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    Re: Real accuracy of the method of lunar distances
    From: George Huxtable
    Date: 2004 Jan 6, 21:41 +0000

    Jan Kalivoda started off-
    >Bill and George,
    >you are touching my sore tooth by your tongue.
    Jan, I think your quaint English constructions are wonderfully graphic!
    >I remember very well, what you are referring to. George Huxtable had
    >stated in his paper on lunars and in other postings to the list that the
    >effect of the daily parallax changing with altitude alters the rate of the
    >momentary change of a lunar distance considerably and that this effect is
    >the more sensible, the nearer the Moon approaches the local zenith in her
    >daily path through the sky. As George said, no mention about this effect
    >was made in the rich literature on lunars in the past, with one exception
    >of the short passage in an old German handbook.
    >I corresponded about this matter with George off list - I supposed that
    >such effect (which is undeniable, owing to George's observed values of
    >lunars) is present only in uncleared, "apparent" distances and removed by
    >clearing them from the influence of the daily parallax. In my opinion, it
    >would be very awkward if this effect were observed in true distances and
    >unnoticed in all the literature on lunars written since 1755.
    Jan, you are quite correct, as usual. The effects of parallax alter the
    apparent (that is, as-measured) slope of lunar distance against time. The
    clearing operation removes those effects. But not the effect of
    misalignment of the object from the Moon's path across the sky, which is
    accounted for in the lunar-distance tabulations in the almanac.
    One effect remains, however. Let's say, for argument, that the effect of
    changing parallax halves the apparent rate of change of lunar distance
    (which may not be far from the truth, in a bad example). Then measuring the
    apparent lunar distance to a certain accuracy implies that the true lunar
    distance is only being measured to half that accuracy, because only half of
    the change in apparent distance results from changes in the true distance,
    the other half coming from changing parallax.
    >I planned to compute a series of true lunars from ephemerides values for a
    >geographical position where the Moon crosses the sky near the zenith, to
    >unclear them to the apparent lunars and to compare both - would be the
    >retardating effect of the parallax changing with altitude observable only
    >in apparent distances (as I suppose) or in true ones, too? But I didn't
    >fulfill this my plan yet. Therefore, I didn't discuss this matter in the
    >list. Only now, when you mention it, Bill, I should respond to you.
    Arthur Pearson has made, and made-available, a series of lunar calculations
    to demonstrate this effect, at www.ld-DEADLINK-com
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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