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Thanks to Dave Walden for clear replies to my questions about his simulation
of Bennett tables for calculating lunars.

============================
This is a bit of a side-issue, but I had written-
"...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."

and he replied-

"Not quite true.  Since real ephemeris data was used, actual rates are
available."

I phrased that badly. What I meant was that the user of the Bennett tables
couldn't know that rate of movement, unless he predicted lunar distance
twice, as Bennett proposed. Dave himself was in a much stronger position, of
course.

===============================
He explains-
"The cleared distances calculated using Bennett were compared to ephemeris
values.  Simulating almanac precision or simulating using tables to
calculate lunar distances from RA's and Dec's would have "muddied the
waters".  All things are possible.  The code is there for the interested
student."

That's the only shortcoming that I can put my finger on, then, in D Walden's
analysis. All right if you think of determining the distance itself as the
end-product, but lunar-distance is a complete procedure, to end up with a
measure of Greenwich time, whatever Frank Reed may think about that. See our
recent discussion, navlist [5646], and [5647]. So the cleared measurement
must be compared with a predicted value; otherwise only half the job has
been done. In his 2003 paper, Bennett himself recognised that, and showed
how the navigator could predict those distances from the Almanac, using his
tables. It's a necessary part of the lunar procedure, and any scatter in
that prediction has to be folded-in with the scatter in the cleared
distance. It can only increase the overall scatter, but not, I think, by
very much. Still, it needs to be done. And I don't see how including it
would have "muddied the waters".

I don't see any difficulty in including those errors in the prediction. As
the Bennett tables only work to the nearest arc-minute, and the Nautical
Almanac works to the nearest tenth, quantisation errors from the Almanac
itself can surely be ignored, and precise ephemeris values could be used
instead as inputs to the Bennett tables.

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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