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Re: Trakstar and satellite latitude.



Bill,

You're seeing the difference between "geoCENTRic" and "geoDETic" latitude.

Geocentric latitude is what you get when you compute

 arcsin ( z/sqrt(X^2+Y^2+Z^2))

It represents the angle, measured at the center of the earth, between
your location and the equatorial plane.

But the word "latitude" usually means geodetic latitude, not
geocentric latitude. They differ because the earth is not a perfect
sphere. To a good first approximation, it's an oblate spheroid.

The earth is oblate for a simple reason: it spins. The actual shape of
the earth is much more complex, but the oblate spheroid ("ellipsoid")
is such a good approximation to reality that it is a primary reference
in GPS and many other mapping and positioning applications. (Try
searching Yahoo for "WGS84 ellipsoid").

Geodetic latitude is defined as the angle, with respect to the polar
axis, of the tangent to the ellipsoid that runs through the location
in question. If you draw this out, you'll see that this tangent is not
quite perpendicular to the line running from the center of the earth
to the tangent. The only exceptions are at the poles and on the
equator, where geodetic and geocentric latitudes are the same. At all
other points, the geodetic latitude is somewhat greater than the
geocentric latitude.

Geodetic latitude is (approximately) what you get when you measure
your latitude by the stars. That's why it's the usual meaning of
"latitude" for maps and such.

Here's another way to look at it. Consider a plumb bob hanging freely
at your location. You might think that it points directly at the
center of the earth. But it doesn't, unless you're on the equator or
on one of the poles. Due to the centrifugal force of the rotating
earth, your plumb bob points slightly south (if you're in the northern
hemisphere) or slightly north (southern hemisphere) of the true
direction to the center of the earth. This deflection is (ignoring
local gravitational anomalies) equal to the difference between your
geodetic and geocentric latitudes.

Phil
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