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    Re: Star - Star Observations
    From: George Huxtable
    Date: 2010 Mar 12, 09:14 -0000

    Brad has now concluded-
    "Now there is no difference between my two results and therefore can readily
    retract my question about which is better.
    Corner Cosines and Young's Equations yield the same result."
    That's exactly as we should expect, with such small adjustments as the
    refraction correction gives rise to, in a star-star observation..
    However, differences are likely to occur when the same methods are applied
    to correcting a lunar distance, which is (almost) exactly the same problem,
    but now includes Moon parallax corrections, which can amount to 1 degree in
    altitude. In that case, Young's method remains rigorous, as long as the
    calculations are taken to enough significant figures. That using
    corner-cosines develops errors that are significant for lunar distance.
    Those errors were what the "third correction", table XVIII, in Thomson's
    tables, was intended to put right. Thomson never divulged the basis for that
    table, but when included, it produced an accurate lunar distance with little
    figure-work and head-scratching, and Thomson's tables were highly popular
    among navigators, going through many editions over a long period.
    Young's procedure is easy to implement on a computer or even a calculator
    (especially if it can store a simple program or formula). It wasn't popular
    in the days of table-lookup calculations, because, with a succession of
    multiplications and additions, it called for going into and out of logs,
    more than once.
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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