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    Assumed positions, WAS: IN HONOR OF JEREMY...
    From: Peter Hakel
    Date: 2009 Sep 23, 09:18 -0700
    I have had certain questions since I began to learn about CelNav less than a year ago, and these latest exercises again reminded me of them.  There are some cases in which a fix can be obtained "directly," i.e. without choosing an assumed position (AP).  These include finding the intersection of circles of equal altitudes and parabolic fits to meridian transits.  Yet in nearly all literature I have seen so far, these are hardly mentioned (if ever, John Karl's book is an exception) as practical sight-reduction methods.

    For instance, usually a cartoon with intersecting circles is drawn to show the conceptual idea and then, instead of actually using this for calculations, the intercept method is introduced.  I understand that that is what was proven to work in the age before computers and I completely get the "if it ain't broke, don't fix it" principle.  And yet, it seems to me that this deserves more visible coverage in the literature.  After I solved the intersecting-circle problem as an exercise for myself (by solving it in 3-D space), I thought, "This really is not that hard, someone MUST have done this before."  It took me a considerable amount of digging through the Internet and literature to find the James A. Van Allen 1981 paper in which he used the exact same method.  And yet, 1981 is still pretty late for this in my opinion, and maybe someone in the past has tried to develop it into a usable procedure even before the age of computers.  Would a quadratic equation and some trig be really that much harder than logarithms and haversines?

    Suppose we would want to generalize this method for an ellipsoidal Earth.  Wouldn't Van Allen's 3-D method be easier to adapt than doing "spherical" geometry on the surface of an ellipsoid?  Ditto for geoid Earth shape.  Makes me wonder what STELLA is using, since it reportedly addresses the oblateness of the Earth with high accuracy.

    Similarly, I have a hard time believing that I would be the first one to have derived the "one-body fix" formula, which later proved to be useful in directly solving the "Latitude from Polaris" problem.  People have been doing these things for centuries and the math really isn't THAT complicated.

    Perhaps things have been tried and discarded as impractical which is why we don't get to read about them in easily accessible literature.  Just wondering...


    Peter Hakel



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