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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2024 Feb 29, 11:03 -0800
Revised post:
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° which is a quite reliable angular scaling factor. From that, the Basilica Dome diameter is seen at an angle of 0.15°.
With its published overall height at 70 m and through analyzing 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.
This seems compatible with the picture. My own feeling is that the Observer is slightly under the Basilica ground Level.
(3.3) - Hence the further away from the Basilica (with its 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 from the Basilica.
As I am reading altitudes from Google Earth - which are not referenced to actual/local sea level but to the WGS84 Ellipsoid - let us reason here in terms of Google Earth Altitude differences.
Therefore 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 an Altitude of 450 m, which certainly looks consistent with our observed Google Altitude reading at 455 m.
So, 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.
(4.1) - Let's then compute the elevation of MonViso over the Observer's local horizon without refraction.
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 length equal to (6,367 km + 3.841 km).
From this we immediately derive that without refraction, MonViso summit would show at 2.015° - i.e. at 2°01' - above the Photographer's own local horizon.
(4.2) - Let's apply inverse refraction to MonViso knowing that:
(4.2.1) - The lower the atmosphere layers, the higher the refraction effects. And also:
(4.2.2) - We should apply only part of the full atmosphere 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 default 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-above we will assume that the effect of inverse refraction is about 1/2 of its overall effect over the entire atmosphere thickness.
(4.3.3) - We then obtain a wet finger inverse refraction close to 10', hence an expected MonViso summit altitude close to 2°11', which - given the inverse refraction uncertainties in this overall exercise - is consistent with its picture altitude at 2°13' (i.e. Moon UL - 2').
As an overall, conclusion :
YES, 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.
Warmest Congratulations to its Author M. Valerio Minato .
Kermit