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    Re: Lunars: altitude accuracy
    From: George Huxtable
    Date: 2004 Nov 1, 11:19 +0000

    Frank Reed wrote-
    >I general, good (slightly approximate) expressions for the required accuracy
    >of the altitudes are:
    >AccuracyBody = 6' * sin(Distance) / cos(BodyAltitude)
    >AccuracyMoon = 6' * tan(Distance) / cos(MoonAltitude).
    >I have never seen these expressions in print anywhere. Has anyone else
    >encountered them?
    No, and they don't "feel" correct to me. I would like to see the argument
    that justifies them.
    Do Frank and I agree, I wonder, that the geometry in which the lunar
    distance is MOST sensitive to changes in altitude, of the Moon or
    other-body, is when the two bodies lie somewhere in an arc that passes
    through his zenith, so they have azimuths that are identical or else 180
    deg apart. In that case the lunar distance is either the difference or else
    (180-sum) of the two altitudes, depending on whether they are on the same
    side of the zenith or opposite sides. If there's any change, or error, in
    either altitude, then a corresponding change in lunar distance, of ?100% of
    that amount, results. This is just as true for large lunar distances as for
    small ones, as I see it.
    (For other geometries, the lunar distance is always less sensitive to such
    changes, so a smaller percentage than ?100% applies. For lunar distances of
    90 degrees, as Frank points out in another posting, the sensitivity can be
    0%, but only, I think, in certain geometries.)
    If, for the most sensitive geometry, the resulting error in lunar distance
    is indeed independent of the lunar distance itself, then the two
    expressions Frank quotes can not apply: the problem requires some further
    Frank has said, on the same topic-
    >generally the required accuracy (for constant altitudes) is proportional to the
    >sine of the distance which means that for short distance lunars, the
    >altitudes have to be significantly more accurate. This is yet another
    >reason why short
    >distance lunars would not have been popular historically."
    >Usually, it's said that you can have 5 or 6 minute error in the measured
    >altitude of the Moon or the other body and it will make no difference in the
    >clearing of the observation. Try it. It's often true. But if you work the math,
    >you'll find that this is true only "on average". Lunars can be much more
    >sensitive to altitude accuracy in many cases.
    What is the geometry which gives rise to such a dramatic increase in
    sensitivity, I ask? And by how much is the sensitivity then increased?
    On a rather different matter, Frank added-
    >Finally, I should note that these
    >expressions are "slightly approximate" because they assume that refraction is
    >insignificant. As as long both objects are above 10 degrees or so in altitude,
    >that's a reasonable assumption.
    I question that. By my reckoning, changes in refraction with altitude are
    actually GREATER than changes in parallax with altitude, at altitudes up to
    about 14 degrees, and don't become "insignificant" until the altitude
    increases significantly beyond 14 deg.
    It's often recommended that altitudes above 10 degrees are avoided. But
    that doesn't imply that refraction is insignificant above 10 deg.
    Corrections for mean refraction are well understood and tabulated, down to
    much lower angles. The reason for avoiding angles below 10 deg is because
    in real-life, atmospheric effects near the horizon can cause the actual
    refraction to differ significantly from its predicted mean value.
    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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