  We explore the change in Jupiter's normalized axial moment of inertia (NMOI)
assuming that Jupiter undergoes core erosion. It is found that Jupiter's
contraction combined with an erosion of 20 M_Earth from a primordial core of 30
M_Earth can change Jupiter's NMOI over time significantly. It is shown that
Jupiter's NMOI could have changed from ~0.235 to ~0.264 throughout its
evolution. We find that a NMOI value of ~0.235 as suggested by dynamical models
(Ward & Canup, 2006, ApJ, 640, L91) could, in principle, be consistent with
Jupiter's primordial internal structure. Low NMOI values, however, persist only
for the first ~ 10^6 years of Jupiter's evolution. Re-evaluation of dynamical
stability models as well as more sophisticated evolution models of Jupiter with
core erosion seem to be required in order to provide more robust estimates for
Jupiter's primordial NMOI.
