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    Re: Towards a basis for Bruce Stark's Tables
    From: Fred Hebard
    Date: 2003 Jan 5, 02:13 -0500

    I worked out the basis for Bruce Stark's method of computing
    intercelestical distances.
    
    He uses logs and Gaussian addition logs to evaluate:
    
    archav{ hav[del(dec)] + hav[del(GHA)]*cos(Mdec)*cos(Sdec) },
    
    where del(GHA) is the absolute value of the difference in GHA between
    the two bodies, del(dec) the corresponding value for declinations.
    Mdec is the declination of one body and Sdec the declination of the
    second; hav is haversine; and archav its inverse.
    
    A haversine equals: [1-cos(theta)]/2.  It also has the beneficial
    property of equaling: sin^2(theta/2).
    
    Using the same notation, the corresponding standard modern formula
    using sines and cosines is:
    
    arccos{ sin(Mdec)*sin(Sdec) + cos[del(GHA)]*cos(Mdec)*cos(Sdec) }.
    
    I'm fairly sure that Stark's method for clearing the distance is a
    log haversine version of Borda's method, so ably laid out by George
    Huxtable last February
    (http://www.i-DEADLINK-com/lists/navigation/0202/0149.html).  If anybody is
    interested, I will see whether I can uncover the haversine version of
    Borda's method.  Bruce's earlier post in this thread explains the
    Gaussian addition logs used to evaluate the summation before taking
    the inverse of log(haversine).
    
    Note also that you could use Bruce's tables for sight reduction to a
    tenth of a degree without interpolation, which might save some space
    and mind strain.
    
    It was a relief to get this done!
    
    Fred
    --
    --------------------------------------------------------------------------
    Frederick V. Hebard, PhD                      Email: mailto:Fred{at}acf.org
    Staff Pathologist, Meadowview Research Farms  Web: http://www.acf.org
    American Chestnut Foundation                  Phone: (276) 944-4631
    14005 Glenbrook Ave.                          Fax: (276) 944-0934
    Meadowview, VA 24361
    
    
    

       
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