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    Re: Spherical earth model vs. ellipsoid
    From: Jim Manzari
    Date: 1999 Mar 15, 5:07 AM

    > Henning Umland wrote:
    > 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.
    I was intrigued by your test.  It appears to have been well planned
    and executed.  Thanks for posting a very interesting summary of the
    You've expressed a doubt as to whether the method may be applied
    elsewhere in the world.  Perhaps my experience in a similar experiment
    might give you some food for thought.
    Some years ago I did some work with precision tracking radars.
    Mechanical alignment of the pedestal and precise geodetic position of
    the radar were two of the many values that we worked hard to
    determine.  In the beginning we used a device called an inclinometer
    (a micrometer precision bubble level) to determine the levelling errors
    in the vertical axis of the radar.  The results we got were not what
    we expected and had us scratching our heads for awhile.
    The problem was that no one had thought of a thing called "tilt of the
    local vertical".  The bubble did not seek the geometric (geodetic or
    geocentric) center of the earth, but rather the center of the "local"
    mass or gravity field.
    Most of these radars were located on islands around the world, these
    islands being mountains rising many thousands of feet above the sea
    bed.  Most, if not all, of these islands were the remnants of extinct
    volcanos.  The "local vertical", as we called it, was deflected toward
    the local center of mass which might be the magma plug in the extinct
    My guess is that your results are valid given the uniformity of
    "local" mass distribution in N. Germany, but tilt of the local
    vertical is something to beware of when working with bubble devices
    capable of 5 arc-second accuracy.
    One way to test whether you have found the correct local vertical, ie
    properly levelled the theodolite, is to repeat the test in "plunge"
    mode and compare the two sets of data.  I think "plunge" is the same
    as a "back sight" with a sextant, but someone correct me if I'm wrong.
    In the tests of radar systems we eventually stopped using the
    inclinometer and started using a bore-sight camera to measure
    alignments relative to star reference angles.  Each time we took a
    star angle we also "plunged" the radar and took a second set of
    measurements.  The average of these two sets of measurements tends to
    cancel any errors in assumed vertical alignment of the pedestal.
    I have a question for you, Henning, where did you find the theodolite
    used for your tests?  For some years I have been searching for a
    surplus theodolite.  I reasoned that with a advent of laser and GPS
    based surveying the old bubble level theodolites should be plentiful
    and cheap, but I've had no luck finding one.  My guess is that the
    theodolite manufacturers are destroying these, so they don't compete
    with newer models.
    Jim Manzari
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