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    Re: Lunars using Bennett
    From: George Huxtable
    Date: 2008 Jul 4, 09:58 +0100

    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---.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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