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    Re: FW: Re: Chronometer Suggestions
    From: Gary LaPook
    Date: 2009 Jan 15, 14:12 -0800

    The radius of a sphere on which the great circle is 21,600 NM is 
    3,437.746 NM (21600/2 Pi) which compares very closely to the mean radius 
    of the various spheroids e.g. Clarke 1866 of 3440..65 NM a difference of 
    2.319 NM.
    glapook@PACBELL.NET wrote:
    > It may seem counter intuitive that the minute of latitude is longer at
    > the pole since you are 12 NM closer to the center of the earth at the
    > pole than at the equator and you would think that the same angle on a
    > smaller radius would be a shorter arc. The polar radius is 3432 NM,
    > equatorial radius, 3444 NM. The answer is that the angles are measured
    > in reference to the geode at that point. Since the surface of the
    > geode at the pole is "flattened" compared to at the equator, the lines
    > connecting "straight down" do  not come together at the center of the
    > earth but at some point beyond the center. Since a minute of latitude
    > is measured between these "straight down" lines, the radius of the arc
    > is greater than the actual polar radius so the length of the arc is
    > also longer.
    > For celestial navigation purposes, due to the limit of achievable
    > accuracy, the assumption is that the earth is a perfect sphere with a
    > circumference of 21,600 NM (360 X 60) which is the length of a great
    > circle. Such assumptions don't work with GPS due to its high
    > precision. Sextants altitudes are measured in reference to the local
    > geode because the sea horizon is determined by the local gravity field
    > as is the position of the bubble in a bubble octant so the latitudes
    > determined are actually geodetic latitudes but the difference between
    > this and geocentric latitude is ignored and are generally treated as
    > geocentric latitudes.
    > gl
    > On Jan 15, 12:09 pm, glap...@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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