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    Re: Relative motion of moon and other celestial bodies.
    From: George Huxtable
    Date: 2003 Apr 13, 12:01 +0100

    There was a most-informative posting on 9 April by Herbert Prinz, on the
    various factors that influence the real and apparent motion of the Moon
    with respect to other celestial bodies.
    Below, I will quote from a paper which was kindly brought to my attention
    by list member Steven Wepster, on that same topic. It dates from 1875, and
    is part of a contribution by Carl Bremiker, to the journal "Zeitschrift fur
    Vermessungswesen" (Journal of surveying?) of 1875, pages 59 to 79.
    From 1850, Bremiker had been editor of the German Nautisches Jahrbuch
    ("Nautical Annual"), so he knew what he was talking about.
    I am ashamed to admit to having no German: however, my niece Lucy Mellersh
    is fluent in German, but not at all technical. Between us we have put this
    informal translation together.
    What is especially interesting to me is that Bremiker refers to the serious
    effect of parallax on the apparent motion of the Moon with respect to other
    bodies, the effect that I have dubbed "parallactic retardation". Bremiker
    says that it hadn't, to his knowledge, appeared before in the literature,
    and I'm not aware of any English-language mention before or since.
    I like Bremiker's "what-if" speculation about the problems that would face
    a lunar navigator on the surface of Jupiter, which seems to me to be
    advanced thinking for 1875.
    Here goes-
    Concerning the precision with which the longitude can be calculated using
    lunar distance, note that at sea those observations made with the best
    instruments have a mean error of 10 seconds. In addition to this are the
    errors in the tabulated lunar position of about 4 to 6", which are
    transferred onto the predicted distance so that when both errors combine,
    the total error  is 1/4 of a minute of arc. Because the moon generally
    moves half a degree in an hour, an error of half a minute of time or 7.5
    minutes of arc in the longitude would follow, or in low latitudes 7.5
    On land, where observations can be more carefully made and the calculations
    afterwards can be made with improved moon positions, the error is less.
    The instrument error can be substantially reduced when several distances on
    the East and West sides of the moon can be measured one after another.
    On the other hand the error increases at the same rate as the change in
    distance per hour gets smaller, as with the stars Aquila and Fomalhaut
    which are far from the lunar path, and with the Sun and also with Venus
    which can sometimes have considerable motion in the same direction as the
    Moon. It can happen that the relative motion of the moon is only 20 minutes
    in an hour. When in good conditions the errors in the longitude are 30
    times the error in the distance, this can increase here to 45 times.
    Other matters must be considered which depend on the the motion at the
    observation point.  These can considerably increase the errors in finding
    the longitude. As far as I know, these errors haven't been mentioned in the
    relevant literature.  A point on the equator on the Earth moves 900
    nautical miles in an hour, and the moon in its path has a mean speed of
    2000 nautical miles per hour. Therefore, from a point on the equator the
    Moon, when at the meridian, loses 9/20 of the motion with respect to the
    stars that it would have if viewed from the centre of the Earth. In these
    conditions, the error in the longitude can be 60 or 90 times the error in
    the lunar distance. These errors are slightly less in higher latitudes, but
    are always worst near to the culmination of the Moon.
    Luckily our Moon doesn't go backwards, otherwise all distance measurements
    would stop near to the meridians. For an observer on Jupiter, despite the 4
    moons, the situation is comparatively worse. A point on the equator there
    has an hourly movement of 24,440 nautical miles, compared to which the
    movement in the lunar path in the 1st to 4th satellite are 34,536, 27,372,
    21,672, and 16,344 nautical miles per hour. The first two could still be
    used for measuring distance, the two more distant couldn't be used near the
    meridians because they go backwards.
    The translation above is only the final part of what may well be a very
    interesting paper: the rest remains untranslated so I have no way of
    George Huxtable.
    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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