Introduction

This study presents results from a validation campaign combining microgravity experiments with numerical simulations to investigate contact dynamics in asteroid scenarios. The research is part of the ERC-funded TRACES project, which aims to characterize the behavior of granular materials in the environment of rubble-pile asteroids.

Many asteroids, ranging from a few hundred meters to several kilometers in size, are considered rubble-piles, i.e., gravitational aggregates held together by self-gravity and weak cohesion, rather than by the intrinsic strength of their bulk material [1]. Therefore, their dynamics can be effectively simulated as granular systems using N-body simulation tools. The GRAINS N-body code, used in this study, is capable of simulating gravitational interactions and contacts between large numbers of non-spherical bodies, with contact dynamics based on modules from Chrono [2]. Contact models in Chrono depend on numerous parameters, which are typically tuned to reproduce at best the macroscopic behavior of the system, rather than the local-scale properties. TRACES proposes a paradigm shift by focusing on accurate particle-scale physics, rather than relying solely on a macroscopic perspective, to enhance the realism of granular media characterization.

Experimental Campaign

The  GEMS experimental campaign, funded by ESA, included 16 tests conducted at the ZARM Drop Tower facility in Bremen. The first phase took place between October and November 2024, and the second between March and April 2025. Each phase consisted of two half-days in the GraviTower Bremen Pro, followed by six drops in the Bremen Drop Tower.

The experiments involved low-speed collisions between two 8-10 cm asteroid simulant cobbles under microgravity and vacuum conditions, replicating the asteroid environment. The simulant particles were selected to reproduce asteroid materials in terms of mechanical and surface properties. Three different sets were used: two sets were purchased from Space Resources Technologies, with chemical compositions closely matching those of carbonaceous chondrites (CM and CI), while the third set was collected from Mount Etna, with minimal atmospheric alteration. To enable the tracking, markers were placed on the simulants.

A 3D scanner was used to create a digital mesh of each cobble for the numerical replication of the experiments. In each test, the two cobbles were placed in separate bins, and the initial velocity required to obtain the collision was provided by a spring-based release mechanism. The experimental setup was mounted inside a vacuum chamber. Two high-speed cameras were placed outside the vacuum chamber, while GoPro cameras were positioned inside. Markers were tracked (Figure 1-2), and the trajectories of the cobbles before and after the contact were reconstructed.

Figure 1-2: Tracked markers from GoPro before the contact and high-speed camera after the contact.

Numerical simulations

A batch least-squares filter was implemented to estimate the initial conditions (position, velocity, attitude, and angular velocity) of the two cobbles, using the 2D pixel coordinates of the tracked markers as measurements. These pre-contact initial conditions were then used as input for the numerical simulations.

A digital twin of the experiment was developed in GRAINS to validate the contact dynamics models and tune their contact parameters. The shape of the cobbles is modeled as a mesh in Chrono, with collision detection managed through the Bullet library.

Among the contact models implemented in Chrono, namely smooth and non-smooth contacts, the non-smooth contact model with compliance [3] was selected as the most suitable for replicating the collision experiment, since this hard-body method, enhanced with damping, is expected to better reproduce the experimental results. However, all contact models are compared with experimental data to evaluate their performance. Figure 3 shows snapshots from a simulation of a Drop Tower experiment.

(a)Start: t=0s 

(b)Before contact: t=1.12s 

(c)End: t=2.219s 

Figure 3: Snapshots from a GRAINS simulation replicating an experiment conducted in the Drop Tower. The local reference frames of the cobbles are shown, with the global reference frame in black.

To accurately reproduce the post-collision trajectories observed in the experiments, the most relevant parameters to calibrate include the coefficient of friction, coefficient of restitution, compliance, and damping. A parameter estimation algorithm based on the Markov Chain Monte Carlo (MCMC) method has been developed for this purpose. The algorithm evaluates a likelihood function to assess how well the model reproduces the post-contact trajectories, based on the discrepancy between the predicted and observed 2D pixel coordinates of the markers.  The MCMC framework provides parameter distributions, giving both estimates and associated uncertainties, offering valuable insights into the sensitivity of the contact dynamics model.

