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    Spherical earth model vs. ellipsoid
    From: Henning Umland
    Date: 1999 Mar 12, 4:28 AM

    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{at}gmx.de
    �
    �
    �
    �
    �
    �
    �
    

       
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