Influence of triaxiality and second-order terms in flattenings on the rotation of terrestrial planets: I. Formalism and rotational normal modes

Unlike for the Earth, the equatorial flattening of Mars is important and almost of the same magnitude as the polar flattening. The classical semi-analytical model for the rotation of an ellipsoidal rotating planet with an elastic mantle and incompressible fluid core is therefore extended to incorporate the effects of the planet’s triaxiality. As triaxiality effects are nevertheless small, other second-order effects in the small parameters not related to triaxiality have also been taken into account. The absolute values of the frequencies of two rotational normal modes: (1) the free core nutation (FCN); and (2) the Chandler wobble (CW), are found to be smaller than the corresponding frequencies for a biaxial planet. The period change is larger for the CW than for the FCN, for which the triaxiality effect is comparable to the effect associated with the other second-order terms, and amounts to about 1 day for the CW of Mars.