It's unclear what you are looking for. Are you looking for the actual location of the earth's center of mass, taking into consideration non-uniform distributions of mass density? (As a first approximation, why not say right in the middle! )As a first-order approximation I can simply calculate the location and radii of an ellipsoid that contains the center of mass, but that's not good enough. Doing a Google search for "center of mass earth" doesn't pull up anything.
That's the wrong search term. The right search term would be "geocenter" were it not for a slew of companies and organizations that erroneously think they are the center. You'll get a lot of irrelevant garbage if you just search for "geocenter".Doing a Google search for "center of mass earth" doesn't pull up anything.