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Subject: [Nml] Spherical earth model vs. ellipsoid
From: Henning Umland (h.umland@XXX.XXX)
Date: Fri Mar 12 1999 - 06:28:28 EST
Sometime ago, I ran a number of experiments to obtain an estimate of the error caused by the spherical earth model.
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.
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.
In the afternoon, I repeated the procedure. Again, altitude, GHA, and declination corresponding to the median of the intercepts were noted.
With this data set, I calculated a fix using the intercept method. Calculations were reiterated until a virtually constant position was obtained.
All calculations, including altitude corrections, were done with a computer, not with any tables. Altitude corrections included corrections for air temperature and atmospheric pressure.
The resulting fix was compared with a DGPS fix (WGS84 datum).
The distance of the celestial fix from the DGPS fix was approx. 120 m (360 ft).
A second test series yielded a difference of only 70 m (210 ft).
These results show that the error caused by the spherical model is not significant under practical conditions of celestial navigation.
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.
Henning Umland
h.umland@XXX.XXX
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