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    Re: 2-Body Fix -- take three
    From: John Karl
    Date: 2009 Nov 8, 20:56 -0800

    George & all interested,
    Point 1:  The law of sines equation does not change the fact that no
    set of equations derived from Fig 7.3 can determine longitude because
    there is no longitude information in the figure.  Outside information
    must be added.  George's sin(LHA1) equation introduces negative LHAs,
    departing from the commonly used convention.  (And I didn't want to
    depart from convention in my book, nor introduce the Law of Sines.)
    More fundamentally, it shifts the LHA selection question to the other
    fix in Fig 7.3, where (A+B) must be used in Eq. 5.5d, which then
    becomes Sin(A+B) in George's Law of Sines equation.  This makes the
    sensitive decision occur around LHA = 90 instead of 0/180.  That is,
    now one has to decide between the LHA returned by the computer, and 90
    + LHA.  This is much harder for a navigator to do than to decide
    whether a body is on, or too near his meridian.  (This is the same
    reason we don't use the Law of Sines for computing azimuth in St.
    Hilaire sight reductions.)
    Point 2:  A and B are the angles enclosed in spherical triangles and
    have no direction associated with them.  Their definitions remain the
    same under an interchange of GPs.  E.g., A is always the interior
    angle between sides Dec1 and D12.
    Point 3:  Using the equation LHA = GHA + Lon, good for all GHAs and
    Lons, requires only the convention that west Lons are negative and
    west are positive.  I can't see any room for confusion here if just
    the simplest algebra is understood.  Of course we could switch the Lon
    sign convention and the equation accordingly.  As George points out I
    picked the one that's used by Cel navigators and not the one of
    astronomers, irritating both George's and Meeus(and maybe me, to a
    lessor extent).
    I sympathize with George and Meeus as I've also been forced to adopt
    another commonly used CN convention in my book that I find irritating
    to no end.  My pet peeve is the term "Assumed Position" in the St,
    Hilaire sight reduction.  I wanted to call it the "Reference Point"
    because in the St. Hilaire method there are no assumptions at all, as
    I've preached on this List, in my book, and in an article "Assuming
    Nothing" in Ocean Navigator, Nov/Dec 2008.  But there are
    communication advantages to sticking with convention.
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