  The problem of the long-period gravity modes of the Earth outer fluid core is
investigated using either the subseismic or the anelastic approximation These
two approximations aim at filtering out the uninteresting short-period seismic
or acoustic oscillations while taking into account the density variations
across the core However, they differ on the form of the equation of mass
conservation since the density perturbations do not contribute to the mass
balance in the anelastic case Here we show that these two approximations lead
to the almost same results because of the weakness of the core stratification
due to the convective mixing The anelastic approximation should be however
preferred because it is simpler, mathematically self-consistent and is the only
one which can be applied to problems with a stronger stratification such as the
ones encountered in radiative zones of stars
