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    Re: Northern lights navigation puzzle
    From: Antoine Couëtte
    Date: 2022 Nov 21, 12:44 -0800

    Good day to all,

    Frank, Thanks for your Nav Puzzle.

    I identified 5 Navigation stars : Castor, Pollux, Procyon, Regulus and Algeiba.

    I do not think the planet in the Lion can be Jupiter because it seems too far from the ecliptic (Regulus is almost spot on) and it also would be far too bright. Ruling out Mars due to its missing reddish color, I would then favour Saturn, which seems also confirmed by both its tabular magnitude (+2.3 for the computed date at § (10) - which seems reasonable here) and its colour. Then I go for Saturn. If no error on my behalf, last time it was in the Constellation of The Lion occurred by the end of 2007- beginning of 2008 which significantly departs from your published date (19 March 2012).

    The way I started solving this Nav Puzzle is as follows :

    (1) Print the picture on a sheet of paper. And draw an horizon line from "best visual" guess all the way through the picture. Assume HoE = 6' and T = °0C for all CelNav computations.

    Assume this picture is equidistant (i.e. respects all distances).

    (2) Measure distances on the printed picture:

    Regulus - Castor = 165 mm  No refraction, computed tabular distance from Ephemeris = 40.5233° yielding scaling factor = 0.245 mm/°

    Algeiba - Pollux  = 148 mm    No refraction, computed tabular distance from Ephemeris = 36.1200° yielding scaling factor = 0.243 mm / °

    Regulus - Pollux = 149 mm to be used later

    Algeiba - Castor =  161 mm to be used later

    Use the average no refraction scaling factor of 0.244

    (3) Measure heights above the Horizon with this provisional scaling factor

    Regulus 106.5 mm = 26°01.8'

    Algeiba 142 mm =  34°42.5'

    Procyon 31 mm = 7°34.6'

    Castor 134 mm = 32.45.1'

    Pollux 120 mm = 29°19.8'

    (4) Compute Castor / Algeiba Fix et N69°35.0 / 094°30.9' and Procyon / Regulus Fix at 69°11.8' / E096°48.5' . Here ONLY the Latitudes are relevant.

    (5) From Approximate position taken at N69° / E095° compute apparent refracted positions of Castor, Pollux, Algeiba and Regulus

    (6) From (5) compute apparent refracted distances for all 4 pairs in (2) . Get an updated refracted scaling factor of 0.245°/mm . No significant change whatsoever as expected but it was worth checking.

    (7) Then from all 5 bodies compute a Fix at N69°20' / E 096° with a quite important dispersion of 21 NM (1.5 mm on paper). We should recognize that all "measured" angles given here have a rather important uncertainty : range estimate probably up to 1°.

    Computed Azimuths : Regulus 227.6° / Algeiba 226.9° / Procyon 262.4° / Castor 273.9° / Pollux 269.0° with their relative directions all matching quite well here.

    (8) No way to extract any significant constant error out of the various heights (a topic addressed a few years back on NavList) because all observations in one same direction. It would certainly have been very nice here because of the significant uncertainty on the horizon.

    Never mind ...

    (9) Simple extra considerations can help you narrowing the time period :

    You do not want this to happen in the Northern hemisphere summer, especially at such high latitudes. So you should rule out the Mid April-Late August time period, at least.

    You do not want Saturn to be at opposition either because it would be far too bright for the picture.

    (10) - From the Saturn - Castor refracted distance = 200 m = 48.9 ° , get a time frame of Early December 2007 until late March 2008 for this picture to have been taken. Furthermore, date determination is also a bit tricky here since Saturn - Castor distance stays at a maximum by Dec 21 st 2007 (retrogradation)

    (11) To recap : probable Latitude at N 69°30' , maybe +/- 30' if I am lucky, and maybe also up to +/- 2° does not look unrealistic either given the individual heights errors (certainly +/- 0.5°) and the dilution factor which cannot be neglected here (All bodies in one same azimuth +/- 23° ...) One huge city in this Latitude range : Mourmansk ... also well known for its Northern lights.

    (12) Now I quit because I cannot find any other method of refining Longitude ...  Except the fact that the shore line seems to oriented 245°.

    Eager to learn more here. Where are we actually ?

    After punching the "send" button, I can now consult any extra information ...

    Kermit

       
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