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One important point here is that you are not measuring the _rate_ of
the moon's motion around the heavens, which is varying, but the
_absolute distance_ between the moon and another body.  You essentially
calculate the time at which the moon would be that distance from the
object.  One assumes the calculations are correct.  The measurement
error is not affected strongly during the clearing process, so that an
error of 20" of arc measured essentially leads to an error of 20" in
the cleared distance.  This would put one off by about 40 seconds of
time.

I thought I had explained this rather well in a post on January 11, but
find it has been roundly ignored, so I guess I didn't do a very good
job there.

Fred

On Jan 14, 2004, at 6:52 AM, George Huxtable wrote:

> 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.
>
> ================================================================
> 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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