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    Re: 2-Body Fix -- take three
    From: George Huxtable
    Date: 2009 Nov 8, 19:38 -0000

    John Karl wrote-
    
    | It should be apparent both from Fig 7.3 and from Eqs 7.5a-e, that
    | these five equations do not contain information on the zero of
    | longitude.  Thus they can not determine longitude, which must be
    | determined from another source -- such as the navigator.
    
    Simply from the longitude, with respect to Greenwich, of GP1, via 7.5f,
    putting in the correct sign of LHA1. It's best to choose the
    furthest-from-meridian, of the two bodies, to work from, and label it GP1,
    as John suggests.
    
    ===================
    
    | The navigator should label the body that is clearly off his meridian
    | as GP1, the longitude reference body.  Then if this body has its LHA
    | greater than 180, of course, that solution should be picked as the
    | inverse cosine in Eq, 7.5e.
    
    Why not just use for 7.5e
    sin LHA1 = sin (A-B)  cos H1 / cos Lat ., which removes the  second-stage
    ambiguity?
    
    | (Fig 7.3 will have its LHA2 corrected in the next printing.)
    
    Is that correction to show LHA2 as an angle measured Westerly, round the
    World, from the ship?
    
    I presume, then, in a geometry such as that of 7.3, the labels of GP1 and
    GP2 would be exchanged.
    In that case, does that bring up questions about the way the angles A and B
    are to be defined? Is A always the clockwise bearing, from North, of the
    line from what's now become GP1, to GP2. And is B always the relative
    bearing of that same line, measured clockwise from the direction of the ship
    from GP1?
    
    =====================
    
    Now for a separate issue, if John will forgive me for adding another twist.
    I can't resist bringing out an old hobby-horse of mine once again,
    concerning 7.5f. John wrote-
    "We're using the convention that LHAs are measured westward to 360, and that
    west Lons are negative."
    
    Some reader-confusion is added because we are having to add or subtract
    amounts, longitude and hour-angle, which are of the same quantity (angle
    measured with respect to the Earth's polar axis) but which are defined as
    going positive in opposite directions. I wonder if anyone can think of
    another example, in any field of mensuration, where this occurs? I can't.
    
    I don't blame John for this; he has been constrained by a decision of a
    committee of astronomers to define longitudes positive-Easterly (you could
    call it Eastitude), against protest from some respected astronomical names,
    including Meeus. Hour-angles are always measured Westerly, beacause that's
    the direction in which they increase with time, as the World turns. It
    presents no problem to astronomers, who hardly ever concern themselves with
    hour-angles, using right-ascensions instead, which increase Eastward
    (mostly). But in Navigation, I contend that we would be better to use
    Westitude, 0 to 360, using that name to avoid any confusion. Longitudes East
    of Greenwich can be Westitudes of 180 to 360, or of -180 to 0; there's no
    confusion arises with either choice.
    
    George.
    
    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.
    
    
    
    
    
    
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