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    Re: Time of meridian passage accuracy
    From: Douglas Denny
    Date: 2009 Sep 25, 15:29 -0700

    The declination on the example was calculated for the time of Mer Passage at 
    Greenwich for simplicity and because there is practically no difference from 
    here at 51 minutes West to Greenwich.
    
    Mer Passage at my location at Long 51.2 minutes West is three minutes 24.8 seconds later than Greenwich.
    
    On the 29th April 2009.  By my calculator, programmed with Smart's formulae 
    for Equation of time; and formulae from Meeus and Explanatory Supplement for 
    the Astronomical Almanac:
    
    At Greenwich, at Mer Passage the Declination was  14.4398056824 Degrees N.
    At Bosham (three min 24.8 sec later) it was       14.4405427504  Degrees N.
    
    The difference is 0.000737068 degrees,  or 0.04422408 minutes,  or 2,6 seconds of arc.
    
    Utterly  negligable -  unless you are concerned with the time of an occulting 
    star with the Sun (if you could see it), or checking Einstein's Special 
    relativity.
    
    ----------
    
    The comment asked for,  was concerned with  _practical navigational_  use: the 
    quote from Bowditch. More specifically mentioned:- if the Equation of Time 
    within one minute is adequate.
     
    It has long been the case in Marine navigation that Mer Passage can be 
    adequately useful in practical navigation with simple calculation using Mer 
    Passage for Greenwich for the day (which is why it is still given in the 
    Nautical Alamanac for each day), and an allowance for local longitude.
    This is more than adequate for navigational use.
    ---------
    
    You will also note from the graph of my example, that the maximum altitude was 
    within one minute of arc for approx plus and minus ten minutes of time. This 
    is the main point in question here I believe - that obtaining Mer passage at 
    the location to within one minute of time using an Equation of Time within 
    this limit is  _more_  than adequate.
    
    Correction for declination change in practical navigation for Mer Passage is, 
    I think, academic.  It might be useful perhaps for the sake of better 
    accuracy, with times of the year with maximum change of rate of declination,  
    and local longitudes approaching 180 degees from Greenwich. Still negligable 
    for marine navigation. One minute of arc accuracy is the best one would 
    normally expect anyway.
    
    Douglas Denny.
    Chcihester.  England.
    
    
    
    
    Throughout his posting [9923], Douglas Denny appears to presume that
    Meridian Passage of the Sun occurs at the same moment as the maximum
    altitude of the Sun, at the peak of the curve of altitude with time.
    
    But it doesn't, except at the solstices, because of the Sun's changing
    declination. On the 29th April, the Sun's declination is increasing
    (Northward) by about 0.8 arc-minutes per hour. By a bit of rough guesswork,
    that's enough to delay the moment of peak altitude, to be somewhere between
    1 and 2 minutes later than Meridian Passage. Which will throw out his
    assessments by that amount.
    
    To set up a precise North-South line, it's a factor that must be allowed
    for. For star observations, there's no such problem, as the declination
    stays constant.
    
    George.
    
    contact George Huxtable, at  george---me.uk
    
    --------------
    
    Also:-
    
    I just wrote-
    
    "On the 29th April, the Sun's declination is increasing (Northward) by about
    0.8 arc-minutes per hour. By a bit of rough guesswork, that's enough to
    delay the moment of peak altitude, to be somewhere between 1 and 2 minutes
    later than Meridian Passage. Which will throw out his assessments by that
    amount."
    
    However, that guesswork was a bit too rough. On second thoughts, I would
    reassess that time offset, due to changing declination of the Sun, to be
    about half a minute of time. Still well worth correcting for, however.
    
    George.
    
    contact George Huxtable, at  george---me.uk
    
    
    
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