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    Re: One-body fix
    From: Peter Hakel
    Date: 2009 Apr 28, 03:14 -0700
    Thank you, John.  The two formulae are indeed equivalent.   Peter


    From: John Karl <jhkarl---.net>
    To: NavList <NavList@fer3.com>
    Sent: Monday, April 27, 2009 2:59:36 PM
    Subject: [NavList 8081] Re: One-body fix



    > I hereby display the solutions to this "one-body fix" problem, if only as a curiosity.  I expect that these have been worked out before but I haven't found them anywhere so far (references would be much appreciated).  The known quantities are the GP (Dec, GHA), observed altitude (Ho), and azimuth to GP (Zn).  From the navigation triangle we can calculate the LHA and then the Latitude:
    >
    > sin LHA = sin Zn * cos Ho / cos Dec
    >
    > sin Latitude = ( sin Ho * sin Dec  -  cos Ho * cos Dec * cos LHA * cos Zn )  /  ( 1  -  cos Ho * cos Dec * sin LHA * sin Zn )
    >
    > Peter Hakel


    I don't know of a reference for Peter's second equation above.  But, I
    easily calculated a different one from the standard altitude and
    azimuth equations:

    Sin L = (cosA cosH sinH - sind cosd cosLHA)/(sind cosA cosH - cosd
    sinH cosLHA).

    Since both this and Peter's check out for the special case at LAN,
    they're probably both OK.
    --JK



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