The precession and nutations of a rigid Mars

The nutations of Mars are about to be estimated to a few milliarcseconds accuracy with the radioscience experiments onboard InSight and ExoMars 2022. The contribution to the nutations due to the liquid core and tidal deformations will be detected, allowing to constrain the interior of Mars. To avoid introducing systematic errors in the determination of the core properties, an accurate precession and nutation model for a rigidly behaving Mars is needed. Here, we develop such a model with adequate accuracy based on the Torque approach and compare it to previous models. We include in the model the forcings by the Sun, Phobos, Deimos, and the other planets of the solar system. We also include the geodetic precession and nutations. We use semi-analytical developments for the solar and planetary torques, and analytical solutions for the effect of Phobos and Deimos and for the geodetic precession and nutations. With a truncation criterion of 0.025 milliarcseconds in prograde and/or retrograde amplitude, we identify 43 nutation terms. The uncertainty on our solution mainly derives from the observational uncertainty on the current determination of the precession rate of Mars. Uncertainties related to our modeling choices are negligible in comparison. Given the current determination of the precession rate ( $$7608.3\pm 2.1$$  mas/yr, Konopliv et al. in Icarus 274:253–260, 2016. https://doi.org/10.1016/j.icarus.2016.02.052 ), our model predicts a dynamical flattening $$H_{{D}}=0.00538017\pm 0.00000148$$ and a normalized polar moment of inertia $$C/\mathrm{MR}^2=0.36367\pm 0.00010$$ for Mars.