Conclusions

In conclusion, useful data on contact dynamics in asteroid environments were collected during the microgravity campaign. Collisions between different pairs of cobbles were successfully observed, and the trajectories were reconstructed with satisfactory accuracy. A digital twin of the experiment and a parameter estimation algorithm were developed to validate and calibrate the contact dynamics models in GRAINS against the experimental results. The outcomes of this validation campaign will contribute to improving the realism of local-scale interaction modeling, enhancing our ability to simulate the full-scale dynamics of rubble-pile asteroids and their response to external forces.  A new experimental campaign is being designed, involving a parabolic flight with full granular media, along with a corresponding  numerical analogue scenario in GRAINS replicating the new experiments.

Acknowledgments

This work is funded by the European Union (ERC, TRACES, 101077758). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.

References

[1] K. J. Walsh. Rubble pile asteroids. Annual Review of Astronomy and Astrophysics, 56(1):593-624, 2018.

[2] F. Ferrari, M. Lavagna, and E. Blazquez. A parallel-GPU code for asteroid aggregation problems with angular particles. Monthly Notices of the Royal Astronomical Society, 492(1):749-761, 2020.

[3] A. Tasora, et al. A compliant visco-plastic particle contact model based on differential variational inequalities. International Journal of Non-Linear Mechanics 53, 2-12, 2013.

How to cite: Cremasco, A., Vaghi, S., Delfanti, L. V., Fodde, I., San Sebastian, I. L., Civati, L. F., and Ferrari, F.: Validating and Calibrating Contact Dynamics for Rubble-Pile Asteroids through Microgravity Experiments, EPSC-DPS Joint Meeting 2025, Helsinki, Finland, 7–13 Sep 2025, EPSC-DPS2025-1576, https://doi.org/10.5194/epsc-dps2025-1576, 2025.

1 Introduction

The unique abilities of low frequency spaceborne radars to probe internal structure imaging of planetary bodies at high resolution have resulted in their use on missions dedicated to kilometric-size planetary bodies. Radar instruments on these missions include in particular the upcoming JuRa instrument onboard the HERA mission which aims at imaging the binary S-type asteroid 65803 Didymos [1]. One of the major challenge when exploiting the data to reconstruct the internal structure of kilometric-size planetary bodies lies in the relatively large size of the planetary body with regard to the radar carrier signal wavelength. Given the 60MHz radar carrier frequency, Didymos' 800m diameter and Dimorphos' 160m diameter 3D domains require too much computational resources with current available hardware to perform multiple iterations of a gradient descent algorithm on all radar orbits. This problem is common in spaceborne subsurface radar sounding where the radar signal carrier frequency, driven by geophysical and technical considerations, often results in domains too large to accurately simulate radio wave propagation [2]. In order to overcome this limitation, we propose to investigate the possibility to linearize or use approximate forward operator in gradient descent algorithms. This work aims at developing robust analysis methods to process JuRa data in order to image the interior of the Didymos binary asteroid system.

2 Radar interior imaging

Internal structure imaging from spaceborne radar consists in finding the effective permittivity contrast m={χ(x)}_{x ∈ ℜ³} of the asteroid from the observed scattered field at the radar antenna for multiple locations x_l on the orbit and for angular frequency ω in the radar signal frequency band. It can be understood as a minimization problem of a chosen cost function S (e.g. least squares, Wasserstein distance) with regard to the effective permittivity contrast [3]. Such minimization problem is often solved using gradient algorithms

m_n+1 = m_n - W_n [∂f(m)/∂m]^∗_n [∂S/∂f(m)]_n

where the forward operator f(m) corresponds to Maxwell's equation along with the far-field antenna gain. W_n is a positive-definite operator (e.g. Hessian of the cost function in Newton method), [∂S/∂f(m)]_n  is the usual adjoint source (e.g. weighted residuals in least squares) and [∂f(m)/∂m]^∗_n is the conjugate transpose of the Frechet derivative [3]. JuRa is a monostatic radar, accordingly the kernel of the Frechet derivative can be expressed as a function of the the total electric field E_l,n(x,ω) associated to m_n induced by the radar source. In order to perform internal structure imaging with JuRa, it is thus only necessary to compute at each step n the electric field for each position x_l on the orbit and each angular frequency ω in the frequency band.

Fig.1: (a) Free space background model, (b) homogeneous asteroid background model, (c) true model.

