|MadSci Network: Earth Sciences|
The earth considered independent of the moon is still constantly deforming due to physical factors: The earth's rotation, the gravitational influence of the moon and the sun, and other smaller effects. This deformation includes the changes in the distribution of mass of the ocean (tides) and atmosphere. In short the center of mass is not fixed. I do not have a good answer for where the center of mass is on average, or what it's typical deviation is; but my best surmise is that this should be on a scale of a kilometer on a time scale of hours. There are different ways of defining the geometric center of the earth, depending in which model of the earth you choose. So this too is not a simple thing to determine. Sorry I do not have a better answer for you.
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