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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: FW: Re: Chronometer Suggestions
From: Gary LaPook
Date: 2009 Jan 15, 13:33 -0800

```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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