00°20.65' N 078°41.1'W) let us first draw a Great Circle segment into departing reciprocal Azimuth (336.2° - 180°) = 156°2 with lenght equal to 29.3 NM. We get into position: 00°06.1'S and 078°29.3'W .

2 - And then from this position (00°06.1'S and 078°29.3'W) let us compute the Azimuth and Distance to SVPOE via a Great Circle. We get: Azimuth 336°2 and Distance 29.3 NM, which fully matches our initial Sextant Observation.

Hence I would surmise that the Observer's position is close from 00°06.1'S and 078°29.3'W. I do not think that the ignored refraction and Parallax and Augmented SD corrections woulb be of some significance under this specific environment. 

Last but not least, in this local environment any real world Sextant observation of the Sun LL in order to attempt determining both its height and especially any kind of meaningful Azimuth determination would be extreeeeemely difficult (if not impossible) for such a height.

Thanks for the drill to Bob Morelli and to you Frank,

Kermit

Lesson learnt: Always double check !!!