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    Re: FW: Re: Chronometer Suggestions
    From: Nicol�s de Hilster
    Date: 2009 Jan 15, 21:30 +0100

    While were busy doing some math:
    on Clarke 1866 one arc minute in latitude equals
    at 0 degrees 1842.786m or 6045.886ft
    at 30 degrees 1847.472m or 6061.260ft
    at 60 degrees 1856.910m or 6092.224ft
    at 90 degrees 1861.656m or 6107.795ft
    
    in longitude this is
    at 0 degrees 1855.344m or 6087.087ft
    at 30 degrees 1608.138m or 5276.043ft
    at 60 degrees 930.036m or 3051.299ft
    and zero at the pole.
    
    Nicol�s
    
    glapook{at}PACBELL.NET wrote:
    > The nautical mile used to be defined, in the U.S., as one minute of
    > arc on a sphere having the same area as the earth as defined on the
    > Clarke spheroid of 1866 and was 6,080.2 feet. The length of one minute
    > of latitude varies from 6,046 feet at the equator to 6,108 feet at the
    > poles on this spheroid (I don't know what it is on WGS84.) The length
    > of the geographical mile, one minute of longitude on the equator, is
    > 6,087 feet. (Bowditch, 1977)
    >
    > Also see:
    >
    > http://www.i-DEADLINK-com/bowditch/pdf/chapt02.pdf
    >
    > gl
    >
    > On Jan 15, 10:55 am, Lu Abel  wrote:
    >   
    >> Curiosity question:
    >>
    >> It's well known that the diameter of the earth across the equator is
    >> about 1/300th greater than the diameter across the poles.
    >>
    >> I would intuitively expect, therefore, that the size of a minute of
    >> latitude to change by a like amount.  But looking at this graph, there
    >> seems to be a 1/60 difference in the size of a minute at the poles vs at
    >> the equator.  Is there an explanation that this technically competent,
    >> but ignorant of the math of the oblate spheroid, person could understand?
    >>
    >> Also, I assume this graph is for geodetic latitude and not geocentric or
    >> parametric latitude?
    >> (For people curious about these terms, geodetic latitude is what you get
    >> by drawing a line perpendicular to the surface of the earth down to its
    >> axis.  Due to the flattening of the earth, this line will intersect the
    >> earth's axis on the other side of the equator from the observer's
    >> position.  The other two latitudes are what you get when you draw a line
    >> out from the earth's center. This line is not perpendicular to the
    >> earth's surface except that the poles and equator)
    >>
    >> Lu Abel
    >>
    >> Nicol�s de Hilster wrote:
    >>     
    >>> On NavList 7052 Irv Haworth wrote:
    >>>       
    >>>> "I think it's well known that 1' of arc varies in length as a function
    >>>> (cos)
    >>>> of the latitude."
    >>>>         
    >>> On which Gary LaPook replied in NavList 7053:
    >>>       
    >>>> That is true for one minute of longitude because parallels of latitude are small circles.
    >>>> This is not true for one minute latitude of for any
    >>>> other great circle. (Technically these also vary slightly due to the
    >>>> oblateness of the earth but these small variations are ignored for
    >>>>  celestial navigation purposes.)
    >>>>         
    >>> For those who want to know how much exactly that variation is I posted
    >>> attached graph of it in NavList 4750 on 24/03/2008.
    >>>       
    >>> ------------------------------------------------------------------------
    >>>       
    >>     
    > >
    >
    >   
    > ------------------------------------------------------------------------
    >
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    >   
    
    
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