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    Re: Latitude and longitude around noon
    From: Brad Morris
    Date: 2017 Mar 30, 13:39 -0400
    Hello Frank

    I didn't mean to spoil the quiz.  After checking a few of the answers by asking Google Earth to show me where they were, it dawned on me I could simply invert that process and look for a likely location with a view directly south.  With a few other reasonable assumptions I could narrow the choices.

    Nor did I mean to ruffle any feathers.  I recognize there is a mathematical process that may result in a longitude solution.  As I mentioned before, I was checking those solutions and wanted others to check theirs too.

    You, of course, noted that I used the word "may". Noise in your observations will clearly affect your result, as the quadratic fit of the parabola will be a fit to the data presented.  Even without a change in declination, the noise will present an issue towards an accurate fit.  In the present case we are to manipulate a quadratic equation to adjust culmination based on the change in sun declination over the period of observation.   Understood.  So with enough electronics to determine the coefficients of the quadratic and to shift the point of culmination of that quadratic by the change in declination, we get an answer.  

    Perhaps I'm going to cheat again.  I know the shape of the parabola, the sun's arc in the sky, given the latitude.  That is fixed.  I know the change in culmination over the period of observation, as the Sun's declination is also known vs time.  If I find a least squares fit of the known parabolic arc to your data, we know where culmination occurs given your observations which include the change in declination.  Shift that curve in time, left or right, dependent on the direction of change in declination.  Of course the altitude of culmination will be wrong, yet the time will be correct.  This is still subject to the noise in the data, but less so, as the quadratic fit is given as a function of latitude, not your observations.

    Brad












    On Mar 30, 2017 12:40 PM, "Frank Reed" <NoReply_FrankReed@fer3.com> wrote:

    Brad Morris, you wrote:
    "As a hint to the others, have you checked your answer on Google Earth? Does your positional solution afford a natural sea horizon view due south? If not, you need to rethink your answer."

    That answers a separate question. We can reasonably ask, and often do ask, what is the best celestial fix from the data on-hand, and then separately we ask, what is the best fix based on all available information including clever detective work (also sometimes known as "cheating" *). In the latter category, when faced with a recent digital photo of a celestial phenomenon, a number of people have pointed out that we can use the GPS tag data in the photo to confirm the position. True! But only relevant if the exact position is the actual goal of the discussion. 

    In an earlier message, after comparing the analyses up to that point, you wrote:
    "Proving, yet one more time, that obtaining longitude from the noon latitude observation is fairly worthless."

    You may have missed the boat on this one, Brad, by retreating to the barricades of textbook orthodoxy :). One can indeed get a very good celestial fix from sights around noon by a variety of methods, but you have to do it "right". You need a method for determining the axis of symmetry of the sights that manages statistical noise, and you need a method for pulling the peak altitude from a parabola-like curve, and you need a method for dealing with the changes in the curve that result from motion towards or away from the Sun. Most of the orthodox complaints over this methodology have simply assumed the lowest common denominator approach of "drawing a curve by eyeball" is the only one worth considering. It's a standard that is guaranteed to confirm the bias of a priori belief. By applying simple, proper methods, one can get both an excellent latitude and a "good" longitude from sights of the Sun around local noon. The orthodoxy is wrong.

    Frank Reed

    * I mentioned detective work as "cheating". Speaking of detectives, last night I was watching an episode of "Columbo" from 45 years ago. There is a scene at LAX (airport) about meeting a charter flight from Mexico, and some stock footage shows a plane landing with a great view from beneath the fuselage where we see the landing gear coming down. The landing gear pairs emerge from the fuselage itself from behind big triangular doors. I just happened to look at the screen at that moment and laughed because that clearly was not the sort of plane that might be arranged for a charter flight. It was the unique landing gear configuration of a B-52 bomber. No big deal, of course, stock footage is used for filler frequently and was especially common in tv production back then. But still... I wanted to see where this came from --it was a nice view! So I popped online and started looking for video of B-52 landing gear. I found a number of similar cases but no match. Then it dawned on me: you have to use the Internet the "right way", and in this case, the right way is to assume that someone else has already asked and answered the same question (and with any luck they have answered correctly!). So rather than searching for video of B-52 landing gear coming down, I searched for "B-52 in an episode of Columbo". And of course that worked. I now "know" what movie that footage was taken from.... But it's cheating. I don't really know anything except someone else's best guess until I confirm it myself. At least my curiosity was sated :).

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