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I'm happy that Dave Walden's has responded to my challenge, back in April
[4792], about using the Bennett tables to compute lunar distances, and
answered it in-
http://www.fer3.com/Mystic2008/MYSTIC2008rev3.pdf

And equally happy to acknowledge that his resulting scatter turns out to be
significantly less than my rather pessimistic predictions, which foresaw an
"overall range of scatter of 3 to 4 minutes or so". Does Dave agree that a
fair summary of his results would be that the vast majority of the
calculations fall within a range of 2 minutes of arc?

I can't see anything to object to about the methodology Dave Walden has
adopted, though he has provided little in the way of detail. He appears to
have done his best to fairly simulate, by computer, the steps a reader has
to take to work his way through a lunar distance using the Bennett tables.
But still, one or two questions arise, in the small-print, that I hope he
will clarify.

Interpolation.
In my 2003 edition of the tables, Bennett states clearly "do not attempt to
interpolate the tables", but then, he was not anticipating their use for
calculating lunars. In his paper on obtaining lunar distances, in the Spring
2003 issue of Navigator's Newsletter, he is a bit more ambiguous about
interpolation, saying about the tables in his book - "They are intended for
sight reduction without any interpolation (95% of errors of solution do not
exceed one minute of arc). However, if interpolayed, 95% of errors do not
exceed a few tenths of a minute of arc which may be acceptable." I expect
that Dave Walden has been careful to avoid any interpolation in his
automated procedure, but it would be useful to have that confirmed. If other
Bennett tables, computed with more decimal places, are to be tested in
future, presumably they will always require some interpolation.

Completing the process to get GMT.
Measuring a lunar distance is a means to an end; the end being to establish
Greenwich time, by comparing the measured-and-cleared distance with a
predicted lunar distance at one or two instants in time. In his 2003 paper,
Bennett shows how to use his tables to obtain two predicted values, at times
to bracket an observation, and deduce Greenwich time. Dave is content to
compare his cleared lunar with a single prediction, at some known time, to
discover the angle-error involved. The difficulty in doing that is that the
lunar distance changes at a very variable rate, and Dave could only convert
the angle-error to a time-error by presuming some mean value for the rate,
such as 30 arc-minutes per hour. But leaving aside that problem, whether one
prediction of lunar distance is to be calculated, or two, that calculation
has to be made, and from Bennett's tables, presumably. So I ask Dave to make
it clear whether the end-result scatter was in the overall difference
between cleared distance and predicted distance, both worked from the
tables, or if it was just the scatter in cleared distance compared with a
precise calculation from the astronomy.

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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