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    Re: MonViso, Lady Moon again with a Basilica Nav Puzzle
    From: Antoine Couëtte
    Date: 2024 Feb 29, 08:19 -0800

    Dear Geoff,

     

    Nice to read you again.

    (1) - I agree with your own azimuth determination at 229.549° from Superga Basilica to MonViso.

    Thanks M. Ed Williams whom you just made me to discover for computations on Ellipsoids.

    (2) - Same conclusion as yours also: the actual picture time was certainly closer to 17:54 UT than to 17:52 UT (your result shows 17:53:54 while I am getting 17:53:40). So most probably the Observer's watch was about 2 minutes slow.

    (3) - In order to proceed further, we first notice that the picture was not taken from the Basilica itself but further away from MonViso.

    (3.1) - We can use the picture to guestimate such distance between Basilica and Observer.

    The Moon Diameter is close to 0.54° whish is a quite reliable angular scaling factor. From that, the dome diameter is seen at an angle of 0.15°.

    With its published overall height at 70 m and through analysing various pictures, my best determination for its actual external masonry diameter is 27 meters.

    This puts the photographer at some 5.9 NM (and of course on an azimuth of 049.5°) from the Basilica.

    The Observer's position now lies in the vicinity of 45°08.7'N 007°52.4'E. Its Google Earth Altitude reads 455 m.

    Is this Google Earth altitude at 455 m compatible with the other picture data ?

    (3.2) - From the Position derived in (3.1) hereabove, we can compute the Moon UL to be at 2°15.2'.

    From the picture we can reasonably guestimate that the Basilica ground level to be at about 1° below the Moon UL.

    It then leaves us with an upward slope of 1.25° from Observer to Basilica ground floor.

     the Basilica ground Level.under compatible with the picture. My own feeling is that the Observer is slightly seemsThis 

    (3.3) - Hence the further away from the basilica (Google Earth ground level at 673 m), the lower the Photographer should be, and so by an approximate amount of 125' / NM or 37 m / NM.

    .Altitude differences, let us reason here in term of WGS84 EllipsoidAs I am reading altitudes from Google Earth which are not referred to actual/local sea level but to the 

    Then at a point at 5.9 NM from the Basilica the Photographer can be expected to be some 225 m under its esplanade, i.e. at about 450 m, which certainly looks consistent with our observed Google Altitude reading at 455 m.

    So, let's carry on, and pending confirmation of point (4) here-after, the actual Photographer's distance from the Basilica was slightly under 6 NM, or in other words slightly under 11 km.

    (4) -  Final check : is the angular interval - showing at slightly under 2' - between Moon UL and MonViso summit a realistic value ?

    From The Photographer's Position 45°08.7'N 007°52.5'E (Google Altitude at 455 m) to MonViso (44°40.05N 007°05.5'E (Google Altitude at 3,841m), then M. Ed Williams again is telling us that the WGS84 azimuth and distance are : 229.594° / 43.955 NM.

    .without refraction(4.1) - Let's then compute the elevation of MonViso over the Observer's local horizon 

    Let's assume that close to 45°N the actual terrestrial radius stays unchanged between these both points and is equal to 6,367 km.

    In a plan containing the Earth Center and both points (i.e. Superga and MonViso), we are to compare a vertical vector of (6,367 km + 0.455 km) to a vector offset by (43.955/60)° = 0.733° with a lenght equal to (6,367 km + 3.841 km).

    , MonViso summit would show at 2.015° - i.e. at 2°01' - above the Photographer's own local horizon.without refractionFrom this we immediately derive that 

    (4.2) - Let's apply inverse refraction to MonViso knowing that:

    (4.2.1) - The lower the atmoshphere layers, the higher the refraction effects. And also:

    (4.2.2) - We should apply only part of the full atmospere inverse refraction since here refraction is involved only between altitude 455 m and altitude 3,841m.

    Which part exactly ? Certainly this has been studied and published ... But I do not hold the computing tools here.

    By defaut let's attempt some wet finger approach.

    At Altitude 3,841 m, standard pressure is about 625 hPa, i.e. about 0.6 * sea level pressure. By reason of (4.2.1) here-abovewe we will assume that the effect of inverse refraction is 2/3 of its overall effect over the entire atmosphere thickness.

    (4.3.3) - We then obtain a wet finger inverse refraction close to 11', hence an expected MonViso summit altitude close to 2°12', which - given the inverse refraction uncertainties in this overall exercise - is consistent with its picture altitude at 2°13' (i.e. Moon UL - 2').

    this superb genuine picture, probably taken at some 11 km from the Superga Basilica by 18h54 Local Time (17:54 UT), remains one of the most beautiful, impressive and remarkable sky pictures ever published.As an overall, conclusion, YES, 

     .M. Valerio Minato Warmest Congratulations to its Author 

    Kermit

     

       
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