Thanks for several interesting replies, the technical level is a lot higher here than at comparable forums.
It's true that I ignored the acceleration of the earth. Two hypotheses seem to be offered in the discussion. That the pendulum will show a much smaller deviation or that the deviation...
The center of mass of the Earth is approximately at the center. The center of mass is also where the force vector of the gravitational force is pointing. (down that is).
Now the total gravitational force excerted on me should be the sum of the force excerted by the Earth plus anything else...