Computing the electric field in Didymos and Dimorphos on all radar orbits for multiple steps n corresponds to the usual full waveform inversion algorithm [4]. Such a brute force approach requires considerable computational resources. One straightforward way to decrease the computational load is to linearize the forward operator around a fixed background effective permittivity contrast m_b

f(m) ≈ f(m_b) + [∂f(m)/∂m]_b (m- m_b)

For example, it is possible to use a free space background effective permittivity contrast, i.e. m_b=0 (Fig. 1a), which yields the popular and low computation back-propagation and pseudo-inverse methods. However, the linearization of the forward operator is only valid as long as residuals between the true and background effective permittivity contrast remain sufficiently small. The real part of the effective permittivity of Didymos and Dimorphos is estimated to vary between ε_r ∈ [4 ,7] [2] and has been showed to be too large for the linearization around a free space background to perform well due to poor focusing [5].

Homogeneous asteroid model

Fig. 2: Dimorphos homogeneous asteroid background model E_l,n(x,ω) for a given position and angular frequency along the antenna polarization component.

As an alternative, we propose to use as a background effective permittivity contrast homogeneous asteroid models with an interior effective permittivity set to an a priori estimated average value (Fig. 1b). Homogeneous asteroid models uses the shape models of Didymos and Dimorphos and strongly reduces residuals between the true and background effective permittivity contrast. Unfortunately, unlike the free space background effective permittivity contrast where E_l,n(x,ω) admits a closed form, computing E_l,n(x,ω) still requires to simulate the electric field in Didymos and Dimorphos, albeit only once. Considering Dimorphos’s largest dimension at central frequency, the domain size varies between 70 to 90 wavelengths with the expected range of ε_r. We investigate the possibility to use different numerical schemes to compute the electric field in the asteroid domain and their interior imaging performances including Discrete Dipole Approximation (DDA) and Physical Optics (PO). DDA is an accurate method which naturally handles scattering from far field sources and provides iterative accuracy improvement of E_l,n(x,ω) [6]. Our current DDA GPU implementation on an Nvidia H100 80GB requires ∼10min to accurately compute the electric field inside Dimorphos for a given position x_l and a given angular frequency ω (Fig. 2) which remains prohibitive. In order to process JuRa data volume sufficiently rapidly, a compromise needs to be found between accuracy and computational load.

Fig. 3: Comparison between simulated E_l,n(x,ω) using PO (left) and DDA (right) inside the highlighted area in Fig. 2.

PO is a surface integral method [7] which could be used to estimate E_l,n(x,ω) (Fig. 3). Additional investigation venues include: (i) reducing the number of iterations in the DDA linear solver or (ii) using geometric optics to compute E_l,n(x,ω) and physical optics to compute f(m_b).

References

[1] Michel P et al. 2022 The planetary science journal 3 160
[2] Hérique A et al. 2018 Advances in Space Research 62 2141–2162
[3] Tarantola A 2005 Inverse problem theory and methods for model parameter estimation (siam)
[4] Deng et al. (2022) IEEE Trans. Antennas & Propagation, 70(12) 11934–11945
[5] Dufaure A et al.2023 Astronomy & Astrophysics 674 A72
[6] Yurkin M A 2023 Discrete dipole approximation Light, Plasmonics and Particles (Elsevier) pp 167–198
[7] Berquin Y et al. 2015 Radio Science 50 1097–1109

How to cite: Berquin, Y., Hérique, A., Rogez, Y., Kofman, W., and Zine, S.: Internal structure imaging of Didymos with JuRa using homogeneous asteroid models, EPSC-DPS Joint Meeting 2025, Helsinki, Finland, 7–13 Sep 2025, EPSC-DPS2025-788, https://doi.org/10.5194/epsc-dps2025-788, 2025.

Introduction

Rubble-pile asteroids (those less than ∼10 km in size [1]) are loosely bound aggregates held together primarily by self-gravity between particles that compose them. Understanding their composition is an active area of research with implications for both science [2, 3] and planetary defense [4, 5]. The internal structure of a rubble-pile is an open question; models range from homogeneous distributions of particles throughout the aggregate [6] to layered structures possessing cores with distinct properties from an outer shell [7, 8]. One method of constraining the properties of a rubble-pile’s interior is to link observed surface features to seismic waves transmitted through the body. Both impacts and tidal forces generate body waves [7, 9] and are suspected to contribute to behaviors including regolith migration from micrometeoroid impact [10] or YORP spin-up [6]), body reshaping [11] and particle ejection [12].

