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Peter Fogg has (somewhat naughtily, considering Nav-l restrictions)
supplied in a recent posting a good illustration of my example by a
photo of his globe, defaced by a couple of circles. I wonder whether
it was received by all members, and the .irbs archive, or whether some
have set filters to exclude such messages.

Never mind, it's a fair example, and it would have been even more
dramatically obvious if a larger circle (or a smaller globe) had been
chosen, as I suggested.

Peter followed it up by adding-

"Yes, the courses as drawn are not due north (particularly the outer
ones), but isn't that due to lines of longitude converging towards the
pole? The displaced circle hasn't been distorted at all, since it is
an external fact that has been imposed on the sphere? What would
change that?"

Well that was the point. I was trying to illustrate the matter by
showing its CONVERSE. That initial circle was displaced as a circle
(in other words, not distorted at all), and that could only be done if
different points on its periphery were displaced by different amounts
and in different directions with respect to true North, compared with
the displacement of the centre. Peter appears to accept that as
correct, convinced by his globe.

And so, I was trying to show that conversely, if you insisted on the
shifts of each point on the original circle being identical, in course
and distance, then the end result would not be a circle.

In a later posting, he seems to have been convinced by that argument,
conceding-

| However, if each point of the radii is moved north by the same
distance then
| the new circles formed from those points will certainly be deformed.
And,
| when approaching the pole, since by definition north finishes there,
I can
| even envisage the J curve.

Well, if you shift a position circle so that every point on it moves
due North by the same distance, until its extreme Northerly point
actually touches the pole, you get, not a "J curve", but something
shaped rather like a teardrop, in which a part of its periphery has
been converged into a point at the pole. And if you try to shift it
further that that, you come across an argument of definition; how do
you shift those points further North once they have reached
furthest-North, at the pole? It points up the physical problems with
the concept of course, near to the singularity at the pole.

The curious shape, that Michael Dorl described as a "J curve", and I
would liken to a tadpole with its tail wrapped into a spiral above its
head (a bit like a scorpion's tail) is something that would come about
if you took a position circle that initially came very close to the
pole, and then shifted each point by the same distance Westward, not
Northward.

| But again, isn't all of this simply due to converging lines of
longitude?
| Is that what all this is about?

Well, in a way, it is, if you like to think of it that way. It's
related, really, to the way we define course, in terms of an azimuth
angle with respect to those meridians. It depends on the geometry of
the sphere, just as the convergence of the meridiams does. But don't
think of a circle being distorted just in terms of its mathematical
representation in latitude and longitude coordinates. That it is, of
course, but more simply, a real circle is distorted into a real
uncircle, after a displacement in the way we've defined it, no matter
how its coordinates may be measured..

And this isn't merely an academic matter. If a mariner makes an
altitude observation of a body, knowing nothing more about his
position than that, then steers through a known course and distance,
then observes a second body, he CAN'T simply shift the first position
circle and look for its two intersections with the second. Or if he
does, he will get wrong answers. In fact, using the traditional
position LINE, based on his estimated position, rather than a position
circle, overcomes these problems.

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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