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    Re: Your opinion please
    From: Alexandre Eremenko
    Date: 2004 Oct 3, 14:11 -0500

    Dear Pierre,
    Here is my solution:
    
    A. Answer: Lat 47d50.0 N, Long 87ds55.0 W,
    (that is 15' East of the wrong position).
    
    Explanation. Let us call the wrong position X and let T
    be the wrong GMT used in the reduction.
    The question is: find a (correct) position Y where
    the sky at the time GMT=T-1min (correct time) looked exactly like
    the sky at X looks at time T.
    This position Y is evidently 1min=15' East
    of X.
    So the navigator has to subtract 15' from his Western Longitude.
    
    Another, "more practical" explanation. The only place in
    the sight reduction where GMT enters essentially is the
    GHA Aries. This increases at the rate of 15' per minute.
    So if you use the correct time (which is 1 minute LESS than
    the wrong time), to keep the resulting altitudes unchanged
    you have to DECREASE your Western Long by the same amount,
    because Western Long enters in your computation with the
    opposite sign to GHA Aries).
    
    B. Answer:  Lat 47d50.0 N, Long 89d09'
    
    Explanation. The only place the date
    enters in the sight reduction process is in the reading of the
    almanac entry for GHA Aries. By examining the almanac we see that
    this increases by 59' per day. (This happend because
    of the yearly Earth rotation around the Sun).
    If D was the erroneous date of the observation,
    and the correct date is D-1, then the new (correct) GHA Aries
    is obtained from the wrong one by adding 59'.
    To keep the altitudes unchanged you have to increase your
    longitude by these 59' (Western Longitude enters to the site
    reduction with the opposite sign to GHA Aries).
    
    This is a solution "for practical purposes",
    see the discussion in Georges message
    Wed Sep 29 2004 - 16:04:47 EDT.
    I mean, that corrections that are less than 0.1' are neglected
    in my arguments.
    
    On Sun, 3 Oct 2004, Pierre Boucher wrote:
    
    > Hi everybody,
    >
    > Your opinion and/or solution to a nav-question
    > (from an old examination).
    >
    > Here it is:
    >
    > In ploting sights taken on 3 stars, you get an
     erronous PR at L 47? 50.0'N,
    > Lo 088? 10.0'W.  What will be the exact PR if after revising all
    > calculation you detect the following errors and correct them:
    >
    > A.      The chronometer was 30 seconds slow instead of
     30 seconds fast .
    >
    > -------------------------------------------------------
    >
    > B.      The Greenwich Date was the one day later.
    >
    >
    > Pierre Boucher
    >
    
    
    

       
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