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    Re: Northern lights navigation puzzle
    From: Frank Reed
    Date: 2022 Nov 26, 10:58 -0800

    Antoine, you wrote:
    "I determined Latitude with a little over 1° error."

    Yes, and I think that's about as good as we can reasonably expect from the original photo because of unknown image distortion and uncertainty in the horizon (when we do these analyses, we usually assume that the photo is relatively "level" but that doesn't have to be the case). I got closer than a degree of latitude in my original pass through the puzzle entirely by good luck.

    You added:
    "As regards UT determination, Stellarium undoubtedly helps ... It lets you perform a "trial and error fine-tuning" lunar-type exercise with Mars against its close star-background with distortion problems no longer a factor then."

    That's right, and the motion of Mars should have been good enough, given the scale of the image to determine the UT to +/-2 hours or so. But the image of Mars is trailed and distorted so in practice it's worse than that. Also, even in small areas just a few degrees wide around Mars there are image distortions which I still find puzzling. It's possible that the photographer adjusted the aspect ratio of the image for aesthetic impact. Or maybe there's something else going on. 

    You added:
    "A bit sorry there were so few actual runners this time in view of the time you spent devising this Nav Puzzle. Latitude was workable indeed by classical LOP's, Longitude did require more lateral thinking."

    Thank you very much for joining in, and don't worry that no one else came along this time. I post these things for my own "education" with very little planning and frequently do not know if an interesting solution is possible. In this specific case, just by good luck, I had already found the photographer's location before posting the puzzle, but that's unusual. Thinking these things through inevitably enhances my understanding of celestial navigation. Every puzzle reveals something new.

    As you say, latitude is solvable in cases like this by classical LOPs, but I think most "classical" navigators are uncertain how to pick an AP in a case like this. And what date and time should we use? Of course brute force eventually works, but I feel that it's important to understand that time and longitude can be left as unknowns. One can be treated as arbitrary and the other selected to match the observation. The two quantities that determine the appearance of the sky are Latitude and LHA Aries (the latter equivalent to "Sidereal Time"). It's no coincidence that those are the two parameters that we use to enter short tables like Pub.249. LHA Aries feels like an abstraction the way it's usually taught in celestial navigation, but it's a directly practical number. That and latitude define the sky (stars only, of course).

    You wrote:
    "Of course, it is ... LONGITUDE, one of our favorite brain-teasers over the Centuries."

    Yes, and without Mars in the photo, we would be sunk! The Moon would have made this a genuine problem in "lunars" but the planets can help, and in this case Mars provided just enough narrowing of longitude.

    And you concluded:
    "Anyway, here we are. I also included a view which is an almost perfect match of yours, and we certainly can pinpoint our fix to within a quarter of miles or so then."

    Yes, it is a match. It's fun to see that we can drive there. The location in the original photo looks remote, wild, arctic, inaccessible! But nah... That's just Norway! :) 

    Frank Reed

       
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