Subject: Re: caus straight or irregular
Date: May 04, 2001 @ 22:52
Author: granthutchison@cs.com (granthutchison@...)
Prev    Post in Topic    Next [All Posts]
Prev    Post in Time    Next


Re Peter's point about approximations to the shape of the earth.
The sphere is a first approximation. After that come various second
approximations, all oblate ellipsoids. Your choice depends on whether
you're mapping the whole Earth (in which case the WGS84 ellipsoid is
the best fit) or some part of it (in which case you can choose the
local best fit - Airy in the U.K., Clarke in the U.S.) WGS84 is the
shape the Earth would be if it was a spinning lump of completely
homogenous rock. The third and most accurate level of approximation
is the *geoid* which reflects local variations in density (and
therefore surface gravity). It's the real mean sea level that water
would settle at if it were allowed to seek a level through tiny
frictionless channels bored out under the Rockies, Himalayas etc.
Corresponding to these levels of approximation are various ways of
determining latitude: Geocentric latitude is the angle between your
current location, the centre of the Earth and the equator. Geodetic
latitude is the angle between the normal to the ellipsoid at your
location and the equatorial plane. Astronomical latitude is the angle
between your local vertical (ie the normal to the geoid) and the
equatorial plane.
I labour through all this to respond to Brendan's guess that the line
of sight is equivalent to a great circle. I think more or less yes,
but precisely no. The great circle segment connecting any two point
on the Earth's surface is defined by a plane passing through those
two points and the Earth's centre - it therefore corresponds to the
(rather poor) spheroidal approximation. *But* I think the line of
sight corresponds to a local-vertical sort of situation - you set
your theodolite vertically over one point, and sight on a flag held
vertically over another point. And the local vertical at 49 degrees
latitude is (using the second-level approximation of the WGS84
ellipsoid ... scribble, scribble) tilted by about a fifth of a degree
relative to the great circle - the vertical plane at that latitude
misses the centre of the Earth by close to 30km.
So the line of sight along the 49 deg section of ca-us lies just a
hair north of the great circle, which lies a way or so north of the
parallel of latitude.
Whatever - a gently scalloped edge to the U.S., like a Victorian lace
doily.

Grant