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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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