I am extremely grateful to you for your both explanatory posts about Alnair Identification :
(1) - https://navlist.net/Alnair-identification-Blaskett-nov-2023-g54918 , and
(2) - https://navlist.net/Alnair-identification-Blaskett-nov-2023-g54927 .
First of all, you gave us accurate coordinates of the spot where this initial picture was taken : i.e. from S13°15.0' / W163°06.5'
Then you explained that this initial picture is not conformal since it is best modeled by a Gnomonic Projection with point of contact most probably very close to Peacock.
So, the assumption that the picture is conformal is incorrect indeed. This picture is neither equidistant as well. Hence it is not straightforward to derive accurate and meaningful angles or distances anywhere from it, e.g. actual sextant heights for either AlNair or Peacock as well as for Zeta Cap which is a nice call from yours as it certainly widens the picture "useful" area.
Nonetheless, we can highly benefit from a characteristic of Gnomonic projections : all straight lines are Great Circles.
Hence the Peacock to AlNair straight line is [almost] a portion of a great circle. And by extreme luck, since Peacock is extremely close to the "Gnomonic projection "contact point", the real world vertical line from Peacock to the horizon is very closely approximated by a vertical line from Peacock drawn as a perpendicular line onto the picture horizon.
Hence the actual Peacock - AlNair Position Angle (PA) read from the Picture very closely matches its real world value.
PA = 20.045° as per your own measurement. And cherry on the cake, we have seen earlier that this PA measurement is almost insensitive to both refraction and dip. We should therefore consider that this determination of 20.045° is a very reliable and meaningful one.
Let's then fine-tune our previous computations to our updated position at S13°15.0' / W163°06.5' (vs. our initial position at S13° / W163°) :
(3.1) - At UT = 05h50m00.0s
AlN'Aïr Height/Azimuth=34.90776°/221.44732° and Peacock Height/Azimuth=17.61023°/214.32697°, yielding Distance=1105.4', PA=18.76214° (and HR=1.98224)
(3.2) - At UT = 05h56m00.0s ( i.e. 6 minutes later)
AlN'Aïr Height/Azimuth=33.93557°/221.84989° and Peacock Height/Azimuth=16.78676°/214.35381°, yielding Distance=1105.3', PA=20.02952° (and HR=2.02157).
Backwards interpolation on PA gives us : Picture time = 05h56m04.4s . It is well understood and accepted that so many digits are not meaningful at all. Nonetheless, let us compute the various bodies heights for this time and get :
UT = 05h56m04.4s
AL Nair 33°56.4' / 221.9°
Peacock 16°46.6' / 214.4°
Zeta Cap 28°21.3' / 251.5° . Lo and behold ! This 28°21.3' Zeta Cap height is only 0.7' from your own 28°22' determination, i.e. a UT difference inferior to 3 seconds, with your own 28°22' determination occurring at 05h56m02s.
So, most certainly our initial picture time is extremely close to 05h56m UT (+/- 1 minute) .
We indeed get [almost] identical height values for Zeta Cap for this 05h56m UT. Given the initial picture relative configuration, your published result at 05h51m cannot be anything but a typo since our heights determinations are so close and so consistent with the overall picture.
Finally would you be so kind, Peter, as to indicate your best determinations for Al NAir and Peacock heights, i.e. the ones observed in a sextant over the apparent horizon ?
One last note : if the picture had been taken on a 1st of January, the Sun would have been too close to the horizon (about 8°) for so many stars to be visible. Had it been taken a week before for a same position in the sky, the Sun would have been about an additional 6° under the horizon.
Which makes me surmise that this picture possibly was taken on Christmas Eve at dusk.
Quel beau souvenir !
Thanks to both of you Peter and Frank for a quite interesting challenge which concludes into probably being able to confidently "time" this picture to +/- 1 minute of time.