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Listmembers who are bored by details of the lunar distance method might
just as well press the delete button now. This is for the others.

To my suggestion,
"I hope we are not talking at cross-purposes here."

Frank Reed replied-
>Well, maybe. Let me ask you a question (to see if we are): if the Moon is
>passing nearly but not exactly overhead --let's say 80 degrees high-- and it's
>right on the meridian when you take the lunar, are you saying that you believe
>there's a significant reduction in the potential acuracy of the lunar because
>of the rate of change of the parallax correction?

I think that two different strands have got entangled in this
correspondence. Let me try to separate them-

1. Parallactic retardation.

This is the effect of changing Moon parallax on the apparent lunar
distance, which under nearly all circumstances acts to slow the apparent
motion of the Moon against the star background. It has a very significant
effect on the apparent speed of the Moon. This slowing effect is greatest
when the Moon passes through the meridian, and particularly so at high Moon
altitudes, in which circumstances it can reduce the Moon's apparent speed
against the stars to about half of its nominal value of roughly 30
arc-minutes per hour. The reality of this effect seems to be agreed in
general among list-members. However, Frank Reed has recently expressed
doubt about whether this diminution of Moon-speed due to changing parallax
is indeed at a maximum (or even significant) when the Moon passes the
meridian. Perhaps this is due to a "cross-purposes" misunderstanding which
may be easy to resolve: it certainly needs resolving.

2. Does the effect of parallactic retardation reduce the accuracy of lunar
distances?

Until recently, I have taken the view that if the apparent speed of the
Moon against the stars was halved (by rapidly-changing parallax), then the
accuracy of determining time by lunar distance would also be halved,
because it's based on measuring changes in the position of the Moon in its
path across the sky. I put this forward a year ago, in "About Lunars, Part
4a", and in response to some perceptive questioning by Jan Kalivoda,
restated it on Jan 6 2004. Later that day I had second thoughts about the
matter, and said so in a further mailing. On Jan 8 I posted a message which
completely retracted my original view. I now think that the
rapidly-changing Moon parallax has little or no effect on the accuracy of a
lunar distance measurement, even though it may have a big effect on the
speed of the apparent Moon.

The position has been complicated somewhat by recent off-list messages to
me from Fred Hebard and from Bruce Stark, both of whom I greatly respect,
suggesting that I was right all along. Well, that indicates to me that
there's something worth arguing about, though it puts me in rather a odd
position in arguing against them!

Let me explain an argument that has convinced me to change my original
view. When considering a question of principle, it's often instructive to
apply it to extreme cases, and the extreme case was to consider what would
happen if the Moon, at zero declination, was viewed from the Equator, and
the Earth was allowed to spin about twice as fast as it does now. In that
case the changing parallax would appear to bring the Moon to a stop,
against the stars, when it approached the zenith. So the apparent lunar
distance to a star wouldn't be changing. Originally I argued to myself, "if
the apparent lunar distance isn't changing with time, what would be the
point of measuring it, to determine the time?", and on that basis presumed
that there was no correlation between that measurement and GMT. And on that
basis, argued that the accuracy in determining GMT from a lunar was
proportional to the speed of the apparent Moon across the sky.

But there really IS a point in measuring the apparent lunar distance in
those circumstances, even if it's unchanging. To that measurement, you have
to apply a correction to get the true lunar distance, and that correction,
(due to changing parallax) is changing fast. It's important to know that
correction (clearing the distance) precisely. It's (approximately) an
amount to be added to the observed distance, not a multiplier, though the
maths look more complicated than that. The result is a true (corrected)
lunar motion that always ends up near 30 arc-minutes per hour, and an
overall accuracy that relates to that motion, which isn't affected by what
the apparent lunar motion happens to be.

It may be obvious that I have been struggling with these concepts and am by
no means certain that I have section 2 right, though I have little doubt
about section 1, the effect of parallax changes on the apparent speed of
the Moon.

Nor am I sure that the arguments above are convincing, or easy for others
to follow. Perhaps this is the place to stop, to see what others have to
say.

George.

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