A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2021 Jun 28, 17:49 -0700
Robin Stuart, you wrote:
"I was hoping to be able to put this down but it was not to be."
Good. I'm glad it's keeping you out of trouble. Ha!
"Measuring the zenith-ε Scorpii-Antares angle at 111° and"
Interesting choice. But stop right there; you convinced me. Of course. Any two altitudes with a reasonable azimuth diff between them (or any equivalent pair of potentially observable data, such as you've selected here) will necessarily determine one and only one pair of latitude and local sidereal time. This, after all, is what is published on every line of Pub.249 Volume 1. For any given page of latitude, a single row of LHA Aries (identical to Local Sidereal Time) uniquely determines the appearance of the sky, and two altitudes are enough to lock it down. And that's it then. We can determine the latitude within a narrow range, and as you say (and Russ also said), it's quite close to the equator.
So why did I say there were options on the latitude? My mistake was to look at the wrong question. I set this up asking where the sky could look like this, and by that I meant where could you see the sky like this behind some other lighthouse assuming all other things are equal. Clearly we have to throw out the azimuth, but I suggested that we could reasonably keep the altitude of the lighthouse beacon --and stars at the same elevation in the image-- at around 10° above the horizon. And for that, as you both have said, close to the equator is the correct answer.
A separate question is where the sky could be photographed looking like this. We can do this in two stages: first keep the horizon horizontal but let the angular altitudes float. That's what leads to the different latitudes further south that I was imagining. Then throw that out, too. If the sky could be rotated relative to the horizon as well as altitude changed, then the only limitation from the sky image is the most southerly declination visible among the stars in the photo and the fact that there's no apparent near-horizon extinction anywhere across the image. I can find individual stars near -60° dec and they show no apparent extinction so their altitudes should be higher than 7 or 8°. And that implies a latitude of roughly 22°N or further south from there. There is no possible interpretation of the background sky image that would imply it was photographed from southern New England.
And you wrote:
"To me 0° latitude is pretty is a pretty good fit with Antares about 11° above the horizon at the time. Maybe it was taken from the Galapagos Islands. It might be something that an enthusiastic vacationer would try to capture"
See, that second part would only be something we could talk about if we knew that the sky in the image had been aligned with the correct altitude and also aligned with the apparent horizon parallel to the true horizon. It's distinct from the original question.