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    Re: Possible limitaion for lunar distance measurement
    From: George Huxtable
    Date: 2009 Mar 2, 23:39 -0000

    What Frank Reed has written below is all very well, but has little to do
    with the question being asked, which was about deficiencies in a particular
    full formal clearing procedure, not some shortcut.
    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message ----- 
    Sent: Monday, March 02, 2009 8:49 PM
    Subject: [NavList 7518] Re: Possible limitaion for lunar distance
    George wrote:
    "It's certainly the case, as Frank has frequently pointed out, that when the
    lunar distance is near 90�, it's very insensitive to the details of the
    To elaborate on this, there are several things at work:
    First, there's the simple practical point which I mentioned a few days ago.
    Navigators seem to have preferred shooting Sun-Moon lunars, and that's most
    convenient from an observational perspective when the Moon is close to 90
    degrees elongation.
    Second, there are shortcuts in some clearing methods that can be applied
    when the distance is close to 90. When using one of the series methods, the
    quadratic correction is proportional to cot(LD) so it can be ignored near 90
    degrees (except in some methods, like Bowditch's principal method, where the
    quadratic correction is rendered always positive by adding a constant at an
    earlier step). This is not a significant savings in work since the quadratic
    correction was usually just a simple table lookup.
    Third, as I discovered a few years ago and have mentioned many times since,
    the clearing of lunar distances has a remarkable, and as I have said
    "seemingly miraculous", freedom from errors in the Moon's altitude when the
    distance is close to 90 degrees. If the observed lunar distance is between
    85 and 95 degrees (and the objects aren't too low in the sky), the observed
    altitude of the Moon can be wrong by a degree or more and it won't make any
    difference. This makes the whole observation and calculation much more
    convenient since it means a quick observed altitude for the Moon is
    Fourth, and almost certainly not relevant historically, it's possible to
    clear lunars when the distance is close to 90 degrees (and over a rather
    broad range around that) without solving any spherical triangles at all. Any
    observation can be reduced to the geometrically "degenerate" case of
    vertically aligned bodies when the measured lunar distance is around 90
    degrees. That makes clearing lunars in many common practical cases a
    relatively trivial project. Too bad they didn't know this two hundred years
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