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    Re: The elegant 2 body fix
    From: Fred Hebard
    Date: 2005 Jun 4, 11:30 -0400

    On Jun 4, 2005, at 10:52 AM, Peter Fogg wrote:
    >> From: Fred Hebard
    >> Without knowing GMT, one could not determine longitude from an
    >> altitude
    >> of the Sun when it is due East or West.  I also wonder how much the
    >> altitude of the sun varies with azimuth at various locations when it
    >> is
    >> due East or West; it's azimuth can only be measured to perhaps 0.1
    >> degrees, how much would that limit the precision of the measurement?
    > The moment is calculated using the DR (assumed position, and the
    > accuracy is
    > dependent on this). Then as many sights as possible are made over
    > about five
    > minutes, a few minutes on either side of the desired moment. These are
    > then
    > plotted on a simple graph; time on one axis, altitude on the other. The
    > slope of apparent rise or fall is compared with the pattern of sights
    > to
    > find the same slope that best fits this pattern. Then the desired
    > moment is
    > used to intersect with the slope to indicate the altitude to be used
    > for
    > sight reduction. The azimuth is then 90 or 270 degrees, the LOP runs
    > due
    > north/south, thus a line of longitude.
    In pseudocode, or pseudomath, I was wondering about d(alt)/d(az) for
    various spots and times on the earth, and wondering whether the slope
    is appropriate for the limited precision of azimuth determinations.
    Using only altitude, as you propose, it seems that the problem is
    underdetermined: trying to fit more variables than are observed.  Here
    you are proposing using d(alt)/d(DR,t) to find DR.  However, as I said,
    I haven't worked this out and am proceeding on a very rough, very
    ill-honed intuition.

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