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    Re: Position from altitude and azimuth.
    From: Andrés Ruiz
    Date: 2020 May 13, 19:22 +0200
    Solution with corrected azimuth Z = 120.0 + 27.9 / 60.0;
    Very sensitive to Z

    One Body Fix by HZ
    06/05/2020 15:00:00 UT1 Sun
    Hc = 54.9317 º =  54º 55.9'
    Zn = 120.4650 º

    NAUTICAL ALMANAC
    Sun
    GHA = 45.852082 º =  45º 51.1'
    Dec = 16.779705 º =  16º 46.8'
    SD = 15.8518 '
    HP = 0.1453 '

    LHA = 43.852082 º =  43º 51.1'

    Fix PositionByAltitudeAndAzimuth
    B = 39.000079 º =  39º  0.0'
    L = -77.000274 º = -77º  0.0'

    Fix PositionByAltitudeAndAzimuthJK
    B = 39.000079 º =  39º  0.0'
    L = -77.000274 º = -77º  0.0'

    Fix Differential Equation
    B = 39.000079 º =  39º  0.0'
    L = -77.000274 º = -77º  0.0'

    Fix Differential Equation Z(B,L,H)
    B = 39.000079 º =  39º  0.0'
    L = -77.000274 º = -77º  0.0'

    DifferentialEquation
    iter B L Zo Zc
    0 42.3166667 -3 120.465 248.30433
    1 121.05997 -59.0828787 120.465 166.975852
    2 56.9181029 -110.223338 120.465 102.375738
    3 25.591603 -72.1155323 120.465 104.618217
    4 36.8185711 -79.2993286 120.465 115.139589
    5 39.1743952 -77.1073953 120.465 120.550814
    6 38.9997545 -77.0005092 120.465 120.46432
    7 39.0000795 -77.0002736 120.465 120.465

    DifferentialEquationBLH
    iter B L Zo
    0 42.3166667 -3 120.465
    1 121.05997 -59.0828787 120.465
    2 56.9181029 -110.223338 120.465
    3 25.591603 -72.1155323 120.465
    4 36.8185711 -79.2993286 120.465
    5 39.1743952 -77.1073953 120.465
    6 38.9997545 -77.0005092 120.465
    7 39.0000795 -77.0002736 120.465


    Geoffrey one of the direct method, is the same as you describe.
    The use of an iterative method, provide a more general solution, for example for one altitude and two azimuths, or other set of equations. 

    Fair wind and following seas.
    --
    Andrés Ruiz
    Navigational Algorithms
    http://sites.google.com/site/navigationalalgorithms/
       
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