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    Re: Exorcizing the Evil Effects of Parallactic Retardation
    From: George Huxtable
    Date: 2004 Mar 19, 07:39 +0000

    I have to thank Fred Hebard for his continuing interest in this question of
    the accuracy of lunar distances.
    More than a year ago, in :About lunars, part 4a", I presented the view that
    the accuracy of lunar distance measurements was seriously impaired when the
    apparent speed of the Moon against the star-background was reduced by the
    effects of parallactic retardation, particularly when the Moon was high in
    the sky..
    A perceptive contribution from Jan Kalivoda on 30 Dec 03, under the
    threadname "Real accuracy of the method of lunar distance", and a
    subsequent lively correspondence, caused me to revise that view.  This
    culminated in my posting of 24 Jan 04 labelled "About lunars, part 4b".
    This explained that even when rapidly-changing parallax slowed the Moon's
    apparent speed, this did not detract from the accuracy of a lunar, and
    withdrew my previous view of the matter.  Several listmembers had resisted
    that change, in a thread "Parallactic retardation - don't give up so
    Fred Hebard expressed some initial scepticism about that altered view. Now
    his promised response has appeared, and it's pleasing to note that he now
    supports that new approach.
    Unfortunately, I am unable to comment in detail, because my old Mac was
    unable to translate his attached table. My old version of Adobe Acrobat
    (which can't be upgraded) was quite unable to cope with his more modern
    version of a pdf. file. If there's any way round that problem (short of
    replacing my computer system, which I will have to do some day) such as
    Fred sticking a copy of his table in the letter-post, or by fax, or sending
    a tiff image, I would be obliged.
    Thanks, Fred.
    Fred Hebart wrote-
    >In January, George Huxtable surprised us all by saying that he no
    >longer felt that parallactic retardation affected the accuracy of
    >observation of time by lunar distance.  I've finally had time to look
    >at this numerically, and, by golly, George is right, which should come
    >as little surprise to most of us.
    >The table below gives some simulated observed distances between the
    >Moon and Jupiter on 1/14/04 at 1*31.3'S latitude and 0*0.0'W longitude.
    >  The altitudes of the Moon and Jupiter were calculated from the time in
    >the first column.  The horizontal parallax of the Moon was taken from
    >the Nautical almanac and used to calculate the real parallax for the
    >Moon at that altitude and latitude, using Young's Method of Clearing
    >that George Huxtable presented to the list in 2002-2003.
    >Observations near the equator give the greatest "parallactic
    >retardation," combined with the time when the moon is near zenith,
    >which is 5:00 hours in the table below. The retardation can be seen by
    >comparing the difference between the "observed sextant reading" of
    >lines 1 and 4, 17'55" of arc, with that of lines 5 & 8, 29'52" of arc.
    >The Moon is only moving through 17'55" of apparent arc from 5:00 hours
    >to 6:00 hours (lines 1 & 4), when it is near zenith, compared to 29'52"
    >of arc from 0:00 hours to 1:00 hours (lines 5 & 8), when it is near the
    >The thinking has been that since the moon is moving through such a
    >smaller swath of arc (17'55"), then any errors in measurement of
    >distance will be magnified.  If the error is 30" of arc, one will be
    >measuring to only 1 part in 35 (30"/17'55"), rather than 1 part in 60
    >(30"/29'52").  This is the supposed "evil effect of parallactic
    >However, George has been trying to point out to us that there are two
    >components to measuring a lunar distance, one the distance itself, and
    >two the altitude of the bodies.  The parallax is fixed by observation
    >of the moon's altitude, not the distance, and it is the large shift in
    >the _COMPUTED_ parallax between 5:00:01 and 5:59:59 that gives rise to
    >the retardation.  Between 5:00:01 and 5:59:59, the computed parallax of
    >the Moon increases from 3.2' to 11.6' of arc, almost a 4-fold
    >difference.  In contrast, between 0:00:01 and 0:59:59, the parallax
    >decreases from 53.3 to 51.2, only a 10% difference.
    >But if one holds the parallax constant, in this table by holding the
    >assumed time constant, such as at 5:00:00 between lines 1 and 2, then
    >the observed sextant reading has to increase by 33'10" of arc, from
    >37*0'57" to 37*34'7", to move the time by lunar up by one hour.   You
    >can also see that the observed sextant reading changes 33'20" between
    >lines 3 and 4 of the table to move the lunar time back one hour from
    >5:59:59 to 5:00:01.  The error has dropped back to 1 part in 60.  AND
    >So this is what George has been trying to tell us.  Perhaps he can
    >explain these numbers more clearly than I have; but it was the numbers
    >themselves that convinced me.
    >Fred Hebard
    >Attachment converted: 320Mb HD:Table.pdf 1 (PDF /prvw) (0001061B)
    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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