In this work we are interested in the seismic waves generated from hypervelocity impacts and how a layered structure influences their surface expression, motivated by the HERA mission’s [13] upcoming observations of the DART impact site. We consider seismic waves generated in rubble-piles with inner cores made of larger particles than those in the outer shell. This configuration could be common if granular motion is driven by inward migration of larger particles [14]. Layering on the Moon has been suggested to enable seismically-induced surface modification over larger distances than previously known [15]. We consider how interactions between granular layers of distinct particle sizes influence the seismic disturbance of a rubble-pile’s surface, evaluating a hypothesis that larger particles in the core increases the extent of effects.

Methods

We evaluate two types of rubble-piles, comparable to Didymos (∼800 m diameter) and Dimorphos (∼150 m diameter). We build rubble-piles using GRAINS [16,17]. GRAINS simulates particle-particle contacts using the soft-body discrete element method with the ability to model non-spherical particles. Particles are randomly shaped convex hulls subject to self gravity, Hertzian contact forces and friction. While continuum-based models are often used to study impact events, they can obscure microscopic processes that may play a role in the energy transfer of wave propagation (i.e., grain scale collisions [18]). Our model is similar to [12], accounting for rough particles and layering. Our large aggregate (Fig. 1A) is made of ∼10,000 particles of ∼20 m diameter and a smaller aggregate contains meter scale boulders (∼100,000 particles, under construction).

The initial rubble-pile is aggregated from a randomly seeded cloud of particles [19]. To achieve layering, we replace the core of the homogeneous aggregate with larger particles than those in an outer shell (Fig. 1B). Layered rubble-piles undergo a settling period to ensure they are in a dynamical equilibrium state (Fig. 1C). We generate the seismic waves of an impact using the same scaling approach as [12]. A particle in the equatorial plane is selected as the synthetic impactor and given a scaled mass and velocity directed through the barycenter, equivalent to an impact’s residual seismic energy. Figure 2 shows synthetic impacts in our large rubble-pile.

Figure 1: 2D slices of our rubble-piles∗ showing their construction. A) Initial homogeneous rubble-pile, B) Cored aggregate from A, C) Aggregate from B after settling. ∗Images are non-dimensional, Fig. 2 has physical dimensions.

Figure 2: 2D slice in the impact plane of our large aggregate. Particles are colored by radial velocity for cores of half (A) and 3/4 (B) the size of the aggregate.

Results

We confirm our procedure for tracking the wavefront and assessing surface effects (Fig. 3). Preliminary results are inconclusive as to the effect of layering on surface modification due to the MPa elastic modulus (E) of our particles (Fig. 3A). However, we expect substantial disturbance of particles in the vicinity of the impact site as supported by other works exploring the surface effects of impact-induced waves [12]. Figure 3B and 3C show that our wave speed is lower than is typically considered for rubble-piles [10, 7, 9]. Increasing the E of our particles will yield larger body speeds since propagation speed in the Hertzian model is a function of E (this process requires further settling time - currently underway). Assessing how rough particles and layers of varied thickness influence the impact process may provide important context for connecting HERA’s upcoming observations of Dimorphos to its pre-DART impact state and provide insight into how the surface effects of impact reflect the internal structure of rubble-pile asteroids.

Figure 3: A and B show radial velocity vs time for particles in the outer hull (B, color corresponds to radial angle from the impact site) and interior to the rubble pile (B, color corresponds to depth). C plots the position and time of the minimums from B for impacts into different rubble-piles corresponding to a wave speed of ∼ 2 m/s.

Acknowledgments: Funded by the European Union (ERC, TRACES, 101077758). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.

References:

[1] Walsh et al. 20204, Annual Review of Astronomy and Astrophysics.

[2] Bagatin et al. 2020, Icarus.

[3] Barnouin et al. 2024 Nature Communications.

[4] Graninger et al. 2023, International Journal of Impact Engineering.

[5] Raducan et al. 2024, The Planetary Science Journal.

[6] Zhang et al. 2022, Nature Communications.

[7] Murdoch et al. 2017, Planetary and Space Science.

[8] Raducan et al. 2019, Planetary and Space Science.

[9] DellaGiustina et al. 2024, Monthly Notices of the Royal Astronomical Society.

