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    Re: Pear shaped Earth
    From: Richard B. Langley
    Date: 2002 Oct 3, 09:22 -0300

    Here are 3-term expressions for the distance in km for a degree of latitude
    and longitude that I developed for the Royal Astronomical Society of Canada
    Handbook a couple of years ago based on the WGS 84 ellipsoid:
    1 degree lat = 111.13295 - 0.55982 Cos[2 phi] + 0.00117 Cos[4 phi]
    1 degree long = 111.41288 Cos[phi] - 0.09350 Cos[3 phi] + 0.00012 Cos[5 phi]
    where phi is the latitude.
    The series were obtained by truncating the relevant series expansions
    developed from first principles.  The 3-term expressions should be accurate to
    about 1 centimetre or so for distances on the ellipsoid. I spot checked
    several values with a table in the American Practical Navigator to confirm
    -- Richard Langley
       Professor of Geodesy and Precision Navigation
    >David Weilacher wrote:
    >> My conclusion from this is that a pear shaped earth has a negligible effect on
    >> the accuracy of sight reduction.  It doesn't matter what distance you are from
    >> the center of the earth (well there is an over-simplification) as long as the
    >> horizon is also at the same level.  Since the horizon is likely to be only 4
    >> to 10 nm away, this pear shape notion becomes moot because you and the horizon
    >> are at the same height.
    >Agree with this.
    >> so, if I've understood correctly, a degree at
    >> 10d of lat.is 59.71 nm, and a
    >> degree at 90d of lat. is 60.007 nm.
    >Woke up in the middle of the night, an attack of logic: if the earth bulges out
    >at the equator and is flattened at the poles, then shouldn't a degree, expressed
    >as nm, be longer at the equator and shorter at the pole?
     Richard B. Langley                            E-mail: lang@unb.ca
     Geodetic Research Laboratory                  Web: http://www.unb.ca/GGE/
     Dept. of Geodesy and Geomatics Engineering    Phone:    +1 506 453-5142
     University of New Brunswick                   Fax:      +1 506 453-4943
     Fredericton, N.B., Canada  E3B 5A3
         Fredericton?  Where's that?  See: http://www.city.fredericton.nb.ca/

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