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    Re: Latitude and longitude around noon
    From: Michael Bradley
    Date: 2017 Mar 5, 08:45 -0800

    Being on a beach somewhere pretending I have no celnav resouces available to me, but a solid wifi signal from the hotel for my tablet ....

    The problem here has been heavily hinted at by Frank - how to find the true LAN time and Sextant Height, after which all is simple .....

    Thinking about it like a mathematician ( which I'm not ), the graph of Hs vs time would be parabolic if the sun's declination were constant.

    As it is, the sun's declination is linearly depenedant on time.

    So the whole thing comes down to a sum of a parabolic function and a linear function, otherwise called a quadratic equation. How to solve it? -  fit three of the data ploints to a quadratic in the area of interest, and plot the curve of the function.

    Stripping the degrees out of the Heights, and 17 hours from the times ( to make a graph of the fine detail ), choosing the three 'central' data points we get

    t        -261         38.0      166  time in seconds       

    H        28.8        30.0      28.7  arc minutes

    Idly submitting this data set to good old 'mycurvefit.com' , asking it  for a polynomial/quadratic fit, we get a data curve displayed which peaks with the value 30.3 minutes at the time -50 secs ( approximately, as read from the displayed graph). 

    So my offer is LAN  at 16:59:10 to the time sight department, and the peak sextant height of 40 degrees 30.3' to the Mer Pass department. Any  good?

    Michael Bradlley

    Playa de las Canteras

       
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