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    Re: Smart and Shearme Position Line Tables
    From: Lars Bergman
    Date: 2020 May 3, 09:22 -0700

    The tables are defined by

    cot(U)=tan(latitude)·sec(hour angle) and V=log10[sin(latitude)·sec(U)]+10

    Out of the 368 values on the page shown by David, 16% have an error of one unit in the last decimal, but never larger than that. Approximately equally distributed between U and V.

    The tables are derived by letting v·cos(U)=sin(latitude) and v·sin(U)=cos(latitude)·cos(hour angle). This gives cot(U)=tan(latitude)·sec(hour angle). Then putting these expressions into the altitude formula

    sin(altitude)=sin(latitude)·sin(declination)+cos(latitude)·cos(declination)·cos(hour angle) gives

    sin(altitude)=v·cos(U)·sin(declination)+v·sin(U)·cos(declination)=v·sin(U+declination), or with logarithms log[sin(altitude)]=log(v)+log[sin(U+declination)]=V+log[sin(U+declination)]

    Lars

       
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