[10] Garcia et al. 2015, Icarus.

[11] Quillen et al. 2019, Icarus.

[12] Tancredi et al. 2023, Monthly Notices of the Royal Astronomical Society.

[13] Michel et al. 2022, The Planetary Science Journal.

[14] Cheng et al. 2024, Communications Physics.

[15] Frizzell et al. 2025, Icarus.

[16] Ferrari et al. 2017, Multibody System Dynamics.

[17] Ferrari et al. 2020, Monthly Notices of the Royal Astronomical Society.

[18] Makse et al. 1999, Physical Review Letters.

[19] Ferrari et al. 2022, Icarus.

How to cite: Frizzell, E., San Sebastián, I., and Ferrari, F.: Modeling the surface effects of impact-induced seismic waves in layered rubble-pile aggregates with nonspherical particles, EPSC-DPS Joint Meeting 2025, Helsinki, Finland, 7–13 Sep 2025, EPSC-DPS2025-1470, https://doi.org/10.5194/epsc-dps2025-1470, 2025.

The European Space Agency (ESA) Hera mission is the second part of the international Asteroid Impact & Deflection Assessment (AIDA) collaboration, following NASA’s successful double asteroid redirection test (DART) impact on the binary asteroid system 65803 Didymos. Hera’s primary target is Dimorphos, the Didymos asteroid moonlet, whose structural and dynamical properties are being investigated to understand the results of kinetic impact deflection strategies. One of the mission’s core objectives is to reveal the internal composition and porosity distribution of Dimorphos through radar tomography, offering unprecedented insights into the mechanics of rubble-pile asteroids. Two CubeSats, Juventas Radar (JuRa) carrying low-frequency monostatic radar, a gravimeter and an accelometer, and Milani carrying near-infrared imager and a microthermogravimeter will be deployed near Dimorphos and send the gathered information back to Hera through Intersatellite Link (ISL) [3]. Rubble piles, which consist of loosely bound aggregates of rock held together by gravity and weak cohesive forces, pose a modeling challenge due to their granular heterogeneity and complex internal geometry. Recent works, including direct observations of the interior of the asteroid and the structure of the regolith [4], underscore the importance of validating radar-based inversion methods against known analogs. To this end, physical models with controllable structure and material properties offer a practical route for calibration and benchmarking.

In this study, we present a complete pipeline for generating, printing, and validating analogue models of Dimorphos. Using MATLAB, a synthetic rubble-pile interior was generated procedurally on the basis of a combination of stochastic field generation, ellipsoidal particle packing (EPP), and surface conformity to topographic models derived from the optic mea surements done by Didymos Reconnaissance and Asteroid Camera for OpNav (DRACO) scientific camera involved in NASA’s DART mission. These internal geometries were exported to STL format and printed using the fused filament fabrication (FFF) method [2,5],
combined with permittivity-controlled ABS filament, ensuring mechanical robustness, accurate electrical properties and radar transparency. In this context, FFF has recently gained attention in radio frequency and microwave engineering applications, owing to advances in permittivity-controlled plastic filaments [2, 5]. This development has enabled the fabrication of complex microwave-transparent structures with tunable dielectric constants, making FFF an attractive candidate for producing radar-interrogatable analogue asteroids [2, 5]. By modulating the volume fraction between filament and air both between individual boulders and inside some of them, effective permittivity can be engineered to approximate that of asteroid minerals. This presentation describes a 18 cm diameter analogue for Dimorphos which simulates the actual rubble pile structure via EPP, taking into account the granular convection and the power-law for particle size found by examining the optical data of Dimorphos [4]. The total number of ellipsoids in this model is 18.084 with the ellipsoid diameter varying between 8-16 mm following the boulder size frequency distribution (SFD) observed in [4]. Figure 1, shows the external structure of the EPP-based analogue together with a cross-sectional slice demonstrating the actual and effective internal real relative permittivity of the body. The latter one of these corresponds to 8 GHz signal bandwidth [1] for which the average effective real relative permittivity is about 2.7 and the signal envelope wavelength inside the body about 4.6 cm (3.9 diameter-to-wavelength ratio).

