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    Re: Lunar trouble, need help
    From: Kent Nordstr�m
    Date: 2008 Jul 2, 17:11 +0200

    George Huxtable wrote [5615]: I'm delighted that Kent Nordstrom is still
    interested in resolving differencies between his own analysis of Jeremy's 
    lunar, and my
    own.....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.
    
    My values were taken from Umland "by inspection" in such a way that I knew 
    (in this case) that the correct GMT was around 06-30-00. From my model I 
    predicted true lunar distances for 06-00-00, 09-00-00 and 12-00-00. When 
    collecting GHA and declination data for 06, 09 etc I just read out "by 
    inspection" what the SD's and moon's HP should be :
    Sun SD: 15m 45s
    Moon SD: 15m 25s
    Moon HP: 56m 36s
    
    For my GMT 06-25-51 the values according to Umland shall be:
    Sun SD: 15m 45,1s (USNO 15m 48s)
    Moon SD: 15m 25,5s (USNO 15m 36s)
    Moon HP: 56m 36,5s.
    
    It is unclear to me how George reached his local moon's parallax.
    
    My augmentation in the moon's altitude reduction was -12,96s. Minus because
    the UL was observed. This figure also includes a small correction for 
    refraction of +0,34s.
    
    My moon parallax incl. corrections for earth flattening was 26m 50,39s. It 
    is not clear to me how George corrects for earth flatteing.
    
    The angles between the distance line and the verticals were not calculated 
    by me and therefore I did not put in any corrections for:
    - the decrease of SD's in my distance reduction. The altitude of the moon is 
    high and does not require any correction. The sun can be corrected with -1s.
    - the moon's parallax in azimuth. If I do a calculation of these angles this 
    correction is -0,74s (moon in E and sun to the right
    seen by the observer). These angles are small (8 and 13 degr respectively). 
    Anyway, the exclusion of these two small corrections will have minor impact 
    on the final LD.
    
    Kent N
    
    
    ----- Original Message ----- 
    From: "George Huxtable" 
    To: 
    Sent: Monday, June 30, 2008 11:12 PM
    Subject: [NavList 5615] Re: Lunar trouble, need help
    
    
    
    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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