It is the Archimedes principle.
When applied to the globe, you get a centrifugal force (the buoyant force oriented from the center outwards).
Since the globe is not expanding, there must be another force going inwards equal to the buoyant force and that is a centripetal force (as Relative stated). A force called gravity.
And looking at the structure of the globe, indeed we observe more dense materials at the centre and less dense outwards, from the core to the atmosphere.
Everyting fits well. What number do you want?