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    Re: Two-body fix caveat
    From: George Huxtable
    Date: 2009 Nov 4, 00:09 -0000

    Peter Hakel wrote, about John Karl's book "Celestial navigation in the GPS
    "After a brief off-list discussion with John, I'd like to comment on Eq.
    7.5e, which yields LHA1.  Generally, there are two distinct solutions to
    that equation, while the inverse cosine function yields only one of them
    (let's call it C).  I relay John's comment, that the navigator must select
    C, if the ship is east of GP1, and 360-C, if the ship is west of GP1.  John
    also writes that "the body that's to the west should always be labeled #1."
    A difficulty can arise if the ship and GP1 are almost on the same meridian.
    Another problem occurs if these equations are to be implemented in a
    computer program, which does not have the above-mentioned human insight into
    the relative positions of the ship and the two bodies. "
     Peter is quite right, that the suggested way to resolve that ambiguity
    isn't workable when the object is near the meridian, because it's not then
    obvious whether the vessel is East of it, or West. I'm interested to
    discover whether Peter is using the first issue of that book (2007), or a
    later one.
    I, too, discussed the ambiguities in equation 7.5e with John Karl, off list,
    shortly after the first edition appeared in 2007. We later discussed
    possible changes to the book when a new edition was on the stocks, and I
    hope that something was done, then, to clarify equation 7.5e. But if a new
    edition has since appeared, I haven't seen it.
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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