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    Re: Lunar trouble, need help
    From: George Huxtable
    Date: 2008 Jun 22, 23:21 +0100

    Thanks to Kent Nordstrom for spelling out the details of his lunar 
    calculations. I think that between us we can now reconcile many of our 
    differences.
    
    He wrote-
    "Firstly I hope
    we agree that it is the mean time for the LD observation that has to be used
    as reference for calculating altitudes of (in this case) the moon and the
    sun. The mean time for LD observation was 06-22-59 (type of time still not
    completely clear to me)."
    
    Yes, we agree. And the "type of time" is simply UT, which Jeremy took from 
    his chronometer, for which we are imagining that the lunar distance is 
    providing a cross-check. Because the lunar-distance almanac information that 
    Kent used was based on UT, then the time derived from it is also UT.
    
    I think I can see why Kent and I disagree by a few minutes about our 
    calculated Moon altitude. There's a transcription error crept in somehow. 
    Jeremy's first Moon altitude was stated by him to be timed at 06h 20m 44s, 
    but Kent has based his sums on a time of "06-20-13". If Kent recalculates, I 
    suspect he will come much closer to my own figure.
    
    And then he writes, about the Moon corrections-
    
    "Refr -29,5m (George -0,083=4m 58,8s)
    
    It is not clear to me how George�s refraction has been calculated."
    
    Kent's refraction at an altitude of nearly 61�, is far too high, and I 
    suggest it should perhaps have been that number of arc-seconds rather than 
    arc-minutes. And the figure I gave for refraction at that angle wasn't 
    the -.083� quoted by Kent, but -.0083�, which is about right for that 
    altitude.
    
    Putting those matters right, I wonder if Kent and I can now agree about all 
    the numbers that apply to the Moon.
    
    =========================
    
    About Sun corrections, Kent wrote-
    
    "For the sun it seems that we have reached the same altitude, anyway I don�t
    understand George�s data on refraction (seems to be the same as for the
    moon). My refraction for the sun is -1m 21,02s."
    
    Indeed, we agree completely about that, and I'm sorry to have made a 
    transcription error that made the Sun refraction appear so confusing. I had 
    actually done the calculation on another sheet of paper, in which my Sun 
    refraction worked out to be about the same as Kent's value, as can be seen 
    by subtracting the relevant numbers-
    
    "32.9564 alt above true horizon
     -.0083 refraction
    --------
    32.9314"
    
    the difference being 0.025�, or 1.5 arc-minutes, not .0083�. But then, 
    transcribing the value from that sheet into my email page, in error I copied 
    the Moon's refraction rather than the Sun's, which is why the email wrongly 
    read "-.0083 refraction" for the Sun. At an altitude of 32.9564�, my Almanac 
    table gives me a value of -1.5', which is what I actually used in the 
    correction, and this explains why we agree over the final result for the 
    Sun. I don't quite see where Kent gets his refraction of  -1m 21.02s from, 
    but that isn't a big disagreement, between us. Sorry about adding to the 
    confusion, though.
    
    =============================
    
    Having done all that, we can arrive at a corrected lunar distance, and from 
    that the UT at which the observation was made.
    
    Kent used a value of observed lunar distance that differed by more than 30' 
    from mine, because he allowed for the Sun semidiameter by adding it, rather 
    than subtracting, as the peculiar circumstances of Jeremy's observation 
    seemed to call for. As a result, he arrived at a GMT that was over an hour 
    late on the chronometer . He commented-
    
    "GMT 07-26-52,9 (George 06-24-53). This difference depends of course on how
    the LD�s were measured. However the method for measurement by �overlapping�
    edges does not convince me. It seems to be a construction afterwards."
    
    Yes, of course. It's a pragmatic attempt to allow, retrospectively, for how 
    the observation must have been made. What alternative explanation does Kent 
    have to offer? Of course, if Kent won't make that allowance, then an 
    enormous error of over an hour in GMT will arise, and a longitude error of 
    15� or so; the very discrepancy that prompted Jeremy's call for help.
    
    ==============================
    
    But next, the bit that really puzzles me about Kent's treatment is how he 
    manages to invoke sidereal time. That would come in only if he was getting 
    his astronomical positions from an Astronomer's almanac that gave 
    sky-positions in terms of right-ascension, rather than hour-angle.
    
    Once the clock has been set to a GMT that's derived from the lunar (and only 
    differs by a couple of minutes from the on-board chronometer) then it's a 
    simple matter to get the sky position at the relevant moment, from the 
    Almanac, for Sun and/or Moon, then work out and plot the relevant intercept 
    from an assumed position. Each body will then provide a good position line 
    for longitude, one being roughly due East, the other being roughly due West, 
    but very poor information about latitude. It's a standard procedure of 
    latitude-by-chronometer, and has little to to with the lunar distance 
    measurement itself. Because of the discrepancy, between the chronometer and 
    the lunar observation, of just less than 2 minutes of time, there will be a 
    difference of just less than 30' between the longitudes calculated by the 
    two methods.
    
    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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