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    Re: March 22 Lunar Observations
    From: George Huxtable
    Date: 2002 Mar 25, 11:53 +0000

    Arthur Pearson said-
    
    >Gentlemen,
    
    (I do like the way he addresses us as "Gentlemen...")
    
    >George's comments on the error inherent in using the slope of change in
    >computed distance is an important insight. I am still a firm believer in
    >graphic averaging as it retains the element of judgment by the observer.
    >I think having an approximate slope is better than no slope,
    >particularly if we now know from George's discussion that the slope of
    >Ds will always be less than the slope of Dc. Perhaps George could
    >calculate a rough guide for the delta between the slope of Dc and the
    >slope of Ds for different apparent altitudes. Even if we had a delta
    >value for every 10* of altitude, it would refine our ability to judge
    >the best fit line.
    
    I agree with Arthur about the value of graphic averaging, particularly in
    the early stages, as he gains experience and confidence.
    
    But I am unable to help much with his request for a simple way of
    estimating the difference between the slopes showing the rate of change of
    lunar distance, for the true Moon and for the apparent Moon. It will
    certainly be a complex matter, and is probably beyond my mathematical
    skills. The best I can do is to restate a worst-case limit, when the Moon
    is high in the sky, in which case the rate of change of movement of the
    apparent Moon against the sky background could be reduced by about 15
    minutes per hour, below the speed of the true Moon. This worst-case limit
    will vary with Moon altitude as sine (alt), roughly speaking, but there are
    several factors that are not taken properly into account.
    
    Although it's of little consolation to navigators, these parallax effects
    on the apparent motion of the Moon become zero at the poles. There are
    times when parallax effects slightly increase the apparent speed of the
    Moon. In the Northern hemisphere, this can happen when the Moon can be seen
    to the North of the East-West line, but as this happens only near rising
    and setting, when it is low in the sky, it's not a very important matter.
    
    If any listmember with a mathematical bent would like to have a go at
    fulfilling Arthur's request, I would be very happy to cooperate. In the
    meantime, there's part 5 of my monograph on lunars to get out of the way
    first.
    
    A series of lunar distances, as has been taken by Arthur, should allow a
    straight line of estimated best-fit to be drawn by hand, without any
    reference to a theoretical slope, and in my view that ought to be
    sufficient. Indeed, with the revised calculation, Arthur's series,
    scattered though it is, has now provided excellent agreement with the known
    GMT, after presumed rogue observations were eliminated..
    
    I would be very interested to see measurements by listmembers of a
    prolonged set of repeated lunar distances, from which a good value of
    rate-of-change can be deduced.
    
    George Huxtable.
    
    
    
    ------------------------------
    
    george---.u-net.com
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.
    ------------------------------
    
    
    

       
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