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    Re: AP terminology, WAS: 2-Body Fix -- take three
    From: Peter Hakel
    Date: 2009 Nov 12, 11:56 -0800

    I'll try to summarize the way I understand this.

    If we want to quantify (calculate) any geometric object (an LOP for example), we need to choose a coordinate system.  We also need to have a way of measuring distances, which then allows us to put numbers on the axes.  Coordinate systems have origins (reference points) which declare: "this is zero."

    Circular LOP can be parametrized (i.e. "directly calculated") in a number of ways, Van Allen does it in 3-D, you and (Gauss) do it in 2-D, etc.  The parameter can be anything that is not constant throughout the LOP (a meridian can be parametrized by latitude but not longitude) and which does not suffer from ambiguities.  Since the celestial LOP is a circle, it can be parametrized, for instance, by azimuth at the GP, the circle's "center".

    Before computers, none of this "direct computation of the LOP" was very practical.  Thus eventually we got St. Hilaire with the AP.  So let me restate my understanding of the AP concept:

    I now think of the AP as the origin of a local coordinate system for a patch of Earth's surface that,
    a) contains the ship's location, and,
    b) is sufficiently flat and "zoomed in" in order to allow us to plot the relevant sections of the LOPs with acceptable accuracy.
    Then the intercept distance and azimuth are like the magnitude and phase of a complex number.  This local coordinate system is overlayed with the rectangular grid of parallels and meridians in the Mercator projection, which then can be used to extract the latitude and longitude of the fix.

    In order to do anything, we need a coordinate system.  Coordinate systems have origins.  The AP is effectively an origin of a coordinate system that is very convenient for methods and technology of the 19th and early 20th centuries.

    Peter Hakel

    From: John Karl <jhkarl---.net>
    To: NavList <navlist@fer3.com>
    Sent: Thu, November 12, 2009 10:28:05 AM
    Subject: [NavList 10593] Re: AP terminology, WAS: 2-Body Fix -- take three

    Peter & Lu,

    We all agree on the definition of a fix, LOP, DR position, and EP.
    But if AP is not the generic word for the location of the apex of the
    St. Hilaire navigation triangle between the coH side and the coLat
    side, what is that location called??  Is there no generic word for
    it??  If we can't agree on the label for this point, let's call it the
    "controversial Point", the CP.

    Then, for List members, I can rephrase my favorite question:  Why does
    the St. Hilaire method use a CP instead of just calculating the LOP
    directly?  (I think Frank says there's no confusion on the answer to
    this question.)


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