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Geoffrey Kolbe wrote-

Assuming that the error in measuring a lunar
>distance is invariant with time, (or depends only on instrument error,
>rounding errors in the tables and so forth and does not depend
>significantly on the position of the moon or the other celestial object in
>the sky), the accuracy of the lunar distance method depends on the rate of
>change of lunar distance between the moon and any given celestial object.
>
>This being the case, is there an identifiable acceleration (+ or -) in the
>lunar distance as the moon rises in the East, passes the meridian and then
>sets in the West?
>
>If there is, then we can say that there are possibly certain times when it
>is best to take a lunar distance measurement (depending on just how big the
>acceleration is). If not, then it does not matter.

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

Several listmembers are clearly struggling to understand the concepts
involved in this question.

Geoff has made a valiant attempt to simplify the situation, which I applaud.

Unfortunately, it's a bit more complicated than that. You have to think of
both the true lunar distance and the apparent lunar distance.

Let's consider first the true lunar distance, in terms of the Moon's path
through the background of stars, seen as if from the Earth's centre.
Although we measure the lunar distance to one or more particular objects at
any time, we can think of the Moon' continuous progress around the stars,
moving 360 deg in a month, at a reasonably steady rate. Not that steady; it
speeds up near perigee and vice versa, but for our purposes for this
argument, we can think of it as steady, about 0.5 deg per hour. The true
lunar distance, from which we will derive the GMT, does NOT suffer from any
such daily acceleration as Geoff described.

If we could measure that true lunar distance, there would be no problem.
But we can't. Because we are riding round the Earth once per day, and
because the Moon is so close, our view of the Moon changes against the
background of stars. This is the effect which is called parallax. The stars
are unaffected by this parallax because they are so distant. The Sun is
affected, but only slightly. Our view of the Moon is affected very greatly
by parallax, by about 1 degree when it's on the horizon.

Because the Moon's parallax is so great, and varies through the day as the
Moon's altitude changes, it adds a sort-of rocking-about motion to the
position of the Moon with respect to the stars, as seen by a real observer
on the Earth's surface. So what we see is a combination of the
rather-steady motion of the Moon, but superimposed on it is that rocking
motion. These add to gives rise to an apparent motion of the Moon against
the stars, with its reasonably-steady 360 degrees per month, but
superimposed on that a daily speeding-up and slowing-down, which can alter
its apparent position by all of a degree. And this added daily motion
alters the speed of the Moon (the Apparent Moon, the Moon as we see it, not
the True Moon) very significantly. In the worst case, with the Moon passing
overhead, it can roughly-speaking halve the apparent speed of the Moon.
THIS is the daily (negative) acceleration that Geoff referred to

And the trouble is, of course, that when you measure a lunar distance with
a sextant, it's the Apparent position of the Moon you observe, not the True
one. During a day there are times when it's moving particularly slowly
against the stars, and other times when it isn't. And so the argument is
this: is it better (more accurate) to avoid those times when the Apparent
Moon is moving more slowly? Those times are when the Moon is highest in the
sky. If you can answer that question, you have settled the argument.

You can assume that the diffence between the true position and the apparent
position of the Moon can always be calculated with sufficient accuracy:
this happens as part of the "clearing" process of the observed lunar
distance.

Boiled down, it's the same question as you might ask of any observation of
a steadily-changing quantity which is perturbed by the addition of a
sinusoidal fluctuation which is precisely known.

George.

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01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
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