Expected accuracy of Mars rotation and orientation estimation from TGO orbit determination

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The Rotation and Interior Structure Experiment (RISE) on the InSight lander and the LaRa experiment on the ExoMars platform will provide precise measurements (accuracies of a few mas) of the rotation of Mars, in terms of the Mars rotation and orientation parameters (MOP). These parameters include the rate of precession and the amplitudes of the nutations, of the length-of-day (LOD) variations, and of the polar motion components. The MOP are sensitive to the interior properties of Mars, particularly to the presence and size of a liquid core. However, uncertainties of current interior models in other physical parameters describing the internal structure of Mars, such as the temperature distribution, the composition, and the elasticity, limit the information on the interior obtainable from the MOP. Current estimates of the core radius have uncertainties of about 100 km, and suggest a fully liquid core. The improvement of the accuracy of the MOP solution from the landers coming from the inclusion of radio-tracking data from Trace Gas Orbiter (TGO) was studied in this project. Both numerical (through the orbit determination software GINS and Tudat) and analytical (through the ORB software developed at the Royal Observatory of Belgium) methods were employed to asses the sensitivity of the TGO orbit and radio-tracking data to the MOP of interest. In particular, an analytical method based on Kaula’s equations was developed to predict the effect of the MOP on a wide range of orbits. The satellites most affected by CW were found to be those in near-circular orbits at about 40∘ of inclination. The orbiters most sensitive to LOD variations were those in near-equatorial, highly-eccentric orbits. As for the improvements on the MOP estimation due to TGO data, a covariance analysis was performed with different assumptions on the dynamical and observation models, and on the estimated parameters. The improvement with respect to a lander-only solution is of up to 6 % for the CW components, up to 8 % in the LOD variations components, and up to 20% and 12% on the nutations amplification factor and the FCN frequency (the latter two judged excessively optimistic). However, no definite inference on the resulting core radius accuracy improvement could be made.