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    Re: Lunar trouble, need help
    From: George Huxtable
    Date: 2008 Jun 30, 22:12 +0100

    I'm delighted that Kent Nordstrom is still interested in resolving 
    differences between his own analysis of Jeremy's lunar, and my own. Taking 
    exactly the same observations as a starting point, and making the same 
    assumptions for limb-alignment (rightly or wrongly), we should agree very 
    closely in the answer. Yes, we seem to agree, roughly, but not as closely as 
    I would expect. Why not?
    
    I hope that the two of us may have something to learn by going into those 
    calculations in some detail, boring though that might be to others. Kent 
    seems keen to do that, and so am I. As we have approached the same problem 
    in very different ways, any discrepancies may prove to be instructive. Kent 
    has worked his calculations to arc-seconds, and I have calculated to 
    decimals of a degree, to 4 decimal places, so the precision of the 
    arithmetic should be sufficient in both cases. I do NOT claim that any 
    errors are Kent's; they might just as well be mine, or shared.
    
    Trouble is, it doesn't seem easy to point to a single factor and say that's 
    where the difference between us lies. It looks as if an accumulation of 
    errors has built up.
    
    So as a first step, let's look at just one of those details, correcting the 
    observed lunar distance for semidiameters of Moon and Sun..
    
    I think we agree on a mean time of the 5 lunar distances, to which time the 
    other observations are to be reduced, as 6.3831hrs or 6h 22m 59.2s.
    
    We have started by agreeing a figure for the observed mean lunar distance 
    between the limbs, as  86.1717�, or in Kent's language, 86�10' 18.2".
    
    The next step, correcting that to give the lunar distance between centres, 
    is one that has to be done as precisely as possible. We have agreed that, in 
    this unusual case, we need to add the Moon's semidiameter and subtract the 
    Sun's.
    
    I don't have a Nautical Almanac for this year, so to get the Moon 
    semidiameter, I went to my Skymap program which gave me, for the relevant 
    date and time, Moon horizontal parallax (HP) of 0.9435� (to note for future 
    use). But this needs to be multiplied by the ratio of Moon / Earth diameters 
    (= 0.2725) to give the Moon semidiameter as seen from Earth centre, to be 
    .2571� or 15,42'. But then this in turn needs to be multiplied by an 
    augmentation factor 1.0147 to end up with 0.2608�, or 15.65'. (Actually, 
    first time round, I made that to be 0.2606�, but I don't expect to argue 
    about that difference, and will continue to use the earlier value).
    
    Again from Skymap, I get the Sun distance on that day, from which the Sun 
    semidiameter comes out to be .2625�, or 15.75'
    
    So the net correction for the two semidianeters should be to add .2606 and 
    subtract ..2625, so reducing the angle by .0019�., or 6.8".
    
    Kent, on the other hand, in making those semidiameter corrections, goes from 
    86d 10m 18.2 s to 86d 09m 57.9 s, so reducing the angle by 20.3". So there's 
    a difference between us, crept in here, of 13.5". More than I would expect, 
    but it may, at least in part, be due to rounding errors in lookup tables 
    used by Kent. However, I can't find the values that Kent has used for these 
    semidiameters in any of his postings. If Kent will explain what are the 
    values he has used, and where they come from, that might help in 
    understanding this discrepancy, and we can go on to the next step. Let's 
    stop there, for now.
    
    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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