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Jim,

George has answered your point before I could but I will add two
different perspectives on the same problem:

Firstly, to bring this stuff closer to home: You live close to 46 North,
so the offset between geocentric and geodetic latitude is very close to
its maximum in your home waters. (Closer still in mine: 44 degrees 47'
North.) If your celestial LOPs really were geocentic, if you plotted
them on a Mercator chart _and_ if they showed you in the middle of
Northumberland Strait, you would actually be hard aground on the coast
of Nova Scotia. It isn't a trivial difference, though it is one that
most navigators can ignore most of the time.

As to your search for a formal citation of the idea that the horizon
coordinate system is related to the direction of gravity: You really
shouldn't need that verified in writing. Every cel nav observation uses
a reference provided by a liquid surface, be that the surface of a
natural water body, the surface of a fluid artificial horizon, the
bubble in a bubble sextant or attachment, or else the bubble in a spirit
level used to set up a rigid artificial horizon. And all of those fluid
surfaces, naturally enough, end up perpendicular to local gravity (if we
ignore wind, density gradients and other minor complications). More
strictly, they end up perpendicular to the resultant force which
combines gravity and the centrifugal force of the Earth's rotation,
though the latter is very weak.

Except in extreme cases, such as along the west coast of the Americas,
where you have mountains off one beam and deep ocean off the other, the
direction of gravity is very, very nearly perpendicular to the surface
of the geoid -- be it the WGS84 geoid or any other used in geodesy.
Hence astronomic latitude, as estimated by cel nav, is almost the same
as geodetic latitude (which is the one used in preparing charts). That
shouldn't be surprising. After all, the geoid is a smooth approximation
to the shape of the surface of the semi-liquid rock of the Earth's
mantle and, like far less viscous fluids, that surface would be
perpendicular to the resultant of gravity and centrifugal force if it
wasn't for local complications (like mountain ranges floating in the
mantle, volcanic hot-spots and so forth).

All this, incidentally, deals with latitude. Since the various geoids
are centred on the centre of the Earth, as near as makes no difference,
with circular (not elliptical) parallels, geodetic longitude is itself
geocentric. Astronomic longitude only differs from that by the small,
local perturbations in the direction of gravity.

If, after all that, you really want a printed confirmation, go to
article 204 of Bowditch (1995 edition), where the different kinds of
latitude and longitude are explained in the chapter on geodesy and datums.


Trevor Kenchington



You wrote:

> I have not yet found an independant reference to this idea that the
> horizontal coordinate system's horizons are perpendicular to gravity.  All
> the definitions I have found so far refer to the center of the earth, not
> the direction of gravity.  You were challenging my comment that the horizons
> are perpendicular to a line drawn through the center of the earth to the
> observer's position on the surface of the earth.  I think what you meant was
> that this would only be true if the earth was a perfect sphere and if
> gravity pointed to the center of the earth, but the earth is geoid, and so
> the direction of gravity is a more proper reference than the center of the
> earth.  Is that so?
>
> Jim Thompson


--
Trevor J. Kenchington PhD                         Gadus@iStar.ca
Gadus Associates,                                 Office(902) 889-9250
R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
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