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    Re: Thoughts on Celestial.
    From: Frank Reed
    Date: 2012 Oct 31, 09:39 -0700

    Oh GOOD LORD! This could turn into a real mess.

    There is only ONE CIRCUMSTANCE where one should apply this reasoning to a three-body (three sight) fix, and that is when you have "a priori" knowledge of a fixed systematic error in sights that is known to be larger than normal random error. For example, if you KNOW that the index error is substantial and was incorrectly checked, then you can treat the index correction as an unknown. This is NOT a common circumstance, and such tricks should NOT be generally applied. It IS legitimate to do something like this (without a priori knowledge of systematic error) when you have a significantly larger number of sights in multiple directions. For example, imagine shooting three shots each of eight stars, one each due North, NW, East, SE, South, etc., for a total of 24 sights. If they have purely random error, a plot of those 24 LOPS will yield a tight "tangle" of crossing lines with no particular pattern. But if there is a fixed offset systematic error (like an incorrect index correction or anomalous dip), the LOPs will form an open octagon. The fixed offset systematic error in such a case can be eliminated by adding a fixed quantity (positive or negative) to every sight (same quantity added to every sight) until the resulting "tangle" of LOPs is as small as possible. Whatever is left over will be mostly random error which cannot be eliminated.

    I will try to write up a longer account of this issue later. For now, just count this as a "heads up". I apologize for not getting to this sooner. Unfortunately, I have been busy on a project.


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