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    Re: DIY long-term almanac for calculators
    From: Paul Hirose
    Date: 2018 Jan 16, 21:32 -0800

    On 2018-01-15 8:18, Tony Oz wrote:
    > I programmed my TI-83 to do the computations as per Chapter 15 of Henning 
    Umland's excellent "Short Guide to Celestial Navigation", where the author 
    warns on the accuracy:[BEGIN QUOTE]
    > The maximum error of GHA and Dec is about ±0.6'. Results have been 
    cross-checked with Interactive Computer Ephemeris 0.51 (accurate to approx. 
    0.1'). Between the years 1900 and 2049, the error was smaller than ±0.3' in 
    most cases (100 dates chosen at random). EoT was accurate to approx. ±2s. In 
    comparison, the maximum error of GHA and Dec extracted from the Nautical 
    Almanac is approx. ±0.25' (for the sun) when using the interpolation tables. 
    The error of SD is smaller than ±0.1'.[END QUOTE]
    
    I coded his formulas in a program which compares them to the JPL DE431
    ephemeris at 1000 random times in the 21st century. It generally
    confirms Umland's accuracy claims. For Sun apparent place, semidiameter,
    and equation of time the program calculates an accuracy statistic for
    the whole set (square root of the mean squared error) and also remembers
    the single worst result.
    
    Apparent place error is the separation angle between a vector to the Sun
    calculated from the Umland formulas and a vector from the JPL ephemeris.
    It therefore combines the errors in RA and declination into a single number.
    
    .33′ apparent place RMS error
    .95′ max
    
    .006′ semidiameter RMS error
    .007′ max
    
    .90 s equation of time RMS error
    2.95 s max
    

       
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