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    Re: Lunar trouble, need help
    From: George Huxtable
    Date: 2008 Jul 2, 21:49 +0100

    I can see why the Kent's correction to the lunar distance for semidiameters 
    differs, by a fraction of an arc-minute, from my own.
    
    We agree about Sun semidiameter, but differ, a bit, about the Moon's.
    
    Kent used-
    
    Sun SD: 15m 45s
    Moon SD: 15m 25s
    
    whereas mine were (translated into the same units)-
    
    Sun SD. 15m45s
    Moon SD (as seen from Earth's centre) 15m 25s
    Moon SD (augmented, to allow for altitude of 61 and-a-bit degrees) 15m 39s.
    
    Kent has ignored the augmentation factor, which allows for the fact that an 
    observer is significantly closer to the Moon, when it's high in the sky, 
    than when its near the horizon. Indeed, he has taken "augmentation of Moon's 
    semidiameter" into account, in making an exact calculation of Moon's 
    altitude corrections (but when that has little or no influence on the final 
    lunar distance) but neglected to do so in correcting the lunar distance for 
    semidiameters (when it's crucial).
    
    Kent has simply taken the semidiameters from Henning Umland's website, but 
    as Umland doesn't know the altitude at which the Moon was being measured 
    (because it depends on where the measurement is being made from), that 
    correction has be applied next, by him.
    
    If Kent recalculates, taking augmentation into account, I suggest that he 
    will find perfect agreement between us, at least as far as the lunar 
    distance corrected for semidiameters.
    
    Perhaps we can draw a line under that one, and go on to the next discrepancy 
    between us.
    
    ===============================
    
    The next point of issue is the Moon parallax. Kent writes "It is unclear how 
    George measured his local parallax"
    
    It's simple enough. See navlist [5530]. We agree precisely on the figure for 
    Moon HP, quoted by Kent to be 56m 36.5s, and by me, from Skymap, to be 
    .9435�, which works out as 56.61', or 56m 36.6. Can't expect much better 
    than that!
    
    Now, if we're bothered to, we can make the correction for the reduction in 
    the Moon's HP on account of the spheroidal shape of the Earth, described by 
    Kent as "Earth flattening". At such a low latitude of 15�, this amounts to 
    only .01' (taken from a table in a modern Norie's), so we end up with a 
    corrected HP of 56.60'
    
    Then multiply that by cos alt, to get the actual parallax at that altitude. 
    True altitude of the Moon's centre, after allowing for dip and semidiameter, 
    I get to be 60.6523�, or 60� 39' 08' in Kent's notation. This gives me Moon 
    parallax of 27.74', or 27' 44". That has to be compared with the figure Kent 
    quotes of 26m 50.39s. There's a significant difference here, of getting on 
    for a whole minute, so my next question is : exactly how did Kent arrive at 
    a Moon parallax of 26m 50.39, starting from an HP of 56m 36.5s?
    
    Kent doesn't hasn't yet told us what actual values he puts in for his Sun 
    and Moon refraction, or his Sun parallax, and we need to know these for a 
    comparison (or at least, know how they are somehow to be included into the 
    lunar distance calculation.). Did Kent's final figure, for cleared lunar 
    distance, come from some tables, or from a log-trig calculation, or a 
    computer / calculator program, or what? Details would be of interest.
    
    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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