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    Re: lunars with and without altitudes
    From: George Huxtable
    Date: 2006 Nov 28, 21:22 -0000

    Frank Reed wrote in
    [NavList 1757] Re: lunars with and without altitudes
    
    After a bit of personal denigration-
    
    | Well, first of all, you definitely have not invested enough effort
    to
    | understand it yet (evidenced by your comments with respect to the
    Moon's  altitude
    | --see below).
    
    he went on to say-
    
    | I have said AGAIN AND AGAIN that the altitude of the  Moon
    | reduces the accuracy ONLY if the other object is more or less
    directly above
    | or below the Moon (same azimuth, in other words). If the  Moon and
    Sun
    | (that's the only available object in the summer Arctic) are at
    about the same
    | altitude, which they would be for that week or so out of each  month
    when the Moon
    | is visible in the high Arctic, then the accuracy of this  procedure
    is NEARLY
    | THE SAME as when the Moon is straight overhead in the  tropics. Why
    is that
    | so? Because the corresponding "cone of position" intersects  the
    Earth's surface
    | almost vertically when the Moon and Sun are low in the sky  and at
    about the
    | same altitude.
    
    Well, I am doing my best to understand these arguments, but remain
    puzzled.
    
    Here's the problem-
    
    The Moon is displaced from its geocentric position by two effects,
    parallax and refraction, which both vary with altitude, and combine
    together. Part of the clearing process, for a lunar, is to correct its
    observed position for those effects.
    
    I presume that in Frank's proposal, the converse process is being
    used; that by measuring the displacement of the Moon from its computed
    geocentric position, its altitude is being deduced, without benefit of
    horizon. Have I got that right?
    
    I can see how the correction for clearing can be calculated from the
    altitude, but the reverse process is not nearly so simple. If you plot
    the combined effect of parallax and refraction of the Moon, against
    altitude, because refraction and parallax vary in opposing directions,
    you end up with a double-valued result. If for simplicity you take the
    horizontal parallax for the Moon to be nominally 60', then you end up
    with a maximum displacement of about 54.5' at an altitude of 15
    degrees. Either side of that, a certain measured displacement results
    in two values for altitude. If the displacement was 52', for example,
    the resulting altitude could be either 22 degrees or 8degrees. For a
    wide range of
    altitudes near 15 degrees, the displacement hardly changes from 54.5',
    so a displacement of that amount provides very little information
    about what the altitude is. For angles below 30 degrees, the slope of
    the curve of displacement versus altitude is considerably reduced from
    its maximum value at high altitudes, simply because of the (cos alt)
    variation of parallax. That must reduce considerably the precision of
    any deduction of Moon altitude from the Moon's displacement, at low
    altitudes, compared with its high-altitude value.
    
    In an earlier posting, I understood that Frank had recognised that as
    a problem, when he wrote, in NavList 1379, " It has large changes in
    its altitude correction
    with altitude (except from about 7 to 15 degrees)."
    
    But now, in the passage copied above, he appears to say that there are
    circumstances in which the precision is maintained, even at low Moon
    altitudes. I ask him to tell us, then, where any lower Moon altitude
    limit lies, if there is one. Does he claim that the accuracy holds
    even at Moon altitudes of 15 degrees? If so, would he please explain
    how that happens?
    
    I am still hoping to get from Frank, some time, a statement of a
    procedure to adopt (computer program or simply a set of rules to
    follow), and it would be interesting to see how such a procedure
    handles the double-valued curve of displacement with altitude.
    
    George.
    
    contact George Huxtable at george@huxtable.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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