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I have struggled hard to follow Jared's semantic argument, but much of it
eludes me.

He said-

>Parallax does not change as a result of your position, rather, parallax is
>FROM your >relative position, so that when your position changes, the
>parallax shifts relative to >the change in your position. "Parallax"
>itself is not a fungible object, nor does it >change. The amount of
>parallax that you have measured will change.

That distinction is just too fine for me.

Parallax is a quantity, measured in degrees. It's actually a vector
quantity, so it has a direction as well. Whether it is or isn't a "fungible
object" (Jared's words) I just couldn't say, and my dictionaries didn't
help either. It'a a legal term, apparently, which makes me wonder if Jared
may be a lawyer. Perhaps it's a word that's more familiar in the US than in
the UK.

In relation to the Moon, parallax is a displacement of the direction of the
Moon, with respect to its sky background, because the observer is not at
the Earth's centre. When the Moon is just on the horizon, its parallax is
always greatest, and about 1 deg, displacing the observed Moon down by that
amount below its true position. For other Moon altitudes, its parallax
takes other values, less than 1 deg., and may point in various directions,
always away from the zenith. When the Moon is right above the observer,
parallax is zero. Parallax will change if the observer's position changes,
either because he is moving his position with respect to the Earth, or if
the Earth is carrying him around, or both combined. When the parallax is
changing at a steady rate, it gives rise to a velocity correction, to apply
to the apparent motion of the Moon, to obtain its true motion.

Jared introduced the term "knots per hour", but as I didn't use that term
(or indeed anything like it), he was knocking down a straw man of his own
creation.

He went on-

>The "discovery" that there are in fact two parallax corrections rather
>than one needed to >clear a lunar would indicate that all prior lunars
>taken have been wrong, and that the >diagrams in Arthur's PDF file must
>also therefore be wrong, since they only mention one >parallax correction.

Jared has referred to a "second" parallax correction in a previous mailing.
I didn't understand then, nor do I now, what on earth he is talking about.
There's the measurement of apparent lunar distance, with a sextant. There
are some initial corrections to make (index error, semidiameter(s)). Then
there is a SINGLE "clearing" process which corrects for parallax and
refraction of the two bodies concerned, all in one go. The result is a true
lunar distance which has to be compared with predictions (which, in the
lunar-distance era, were tabulated in the almanac).

What may have been confusing (I wonder) is this-

In recent weeks we have been trying to address an "in-principle" question
to understand whether, in geometries where the changes of parallax
seriously slows the apparent motion of the Moon against the stars, the
accuracy of the lunar-distance method is degraded.. To understand that
matter, we have made certain simplifying assumptions, one of which was to
ignore the effects of refraction (as if the Earth had no atmosphere), to
isolate the effects of Moon-parallax..

Jared goes on to ask

>Or, does the one general adjustment made (to correct readings taken on the
>earth's >surface rather than from its core) also conveniently null out the
>problem of earth-lunar >parallax? (What you call "parallactic
>retardataion".)

Jared, you've got it! That's exactly what it does. This is the "clearing"
process, which corrects for both Earth-lunar parallax and for refraction in
the Earth's atmosphere, for both bodies (and also for the alignment of the
target-body, whether or not the Moon's path is heading straight toward it
or not). "Parallactic retardation" is a word that was coined to express the
fact that parallax changes in a way such that apparent motion of the Moon
with respect to the stars is (nearly always) slower than True Motion;
sometimes very significantly so.

Fast changes of Moon parallax don't of itself INTRODUCE any errors in the
above process, because that process succeeds in correcting the effects of
that parallax. Jared refers here to "nulling out", which is a fair
description.

What we have been arguing about recently is a rather special point: whether
the consequent slowing of the Moon's apparent motion reduces the
sensitivity of the lunar, as a measure of GMT, to errors in the sextant
measurement of apparent lunar distance. For the last year I have argued
that it did, and some others seem to have accepted that point of view.
Recently I have reversed that opinion, but several listmembers seem
reluctant to follow suit, which is up to them.

I can see that Jared is having difficulties in understanding the whole
picture, but I don't think it lies in the semantics of the words used
(though that may not help) but at a deeper level. I am very willing to try
explaining further, once I understand what it is that causes the matter to
elude his grasp. It shouldn't call for any deep mathematical knowledge to
understand the principles of lunar-distance observations, and I am sure
Jared has all the intelligence that's required. In addition, whatever it is
that's bugging him may be bugging other list members just as much: so
between us, if we can, let's tackle the problem.

George.


>George-
> I have come back to your question of the 9th, "Is that clearer, Jared?
>And if so, please suggest how you would express it."
>
>And my first step was to simply remove the word "Parallax" from the
>statement before that question, and replace it with a definition of
>parallax. If the definition is reasonably correct, the resulting new
>paragraph will seem logical and correct, so let's take a look at it. I've
>set the definition of parallax in [square braces].
>
>"[An apparent change in the direction of an object, caused by a change in
>observational position that provides a new line of sight] displaces the
>apparent position from the true position (of the Moon). [An apparent
>change in the direction of an object, caused by a change in observational
>position that provides a new line of sight] changes throughout the day, as
>a result of the observer riding round the Earth's surface."
>
>It sounds a lot like someone refering to speed in tems of "knots per
>hour". Simply badly put, if not to say wrong, when one says "I was moving
>at five knots per hour." Or per hour.
>
>Parallax does not change as a result of your position, rather, parallax is
>FROM your relative position, so that when your position changes, the
>parallax shifts relative to the change in your position. "Parallax" itself
>is not a fungible object, nor does it change. The amount of parallax that
>you have measured will change.
>
>That may seem trivial and I may not be making it clear enough, but when
>I'm trying to grasp an obtruse concept in debated spherical trigonometry,
>hearing someone refer to "knots per hour" does not help to make any point.
>Those of us who are not mathematicians by training are easily lost by
>things that professionals would gloss by, and that in turn is one reason
>why historically "navigation" has glazed so many eyes and lost so many
>students.
>
>I'm quite sure that I do not grasp the overall picture of the trigonometry
>involved in lunars despite having looked at the Arthur Pearson's fine
>diagrams in lunars1.pdf (linked from www.ld-DEADLINK-com). The
>"discovery" that there are in fact two parallax corrections rather than
>one needed to clear a lunar would indicate that all prior lunars taken
>have been wrong, and that the diagrams in Arthur's PDF file must also
>therefore be wrong, since they only mention one parallax correction. The
>alternative is to ask whether the second compensation is of any real
>value, and if so, whether anything else has been masking it. Or, does the
>one general adjustment made (to correct readings taken on the earth's
>surface rather than from its core) also conveniently null out the problem
>of earth-lunar parallax? (What you call "parallactic retardataion".)
>
>Have I missed something while my eyes were glazing over, or has there been
>any correction made for the low altitude refraction that must also be
>affecting the parallax correction for a low-altitude moon? And wouldn't
>that then need to be made based on air temperature and density, the same
>way that a conventional sun sight takes these factors into account?
>
>On the bright side, if this can be diagrammed and explained so simply that
>I understand it, then anyone will be able to grasp it. And to grasp why
>the past 300(?) years of lunars have simply been inaccurate. And Arthur's
>diagrams redrawn, and so on.

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