Hydrostatic flattening, core structure, and translational mode of the inner core

Modern Earth models are constrained by an inertia coefficient y ^∗ = J ₂/H ≈ 0.3308 which leads to a so-called 'hydrostatic' flattening f _hyd ≈ 1/299.9. The latter is in rather large disagreement with the observed flattening f ≈ 1/298.3. We show that a more satisfactory value of the inertia coefficient for constraining a standard Earth model is y ≈ 0.332, consistent with a hydrostatic flattening of about 1/298.6. The change of the value of the inertia coefficient from about 0.331 to about 0.332 significantly alters the density structure of the core, notably the density jump at the inner core boundary. It brings, as a by-product, the hydrostatic values of J₂ and H to better agreement with the observed values than is presently thought, and most probably leads for the Slichter mode to a period of much longer than 5.42 h, which is the value computed for PREM.