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In Navlist 4812 I posted the following message. I didn't intend to; it was
the result of a bit of finger-trouble, as my intention was to send it
off-list directly to Andres Ruiz. . However, no harm done.

But I didn't explain the topic that Andres was writing about, in his paper
in the latest issue of Journal of Navigation, so this message is to fill in
that omission. It was "Vector solution for the intersection of two circles
of equal amplitude", by Andes Ruiz Gonzalez.

And the bit I was referring to was his section 2.3, "Correction for the
motion of the observer", which stated-
"When the two sights are not taken at the same time, it is necessary to move
the first CoP [circle of position] to the time of the second one, or both to
a common instant.Many methods have been presented, but the correct way to
move a CoP is to advance or retire the GP [Geographical Position of the
first observed body] due to the motion of the observer [refs 6,7]

Using the technique described in reference [6], the correction is a function
of the estimated position of the observer (Be,Le), and his motion: course
and speed [C.S]. And since what we are looking for is the true position, an
iterative process is required in order to reach the solution for the running
fix. The algorithm is described in the Appendix."

The appendix gives a block diagram of the decision boxes rather than a
description.

I have little doubt that Andres understands well how to tackle this
question, and get the right answer, as he has explained it to us on Navlist.
What I am questioning is his use of the term CoP, or circle of position, to
describe the non-circle of the transferred locus of position. Presumably the
program calculates the intersection of the second circle with that
non-circle, or else with a different circle, which has its centre displaced
further, so that it's tangential to the locus in the region that matters.

This is what I wrote earlier-

=====================

Dear Andres,

Pleased to see your paper in Jounal of Navigation.

Coming from an earlier generation, I didn't really take in vector
mathematics as applied to such problems. So much of your paper went over my
head.

What I want to ask about are your words in 2.3 about correcting for the
motion of an observer.

An observer who has measured the altitude of a star to be, say 30 deg, knows
that his locus is on a circle radius 60 deg centred at the GP of the star,
(say, at dec = 0, GHA = 0, as in the example in paragraph 4 of my paper in
JoN, 59, No3, pages 521-524, which I think you have). And then the  observer
moves a known distance, say 60 miles North. His new locus is a closed
figure, somewhat egg-shaped, but NOT a circle any longer. Does your
algorithm in A2 find the crossings of that non-circle with another circle
centred on another star (say, at dec = 1deg N, GHA = 45 deg W, seen at 45
deg alt, as in that example).? What result does it give?

Yours, George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.


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