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George wrote � Kent's refraction at an altitude of nearly 61�, is far too
high, and I
suggest it should perhaps have been that number of arc-seconds rather than
arc-minutes. And the figure I gave for refraction at that angle wasn't
the -.083� quoted by Kent, but -.0083�, which is about right for that
altitude.�



Refraction for the moon shall of course be -29,5 arc sec�s due to the
altitude of approx. 60 degrees. George comment is correct.



My refraction for the sun is correctly stated.



My refraction values are calculated as Tan app. Altitude x 60,53� for
standard atmospheric conditions (760 mm Hg and +10 degr. C). Then a
correction for actual T and B is made for altitudes from 20 degrees and
upwards . For lower altitudes another way of correction for B and T is done.
You could always argue about the relevance of this approach, we all know
that refraction is difficult to model, in particular on low levels. Anyway,
with the approach taken my results coincide with refraction values taken
from tables quite well (Tables from 1845, based on Janet Taylor, Henry Raper
I assume).



George wrote �I think I can see why Kent and I disagree by a few minutes
about our
calculated Moon altitude. There's a transcription error crept in somehow.
Jeremy's first Moon altitude was stated by him to be timed at 06h 20m 44s,
but Kent has based his sums on a time of "06-20-13". If Kent recalculates, I
suspect he will come much closer to my own figure.�



I agree with George that I should have used 06-20-13 instead of 06-20-44 for
referring the moon�s altitude to the mean time of LD�s. This change has a
very small effect on my LD.



George wrote �But next, the bit that really puzzles me about Kent's
treatment is how he
manages to invoke sidereal time. That would come in only if he was getting
his astronomical positions from an Astronomer's almanac that gave
sky-positions in terms of right-ascension, rather than hour-angle�.



My approach for calculating the MT is as I understand the very same as used
in the old days.

This is of course for finding the difference between the GMT and the MT,
i.e. the longitude. It is a separate calculation. So let me outline what I
do:

  1.. Find the LHA at the predicted GMT (we know (roughly) the latitide,
from the generation of true distances at say time 3, time 6 etc. we can
predict the declination at the GMT. True altitude is from the altitude
reduction. Aries GHA to the GMT can be predicted as well).
  2.. Find the Aries GHA for upper meridian passage in Greenwich, (normally
one day before).
  3.. Convert this GHA to time.
  4.. Correct for assumed longitude and then you get the time for Aries UMP
on your location.
  5.. Find the difference between Aries GHA and the body�s GHA at GMT. This
is the RA.
  6.. Find the sum of the LHA and the RA, which is the sideral time.
  7.. Subtract the value for Aries UMP at the location. Now you have the
difference in sideral time.
  8.. Convert this difference in sideral time and you get the MT at
observation.
And now you can easliy find the difference between the GMT and the MT. I
hope this explaination clarifies. I should also add that one must be very
observant when doing this calculation, it is easy to do wrong.



Kent N

----- Original Message ----- 
From: "George Huxtable" 
To: 
Sent: Monday, June 23, 2008 12:21 AM
Subject: [NavList 5569] Re: Lunar trouble, need help



Thanks to Kent Nordstrom for spelling out the details of his lunar
calculations. I think that between us we can now reconcile many of our
differences.

He wrote-
"Firstly I hope
we agree that it is the mean time for the LD observation that has to be used
as reference for calculating altitudes of (in this case) the moon and the
sun. The mean time for LD observation was 06-22-59 (type of time still not
completely clear to me)."

Yes, we agree. And the "type of time" is simply UT, which Jeremy took from
his chronometer, for which we are imagining that the lunar distance is
providing a cross-check. Because the lunar-distance almanac information that
Kent used was based on UT, then the time derived from it is also UT.

I think I can see why Kent and I disagree by a few minutes about our
calculated Moon altitude. There's a transcription error crept in somehow.
Jeremy's first Moon altitude was stated by him to be timed at 06h 20m 44s,
but Kent has based his sums on a time of "06-20-13". If Kent recalculates, I
suspect he will come much closer to my own figure.

And then he writes, about the Moon corrections-

"Refr -29,5m (George -0,083=4m 58,8s)

It is not clear to me how George�s refraction has been calculated."

Kent's refraction at an altitude of nearly 61�, is far too high, and I
suggest it should perhaps have been that number of arc-seconds rather than
arc-minutes. And the figure I gave for refraction at that angle wasn't
the -.083� quoted by Kent, but -.0083�, which is about right for that
altitude.

Putting those matters right, I wonder if Kent and I can now agree about all
the numbers that apply to the Moon.

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

About Sun corrections, Kent wrote-

"For the sun it seems that we have reached the same altitude, anyway I don�t
understand George�s data on refraction (seems to be the same as for the
moon). My refraction for the sun is -1m 21,02s."

Indeed, we agree completely about that, and I'm sorry to have made a
transcription error that made the Sun refraction appear so confusing. I had
actually done the calculation on another sheet of paper, in which my Sun
refraction worked out to be about the same as Kent's value, as can be seen
by subtracting the relevant numbers-

"32.9564 alt above true horizon
 -.0083 refraction
--------
32.9314"

the difference being 0.025�, or 1.5 arc-minutes, not .0083�. But then,
transcribing the value from that sheet into my email page, in error I copied
the Moon's refraction rather than the Sun's, which is why the email wrongly
read "-.0083 refraction" for the Sun. At an altitude of 32.9564�, my Almanac
table gives me a value of -1.5', which is what I actually used in the
correction, and this explains why we agree over the final result for the
Sun. I don't quite see where Kent gets his refraction of  -1m 21.02s from,
but that isn't a big disagreement, between us. Sorry about adding to the
confusion, though.

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

Having done all that, we can arrive at a corrected lunar distance, and from
that the UT at which the observation was made.

Kent used a value of observed lunar distance that differed by more than 30'
from mine, because he allowed for the Sun semidiameter by adding it, rather
than subtracting, as the peculiar circumstances of Jeremy's observation
seemed to call for. As a result, he arrived at a GMT that was over an hour
late on the chronometer . He commented-

"GMT 07-26-52,9 (George 06-24-53). This difference depends of course on how
the LD�s were measured. However the method for measurement by �overlapping�
edges does not convince me. It seems to be a construction afterwards."

Yes, of course. It's a pragmatic attempt to allow, retrospectively, for how
the observation must have been made. What alternative explanation does Kent
have to offer? Of course, if Kent won't make that allowance, then an
enormous error of over an hour in GMT will arise, and a longitude error of
15� or so; the very discrepancy that prompted Jeremy's call for help.

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

But next, the bit that really puzzles me about Kent's treatment is how he
manages to invoke sidereal time. That would come in only if he was getting
his astronomical positions from an Astronomer's almanac that gave
sky-positions in terms of right-ascension, rather than hour-angle.

Once the clock has been set to a GMT that's derived from the lunar (and only
differs by a couple of minutes from the on-board chronometer) then it's a
simple matter to get the sky position at the relevant moment, from the
Almanac, for Sun and/or Moon, then work out and plot the relevant intercept
from an assumed position. Each body will then provide a good position line
for longitude, one being roughly due East, the other being roughly due West,
but very poor information about latitude. It's a standard procedure of
latitude-by-chronometer, and has little to to with the lunar distance
measurement itself. Because of the discrepancy, between the chronometer and
the lunar observation, of just less than 2 minutes of time, there will be a
difference of just less than 30' between the longitudes calculated by the
two methods.

George.

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






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