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    Re: St. Hilaire -- My Take
    From: Peter Hakel
    Date: 2009 Nov 15, 20:03 -0800
    John Karl writes:

    "B.  PLOTTING VARIABLES:  I think (not sure) that the discussion on the List about parameters is what I would call plotting variables."

    They are exactly that.

    "But the direct calculation isn't robust.  For example, in calculating a Lon corresponding to a selected Lat, a nearly east-west
    LOP can yield a Lon that's too far away.  Worse yet, the LOP might not even intersect the parallel of latitude.  Likewise, specifying Lons
    and calculating Lats gives the same problem with nearly north-south LOPs."

    Yes, that is because neither latitude nor longitude can serve as legitimate parameters for the entire celestial LOP due to its circular shape.  In cases described by John, these would be parameters fail the "uniqueness" requirement.  As Sumner has shown, you can use them to parametrize a section of your LOP, provided that it is not oriented E/W or N/S.  Even if the LOP is only approximately aligned with a parallel or a meridian, it can still pose a problem due to the finite (round-off, plotting) precision of real life.  The true bearing from the GP is the most "natural" choice for the parametrization of the entire celestial LOP. 

    Peter Hakel

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