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We propose an approach to infer large-scale heterogeneities within a small celestial body from measurements of its gravitational potential, provided for instance by spacecraft radio-tracking. The non-uniqueness of the gravity inversion is here mitigated by limiting the solutions to piecewise-constant density distributions, thus composed of multiple regions of uniform density (mass anomalies) dispersed in a background medium. The boundary of each anomaly is defined implicitly as the 0-level surface of a scalar field (called the level-set function), so that by modifying this field the shape and location of the anomaly are varied. The gravitational potential associated with a density distribution is here computed via a line-integral polyhedron method, yielding the coefficients of its spherical harmonics expansion. The density distribution is then adjusted via an iterative least-squares approach with Tikhonov regularization, estimating at every iteration corrections to the level-set function, the density contrast of each anomaly, and the background density, in order to minimize the residuals between the predicted gravity coefficients and those measured. Given the non-convexity of the problem and the lack of prior knowledge assumed (save for the shape of the body), the estimation process is repeated for several random initial distributions, and the resulting solutions are clustered based on global properties independent of the input measurements. This provides families of candidate interior models in agreement with the data, and the spread of the local density values across each family is used to assess the uncertainties associated with the estimated distributions.

Most spacecraft missions to small bodies provide the gravity field of their targets. As the extended gravity field is an expression of the mass distribution within the body, it can provide information about its interior structure, and that in turn can constrain its origin and history. We present a method to detect density anomalies within a small body from the global gravitational potential. As is well known, such an inverse problem is ill-posed [1], and requires regularization. Our main assumption, which mitigates the non-uniqueness of the problem, is that the interior of the body is composed of a finite number of domains, in which the density is uniform. The boundary of each domain is therefore a surface, that we describe as the level-set of a function. This approach, known as the level-set method, has been extensively used in local inversions of Earth’s gravity measurements [2]. It simplifies the manipulation of complex shapes, which in our case delimit the density anomalies. In order to reduce the dimensionality of the problem, we employ parametric expressions for the level-set functions. The aim is then to determine the parameters of each level-set function, which describe the location and size of the anomalies, along with the density within each anomaly and the bulk density of the body.

We report here the results of more than 2 years of monitoring the rotation of Mars with the RISE instrument on InSight. Small periodic variations of the spin axis orientation, called nutations, can be extracted from the Doppler data with enough precision to identify the influence of the Martian fluid core. For the first time for a planetary body other than the Earth, we can measure the period of the Free Core Nutation (FCN), which is a rotational normal mode arising from the misalignment of the rotation axes of the core and mantle. In this way, we confirm the liquid state of the core and estimate its moment of inertia as well as its likely size.The FCN period depends on the dynamical flattening of the core and on its ability to deform. Since the shape and gravity field of Mars deviate significantly from those of a uniformly rotating fluid body, deviations from that state can also be expected for the core. Models accounting for the dynamical shape of Mars can thus be tested by comparing core shape predictions to nutation constraints. The observed FCN period can be accounted for by interior models having a very thick lithosphere loaded by degree-two mass anomalies at the bottom.The combination of nutation data and interior structure modeling allows us to deduce the radius of the core and to constrain its density, and thus, to address the nature and abundance of light elements alloyed to iron. The inferred core radius agrees with previous estimates based on geodesy and seismic data. The large fraction of light elements required to match the core density implies that its liquidus is significantly lower than the expected core temperature, making the presence of an inner core highly unlikely. Besides, the existence of an inner core would lead to an additional rotational normal mode the signature of which has not been detected in the RISE data.

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We present here a method for the retrieval of the internal density distribution of a small body, via a least squares inversion of its gravity field and rotational state. Multiple solutions are averaged in order to limit the effect of the a priori density distribution. Simulations show successful density map estimations even with little to no initial information on the interior structure of the body.

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 compon, Aerospace Engineering

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 compon, Aerospace Engineering