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    Re: Time of meridian passage accuracy
    From: Antoine Cou�tte
    Date: 2009 Sep 25, 23:43 -0700

    George is right : Time of Meridian passage may be significantly different from time of Culmination.
    
    Well known formula (although first order approximation). Let :
    
    - "Delta Time" be the difference is seconds of time between culmination and Meridian Transit, and
    
    - "Lat" the Observer's Latitude at Transit time, with "vLat" his hourly 
    Latitude speed is arcminutes per hour, and
    
    - "Dec" the Body's Declination at Transit Time, with "vDec" the hourly 
    Declination change in arcminutes per hour, then
    
    Delta Time = 48/Pi * (tan. Lat - tan. Dec) * (vLat - vDec) . First coefficient 
    often published as 15.35 or 15.3
    
    Nothing new : this formula has already been posted here and it has been taught 
    for probably (almost and maybe more) one century now.
    
    Let us take a somewhat 'extreme' but still realistic example : Lat = North 15? 
    with vLat = -30 and Dec = 15? South  with vDec = + 12 (Moon case), then we 
    find that Delta Time =  22.5 seconds (actual value does differ by just a few 
    seconds of time)
    
    
    What are the practical implications on position accuracy if and when Meridian 
    transit time not equal to Culmination time ?
    
    If the vessel has a significant north/south speed component, such as in the 
    extreme case listed here-above, then :
    
    Body declination may have changed by up to 1/15 arc minute during that time 
    period, so it is (almost) negligible for conventional Celnav, and
    
    Vessel's latitude will have changed by 0.2 ' during that time period. You may 
    start wanting to take it in account.
    
    
    Antoine
    
    
    Antoine M. "Kermit" Couette
    
    
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