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Geoffry,

My knowledge of pendulum based astronomical devices is quite limited.  My question related to their accuracy is my understanding that a pendulum on the surface of the earth does not always point to the exact astronomical center of the earth.

This pendulum "tilt" is related to the law of universal gravitation and the fact the earth lacks complete uniformity of mass.  It is both oblate and lumpy. The pendulum points to the gravitational center as affected by that location, and in places this may vary from the astronomical "center" or even the overall gravitational center by some value. 

Such places in Bermuda I have seen noted as varying .25 miles in 15, measuring terrestrial distances vs using astronomical calculation.

My curiosoty is how this pendulum issue might create an offset zenith and might affect a pendulum based device taking astronomical sights.  How does this device eliminate the error of astronomical vs. gravitational center.

As the tilt apparently varies with local location, I would think it might throw off calculated positions vs WGS 84. 

I say "I would think" because this particular device and issue is something I am only just learning about, so I could be "out in left field with snowshoes on" too.....