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Andres, you wrote:

"few remarks:
Velocity & speed: as a vector physical quantity. The scalar absolute value
of the velocity vector is speed, and direction is required to define it."

In Spanish, too, huh? Some years ago, an extremely intelligent Dutch
physicist pointed out to me that this particular but of physics and math
culture is language-dependent. In many countries, there is no such
differentiation made. The same individual pointed out rather wisely that
this separate name for the magnitude of the vector is really quite odd. Why
do we need to refer to the magnitude of the velocity vector as 'speed'?
There's no similar dual-naming for other vectors in physics and kinematics.
For example, if I say "acceleration", you can tell by context whether I'm
talking about a vector or the magnitude of the vector. In any case, in
practice, if I say something like "the velocity of the Earth around the Sun
is 30km/sec", there's no chance of confusion, no reason to worry over the
distinction between speed and velocity. All of this convinced me over ten
years ago, that the physics culture's distinction between velocity and speed
is pointless. I don't worry if someone uses the "wrong one".


"The relation between vessel's motion, and Sun motion is not arithmetic, is
a composition of the two motions, a vector composition. The arithmetic you
explained is a first approach."

The only component that matters is the north-south component of the net
vector. As I said in an earlier post, you add the north-south component of
the vessel's motion to the rate of change of declination (which is itself
the north-south component of the velocity of the Sun's GP). This works, and
it's sufficient for the problem at hand, because we assume (and indeed it's
important to the working of this method) that the Sun's azimuth does not
differ much from the meridian for all of the sights in the series. I
recommend a spread from beginning to end of not less than 10 degrees (e.g.
azimuth from 175 to 185) and not more than 20 degrees (azimuth from 170 to
190).

"Running fixes (or DR): to move one position to another, an inertial
reference frame is needed, the ground is adopted usually."

It doesn't seem that an "inertial" frame is needed. What's required is some
standard frame with known properties, and the coordinate-system tied to the
Earth is clearly the standard.


"So the speed for all the calculations is the SOG, (Speed Over Ground) that
is the vessel speed corrected by the effects of Current, Set & drift. Wind,
Leeway, only change the direction of the velocity vector of the vessel. In
vector notation V over ground = V vessel + V current"

Yes. In all running fixes, an important source of error is the uncertainty
in the velocity over the ground --arising mostly from uncertainties in
currents. So if you get your position during daylight by crossing two
sunlines four hours apart, or if you get it by using this wonderfully simple
method of watching the Sun's arc around noon, you always have to remember
that currents can throw off the fix. Fortunately, on the open ocean,
currents larger than one knot are not common, and the areas where they do
occur are well-known.

 -FER



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