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    Re: A noon sight conundrum
    From: Herbert Prinz
    Date: 2003 Nov 29, 14:33 -0500

    Kieran Kelly wrote:
    
    > Thank you for your input but I am now completely lost. If I take the USNO
    > figures they suggest to me, on an equal altitudes basis, that noon occurs at
    > 3h 15m 39s. However you appear to demonstrate that this is not correct.
    
    On the contrary. I said that by coincidence this value is correct to one second.
    One would normally not expect this from an equal altitude observation when no
    correction for the change of declination of the sun has been applied. The reason
    why it is possible at all that the result still comes out correctly despite a
    5.5 second offset of meridian transit from culmination is that there is a rather
    large inherent error margin of several seconds in this method to start with.
    
    My comment was not a criticism of your method per se, which, if you don't need
    GMT to more than a quarter of a minute, may be accurate enough for your purpose.
    It was a remark on Paul Hirose's investigation into the effect of an inaccurate
    value of delta T on the result. My point was that the method is so crude that an
    error in deltaT cannot possibly have an impact on its outcome.
    
    > So I went back to first principles and posed the question: If an observer is
    > standing at longitude 132d 40'E on July 20, 2002 what time will the sun
    > cross his meridian if Meridian  Passage quoted in the Nautical Almanac that
    > day is 12h 06s? Converting the arc of 132dd 40' to time I derive longitude
    > of 8h 50m 40s E.  Subtract his from GMT of Meridian Passage as we are east
    > and I derive a mer passage on that day at Long 132dd 40' of 3h 15m 20s GMT.
    > This is 19s different than the figure provided by an equal altitudes
    > computation from the USNO site.
    >
    > My questions are:
    >
    > 1) Where is my error and why is there such a big discrepancy between the mer
    > passage as indicated from first principles in the Almanac and what the USNO
    > site says?
    >
    
    You copied the wrong value from the almanac. For 2002-07-20 00:00:00 UT the
    Equation of Time is given as 06m 19s.
    
       12:06:19        local time of transit
    -    8:50:40        your longitude
    ----------------
         3:15:39        Greenwich time of transit
    
    All is well.
    
    
    >
    > 2) Is the USNO site not accurate enough to perform this type of observation
    > i.e. test and verify field observations by comparing to USNO data? This is
    > in fact what I was doing.
    
    The problem isn't the USNO data. The method that you are using is not accurate
    enough to determine meridian transit to a precision of 1 second. To see this,
    turn the problem around. Assume you have a good chronometer and the two sun
    sights at 12:07 and 12:23. Plot it and look at the LOPs. Would you be
    comfortable with a fix obtained on that basis? Probably not. It would give you
    an excellent latitude but a very questionable longitude.
    
    And so far we have not even discussed the impact of observational error. We
    discussed this problem under the purely theoretical assumption that the data
    conforms to the nominal accuracy of 0.1' of the USNO program. The method's
    sensitivity to small errors in altitude bears even more weight in the real world
    where measured Ho might be off by 0.2' or 0.3'.
    
    Time (or longitude) should be established from two sights well separated in
    time, and not solely from observations around noon. (The traditional way is the
    early morning or late afternoon "time sight" in combination with one noon
    sight.)  The archives contain articles on time sights in general (by George
    Huxtable, Bruce Stark and others) which you might find of interest in this
    context.
    
    >
    > 3) In your learned opinion what was the time of meridian passage on that day
    > at long 132d 40' E.
    >
    
    3:15:39 GMT
    
    >
    > 4) Am I getting confused between meridian passage i.e. when the sun crosses
    > the meridian and noon i.e. when the sun culminates and reaches its highest
    > point. I thought both were the same. Apparently not.
    
    They are not. See George Huxtable's contribution to this thread.
    
    Herbert Prinz
    
    
    

       
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