Mass distribution within the Didymos system: predicted constraints from future Hera geodetic observations

Constraining the interior structures of asteroid Didymos and its moon, Dimorphos, is key to understanding their origin and history. In the case of Dimorphos, the current interior state could provide additional information on the effects of the impact by the NASA DART spacecraft. The ESA Hera mission will reach the Didymos binary system in 2026 and allow to characterize the gravity environment and rotational state of the two bodies. These properties are in turn sensitive to the mass distribution within the asteroids. 

We perform simulations focused on the retrieval of known mass distributions for Didymos and Dimorphos, based on the observations that are expected from the Hera mission. In our approach [1], which relies on the level-set method, we use iterative least-squares to solve the non-linear problem of estimating a set of scalar functions defined over the body. The 0-level-sets of such functions represent interfaces between areas of uniform density (density anomalies). The interior is discretized via a uniform grid, surrounded by the polyhedral mesh representing the external shape of the body. At each iteration, the solve-for parameters are the values of the level-set functions at the grid nodes, along with the density values within each anomaly. 

Our assumptions over type, resolution, and uncertainty of the geodetic observables are based on the simulations performed by the Hera radio-science team [2]. The synthetic measurements we consider include the coefficients of the spherical-harmonics expansion of the gravitational potential. Additionally, and depending on the spin state of Dimorphos at Hera’s arrival, estimates of its libration amplitude or the full tensor of inertia of both asteroids might be available. While both bodies are expected to be rubble-piles, we consider different types of interior models as ground-truth.  

The interpretation of the data in terms of interior structure is limited by the resolution and uncertainty of the gravity field, which is expected to reach degree 3 (of the spherical-harmonics expansion) for Didymos and degree 2 for Dimorphos. Therefore, the measurements would only allow to detect large-scale heterogeneities, such as those due to large boulders or voids inside the body, or produced by sizeable variations in porosity. 

More problematic is the non-uniqueness inherent to gravity inversion, which prevents unambiguous determination of the interior structure, even when gravity is complemented by the inertia tensor. Combination with other observables sensitive to the interior properties is therefore desirable. Here, we consider the impact of local-gravity information provided by the GRASS gravimeter on the surface of Dimorphos [3]. Radar-sounding information provided by the JuRa instrument [4], along with insights from surface data or laboratory studies, could additionally be introduced in the inversion as direct constraints on the level-set functions and the density values.  

By exploring the range of converged solutions in each simulation scenario, we show how the different sets of measurements and the different assumptions on their uncertainty affect the space of plausible density distributions. 

 

[1] Caldiero, A., & Le Maistre, S. (2024). Small bodies global gravity inversion via the level-set method. Icarus, 411, 115940. 

[2] Gramigna, E., Manghi, R. L., Zannoni, M., Tortora, P., Park, R. S., Tommei, G., ... & Kueppers, M. (2024). The hera radio science experiment at didymos. Planetary and Space Science, 246, 105906. 

[3] Ritter, B., Karatekin, Ö., Carrasco, J. A., Noeker, M., Ümit, E., Van Ransbeek, E., ... & Van Ruymbeke, M. (2021). Surface Gravimetry on Dimorphos with GRASS on Juventas. In 7th IAA Planetary Defense Conference (p. 190). 

[4] Herique, A., Plettemeier, D., & Kofman, W. (2024). Radar Tomography of Asteroid Deep Interior-JuRa/HERA to Didymos and Ra proposed to APOPHIS. In Europlanet Science Congress 2024 (pp. EPSC2024-753).