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Sometime ago, I ran a number of experiments to obtain an estimate of the error 
caused by the spherical earth model.
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The instrument used was a digital theodolite with a specified accuracy of 5 
arcseconds. Ephemerides were calculated with ICE and compared with those 
tabulated in the Nautical Almanac. In addition, a time correction for UT1-UTC 
was applied.
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In the morning, I set up the instrument in my backyard and measured a series 
of approx. 50 altitudes of the sun. Using my GPS position as assumed 
position, I calculated the corresponding intercepts. Fom the 50 intercepts, I 
picked the median and noted the corresponding altitude, GHA, and declination.
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In the afternoon, I repeated the procedure. Again, altitude, GHA, and 
declination corresponding to the median of the intercepts were noted.
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With this data set, I calculated a fix using the intercept method. 
Calculations were reiterated until a virtually constant position was 
obtained.
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All calculations, including altitude corrections, were done with a computer, 
not with any tables. Altitude corrections included corrections for air 
temperature and atmospheric pressure.
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The resulting fix was compared with a DGPS fix (WGS84 datum).
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The distance of the celestial fix from the DGPS fix was approx. 120 m (360 ft).
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A second test series yielded a difference of only 70 m (210 ft).
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These results show that the error caused by the spherical model is not 
significant under practical conditions of celestial navigation.
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The experiment was done in the northern part of Germany. I have no knowledge 
if similar measurements in other parts of the world would result in an error 
of the same magnitude.
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Henning Umland
h.umland@gmx.de
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