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George-
 
 You say (quite rightfully) that these motions cause parallax error. That is, 
we're dealing with the error caused by  parallax in an observation. If none 
of the bodies were in motion, there would be no parallax, and no need to 
account for the errors caused by parallax.
 I don't see why it should confuse you that I'm considering these parallax 
effects to be "error", if there was no problem caused in the final result (of 
time, or position, however you chose to look at the final result of clearing 
a lunar) then the entire discussion of parallax would be meaningless.


 No, I am suggesting that if all the celestial mechanics are precisely allowed 
for, and the real changes in celestial geometry are compared to the observed 
changes caused by parallax, that it would be easier to determine whether 
there is any real world "parallacitc retardation" or whether you are trying 
to debate the thickness of a hair, while using a meter stick as the standard 
for "thickness".
 Theories are all fine, but quantifiable results are of more meaning when we 
are discussing observational errors (i.e., parallax) in lunar clearings. So 
when you say:
 
 OK, that's measurements. If an expert clearing a lunar can expect his result 
to match GMT within plus-or-minus one minute of time, then how much closer 
would his measurement be if parallactic retardation was or was not accounted 
for? Will his result still be accurate within 59 seconds? 45 seconds? How 
much better than 60 seconds do you expect the final result to be--if it will 
be better (meaning, more accurate) at all?


 Several of the comments in the thread (some of which have been off list) have 
referred to the change in the moon's apparent speed, when comparing the moon 
directly overhead to the moon at the horizon. I was unclear if this change in 
speed had any effect on the larger question, i.e. if anyone was arguing that 
the change in relative motion during a longer process was somehow a part of 
the problem. Apparently not, but then again you say:
  So, what are you referring to when 
you say the apparent speed of the moon is slowed> And what accuracy does this 
affect? Frankly, I can't understand why you say this affects ACCURACY but not 
ERROR, to my way of thinking ERRORS cause lack of ACCURACY.

 Well, actually you can. There are folks who use 
lasers to bounce off the retroreflectors kindly left by the US Apollo 
program, and ham radio operators who use microwave transmissions and then 
measure signal echo returns, so yes, the individual observer can measure 
actual lunar distance pretty accurately if they own the instruments. Which 
are no harder to acquire than a sextant is. And in any case, since the 
orbital mechanics of the moon are well known (at least, in some circles, 
pardon the pun) it should also be fairly simple to obtain a set of routines 
allowing the actual compensation of real-vs-apparent moon which would correct 
out any parallax factors. Again, referring to Alan Pearson's illustrations 
from his PDF file, he seems to state that the routine clearing process does 
indeed compensate for this, by taking in to account the moon's apparent 
position versus it's real one, and the observation "adjusted" as if to the 
center of the earth.

 Can you tie this back into the 
observer's expectation to find time within one minute of GMT? How much is 
that 'one minute' going to change if the error in true distance is 0.5 arc 
minutes?

Which comes back to  My third question was something you partly answered: 
The skilled observer may determine local time within one minute of GMT. OK, 
so if there is an error of 0.5 arc-minutes caused by parallax or other 
observational errors, how much does that affect that plus-or-minus-one-minute 
result?

Am I right to understand this as:
360 degrees times 60 minutes (per degree) equals 21,600 arc minutes in one rotation of the earth. Equals:
        21,600 arc minutes in 24 hours. Equals:
                900 arc minutes per hour. Equals:
                        15 arc minutes per minute of earth's rotation, i.e. GMT. Equals:
                                1 arc minute equals 4 seconds of GMT. Equals:
                                        .05 arc-minutes of time would be a two second difference.

So we are talking about an effect that might account for two seconds of error 
in the final cleared lunar, when an expert observer would be happy to be 
accurate within +-60 seconds?? And this last two seconds of error would be 
literally beyond the measurement in the final process?

   

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