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We compute the inertial modes of a freely rotating two-layer planetary modelwith an ellipsoidal inviscid fluid core and a perfectly rigid mantle. Wepresent a method to derive analytical formulae for the frequencies of the FreeCore Nutation (FCN) and Chandler Wobble (CW) which are valid to all orders ofthe dynamical flattening of the core and mantle, and we show how the FCN and CWare the direct generalisation of the purely fluid Spin-Over mode (SO) and ofthe Eulerian Wobble (EW) to the case where the mantle can oscillate freelyaround a state of steady rotation. Through a numerical computation for anaxisymmetric (oblate spheroidal) planet, we demonstrate that all other inertialmodes of the steadily rotating fluid core are also free modes of the freelyrotating two-layer planet.

Inertial modes of a freely rotating ellipsoidal planet and their relation to nutations