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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: Sextant Positions versus Map Datums?
From: Trevor Kenchington
Date: 2002 Jan 17, 12:47 PM

Peter Smith wrote:

> Actually, it is the landmarks that appear to "move" between charts
> with differing datums.

I suspect that that is a matter or relative movement, in which one moves
relative to a reference fixed to the other. If latitude and longitude
are considered fixed, the landmarks move depending on the datum chosen.
If the bedrock is considered fixed, the parallels and meridians shift.

Since the graticule, like the datums, are only conceptual constructs
(with a potentially infinite variety of datums to be invented, each with
its corresponding positions for the grid of lines), I find it easier to
consider that the bedrock is fixed for most purposes. Naturally, when
reducing a celestial sight, it is easier to consider that the meridians
and parallels are fixed.

But that only returns us to Jared's question in another form: Which
datum brings the drifting bedrock into correspondence with the frame of
reference defined by the Almanac and sight-reduction tables? Since the
landmarks move relative to the meridians and parallels depending on
which datum is used, there must be some datum corresponding to
celestially-derived positions and hence other datums must deviate from
those positions.

> The point to bear in mind is that lat and lon are angular measures
> between intersecting planes. Project these planes to the stars and
> you have celestial lat/lon, which, translated into declination and
> hour angle, is the basis for celestial navigation. A position
> calculated from celestial sights references these planes.
>
> Where these planes intersect the surface of the earth, or of an
> earth-size sphere or ellipsoid, you have the geographic lat/lon of
> a point. However, the difference between the lat/lon on the
> celestial sphere and the not-quite spherical earth is vertical.
> The planes and the angles between them remain the same. Only the
> distance from the center of the earth changes with the surface
> we've chosen.

No. You are confusing a vertical datum (such as the datum for soundings)
with a geodetic datum, which is a reference for horizontal position (See
the discussion in Bowditch).

The positions of landmarks on the (irregular) surface of the Earth must
be projected onto the ellipsoid for a particular datum in order for its
latitude and longitude to be determined. Change the ellipsoid and you
will change the point at which the projection intersects it.

> Each horizontal datum begins with a set of reference points whose
> lat/lon is determined as accurately as possible. From these
> reference points, ancient or modern surveying methods are used to
> assign latitude and longitude to other landmarks, and you have a chart.

That is the process of constructing a geodetic grid. The measurements
thus obtained still have to be reduced to datum -- mathematically
projecting them onto the chosen ellipsoid.

> Newer datums have more accurately determined base references and
> more accurate surveys from them. But it's not the underlying
> latitude and longitude that shifts between datums, its the assignment
> of lat/lon to landmarks.

No. WGS83 involves a different ellipsoid from those used previously --
selected to be a good approximation to the true shape of the Earth
everywhere, now that GPS allows high-precision global navigation.
Re-drawing charts to WGS83 caused the apparent latitudes and longitudes
of their landmarks to change without any new geodetic or other surveying
being done.

> Thus, if you take a lat/lon and plot it on charts with two different
> datums, it's still the same lat/lon on both, but the distance and
> bearing from that lat/lon to a given landmark may change. Likewise,
> a landmark, or a point determined by range and bearing from it may
> plot at different lat/lons on the two charts.

There I think you are confusing yourself over relative motion. Yes, your
latitude and longitude remain numerically the same regardless of which
chart you plot them on. However, your plotted _position_ would not be
the same relative to the solid crust of the Earth. Your distance and
bearing from the nearest lighthouse would be different (and the
lighthouse would not have left its foundations).

So what is the answer to Jared's question?

Most of the data in the Almanac relates only to angles relative to the
planes of the Equator and the Prime Meridian, and so are equally
applicable to all regular ellipsoids, or else (as with semi-diameters)
they are values that are effectively independent of the shape of the
Earth. Dip should be affected by differences in the local curvature of
the Earth but our planet's deviations from sphericity are never enough
to worry about that. Maybe the horizontal parallax correction would be
affected by choice of datums. I am not sure.

When it comes to sight reduction, Ageton's tables are based on spherical
trigonometry and thus must assume that the Earth is a perfect sphere
(or, more precisely, that the observer is on the surface of a perfect
sphere centred at the centre of the Earth). Even HO 229, which could
have values separately calculated for each latitude (though not for each
longitude) and so could be adapted to some ellipsoids, is calculated
strictly by spherical trig. (see the computation formulas in Section E.
BACKGROUND of each volume).

Thus, while more than willing to be corrected by those with a deeper
understanding, I still suggest that positions calculated from celestial
observations are suited to an assumed spherical Earth and so do not
exactly match _any_ geodetic datum.

The error (relative to any local or global datum) will be tiny compared
to the effects of observational errors, of course. However,
sight-reduction computations with HO 229 have a maximum error of 0.05
minutes of arc. For comparison, in my area the difference between NAD27
and NAD83 is some  2.5 seconds of arc (0.04 minutes) and the difference
between either and a perfect sphere is likely to be larger. Thus, the
error due to differences in datum between celestial calculations and
charted objects is only just beyond the limits of concern to the navigator.

Another reason not to rely on celestial fixes when in coastal waters.

Trevor Kenchington

--
Trevor J. Kenchington PhD                         Gadus@iStar.ca
Gadus Associates,                                 Office(902) 889-9250
R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555

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