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    Re: Moving Navigator LAN: Culmination to Meridian Passage fully solved
    From: Andrés Ruiz
    Date: 2023 Dec 22, 10:07 -0800

    Thanks Antoine for this interesting issue.

    Solution for the example in "231217-LAN-Part-I-Near-Noon-methods-comparison-.pdf"

    • EX1.Kermit.obs input file for Nautical Astronomy.exe (I did it quickly and I do not know if I interpret Hmoon data correctly)
    • EX1.Kermit.current.png
    • EX1.Kermit.png

    231219-LAN-Part-II-Culmination-to-Meridan-Passage-fully-solved-.pdf

    • LoogBook.xlsx (in zip file) simulated data, B1 example, for anyone who wants to play with it.

       t

       B2

       L2

       gha

       dec

       Hc

       Zn

    Event

    5.9058333

    60.115377

    -143.136

    143.13203

    1.5349944

    31.419617

    179.99534

     

    05:54:21

    Meridian transit

    60º 6.9'

    143º 8.2'

    5.9061111

    60.115171

    -143.1358

    143.13607

    1.5350719

    31.419901

    180.00031

     

    05:54:22

    Meridian transit

    60º 6.9'

    143º 8.1'

    6.3288889

    59.801256

    -142.8163

    149.27507

    1.6530247

    31.636764

    187.58909

     

    06:19:44

    Culmination

    59º 48.1'

    142º 49.0'

     

    It is also interesting to compare with the SR solution as described on paper Celestial Fix - n LoPs - by Least squares Sight Reduction algorithm. Paper & Excel (B1solution.MP.png, B1solution.SR) 

    Back in 2009 I made a lot of simulation,  huge amount of data, to see how time of culmination differs from time of meridian passage: simulacion V.xls, RV 135 100.7z 

    And conclude that Jim Wilson's method gives bad results when SOG is greater than say 10 kn.

    Background

    At culmination celestial body altitude H = maximum/minimum -> dH/dt = 0

    Meridian passage:

    • LHA = 0  (Upper Meridian of Place) or LHA = 180º (Lower Meridian of a Place)
    • Azimuth Zn = 180º/0º 

    References (attached files):

    Pages from A1 - Algoritmos.pdf

    • Latitude by meridian transit (Latitud al paso por el meridiano del lugar)
    • Position by meridian transit (Hs and time of meridian transit)
    • Ex-meridian sight (Latitud por altura circunmeridiana)

    Pages from Position&Time.pdf

    • The equations of the observations: Altitude
    • Time derivatives
    • Stationary observer 

    To solve this problem, I use a matrix integration of all differential equations for each observation, (see Position&Time.pdf).

    Fair winds and following seas!

    --

    Andrés Ruiz
    Navigational Algorithms
    https://sites.google.com/site/navigationalalgorithms/

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