Comparison between the nutations of the planet Mars and the nutations of the Earth

The nutations of the planets Mars and Earth are investigated and compared. A large number of interior structure parameters are involved in the nutation computations. The comparison between the observations and the computations provides several constraints on these parmeters and therefore allows a better understanding of the physics of the interior of the planet. For the Earth, the high precision of the observations of the nutations has led to a very good determination of interior properties of the planet. For Mars, observations of nutations are not yet available, and we review how the amplitude of the Martian nutations depends on the hypotheses considered for its interior. Although Mars is very similar to the Earth, its interior is not well known; for example, we don't know if its core is liquid or solid. Only if the core is liquid, the Free Core Nutation (FCN) normal mode exists and can alter the nutations which are close to the resonance. From the observed geoids, it is known that both planets are not in hydrostatic equilibrium. The departure is larger for Mars than for the Earth, and consequently, the implication of considering a convective mantle instead of a mantle in hydrostatic equilibrium described by Clairaut's equation for the initial equilibrium state of the planet is larger on the Martian nutations than on the Earth nutations. The consequences of the uncertainty in the core dimensions are also examined and shown to be of a very high influence for Mars if the core is liquid, due to the potential changes in the FCN resonance. The influence of the presence of an inner core, which is known to exist for the Earth, could be more important for Mars than for the Earth if the inner core is large. Due to the presence of Tharsis on Mars, the triaxiality of this planet has, additionally, larger effects than on Earth.