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    Re: Error in Nautical Almanac Polaris SHA Feb-June?
    From: Jim Thompson
    Date: 2004 Apr 17, 16:40 -0300

    > -----Original Message-----
    > From: Navigation Mailing List
    > [mailto:NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM]On Behalf Of Jared Sherman
    >
    > Surely the range from 68.6-84.6 minutes isn't allowably precise for you
    > though? 
    
    Jared, That was the range of values for the months where the minutes values
    exceeded 60'.  As you anticipated, each month's value is a single digit
    precise to 0.1'.  Oh wait, I just spotted the VBG!  :)
    
    ----------
    However, now that I look more closely at those star SHA/Declination tables
    on pages 268-273, almost none of the other stars have a similar situation.
    In the 2004 NA only 18 out of 2,076 SHA entries exceed 59.9'!  I would have
    thought that based on random chance alone a far greater proportion would
    range over two adjacent whole degree values.  What causes this seeming
    coincidence?
    
    One way to think of the problem is this:
    - Assume that the whole minutes portion does not exceed 84.9 (in fact
    Polaris is the largest such value in 2004: 84.6)
    - There are 84 x 10 = 840 possible values for the minutes portion, ranging
    from 00.0' to 84.9'.
    - The proportion of values larger than 59.9 in the range of numbers from
    00.0' to 84.9' is (84.9-59.9)/84.9 = 25/84.9 = 0.29, or 29%.
    - There are 12 months in a year and 173 stars, for a total of 2,076 entries.
    - Based on random chance alone, 0.29 * 2,076 = 602 entries would be 60' or
    more.
    
    But given that SHA changes in very small increments for each star, then I
    have not correctly stated the odds of a star having an SHA that ranges over
    two whole degree portions.
    
    At this point in my thinking I run out of gas, in part because I'm beat
    after teaching a marine radio course all day and the Carlsberg Light is
    kicking in, and in part because my understanding of probability math is
    weak.
    
    What am I missing?
    
    Jim
    
    
    

       
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