References:
[1] A Dufaure et al. “Imaging of the internal structure of an asteroid analogue from quasi-monostatic microwave measurement data-I. The frequency domain approach”. In: Astronomy & Astrophysics 674 (2023), A72.
[2] A. Lingua, F. Sosa-Rey, N. Piccirelli, et al. “X-Ray Tomography-Based Characterization of the Porosity Evolution in Composites Manufactured by Fused Filament Fabrication”. In: Experimental Mechanics (2024). doi: 10.1007/s11340-024-01124-3. url: https://doi.org/10.1007/s11340-024-01124-3.
[3] P. Michel, M. K¨uppers, A. Bagatin, et al. “The ESA Hera Mission: Detailed Characterization of the DART Impact Outcome and of the Binary Asteroid (65803) Didymos”. In: The Planetary Science Journal 3 (2022), p. 160. doi: 10.3847/PSJ/ac6f52. url:https://doi.org/10.3847/PSJ/ac6f52.
[4] M. Pajola, F. Tusberti, A. Lucchetti, et al. “Evidence for multi-fragmentation and mass shedding for boulders on rubble-pile binary asteroid system (65803) Didymos”. In: Nature Communications 6205 (2024), p. 12. doi: 10.1038/s41467-024-50148-9. url: https://doi.org/10.1038/s41467-024-50148-9.
[5] Liisa-Ida Sorsa et al. “Complex-structured 3D-printed wireframes as asteroid analogues for tomographic microwave radar measurements”. In: Materials & Design 198 (2021), p. 109364.

How to cite: Pajala, T., Eyraud, C., Geffrin, J.-M., and Pursiainen, S.: Rubble pile asteroid model for Dimorphos --- 65803 Didymos I, EPSC-DPS Joint Meeting 2025, Helsinki, Finland, 7–13 Sep 2025, EPSC-DPS2025-732, https://doi.org/10.5194/epsc-dps2025-732, 2025.

A lot of crucial questions about the internal structure of asteroids remain unanswered. This knowledge is fundamental, as it will provide essential data for modeling the mechanical behavior of these bodies, which is vital not only for science, but also for planetary defense [1]. Imaging the interior of these asteroids is not a trivial problem not only in terms of measurements, but also in terms of imaging algorithms. The challenges being mainly due to the very large size of these structures, and their high density and strong electromagnetic scattering. In recent years, imaging algorithms have been developed and adapted to such bodies. Some methods derive from those developed for observing the Earth and planets and adapted to imaging these bodies such as SAR tomography [2] and others methods derive from electromagnetic inverse problems as Pseudo-Inverse and Back-Propagation methods [3], [4], [5]. These imaging procedures allow structural imaging of the interior of asteroids and have two main advantages: the memory required is relatively small, so it is possible to reconstruct a large domain, which is necessary for such objects, and these procedures are generally robust to perturbations.

In this study, we focused on the algorithm developed in [3], based on Pseudo-Inverse method and combined with Principal Component Analysis (PCA). The electric scattered field on the receiver domain is obtained by the observation equation.  The induced current is estimated for each frequency using the Pseudo-Inverse method from all spatial measurement points. This takes full advantage of the spatial bandwidth of the measured field. PCA is then applied to this series of 3D images to perform a frequency-based analysis and obtain the final 3D image of the scene.

In the present study, this imaging method was applied to the scattered field of analogues measured in the laboratory, in our anechoic chamber, with the Institut Fresnel setup (Figure 1 (a)). Analogue size and wavelength are reduced by the same factor, following the microwave analogy. [6]. The configuration was chosen as quasi-monostatic to be similar to those used in space radars, such as the JuRa radar on board the Hera mission, which will probe the binairy asteroid 65803 Didymos. Figure 1 (b) shows an example of the results for the interior of the asteroid 25143 Itokawa analogue reproduced by 3D printing [7] using monostatic measurement points on a large part of a sphere around the analogue and the frequency band [3.5-10] GHz. In this slice of the 3D image, the interior void of the analogue can be seen at the correct position. The results obtained from different analogues of asteroids will be presented. An analysis of the images obtained as a function of the number of spatial measurements, the bandwidth as well as the number of frequencies will also be proposed.

Figure 1: (a) Measurement configuration in the anechoic chamber of the Institut Fresnel, Marseille 

Figure 1 (b) : Slice of the 3D reconstructed image of a analogue of the 25143 Itokawa asteroid

References

[1] A. Herique and al. Direct observations of asteroid interior and regolith structure: Science measurement requirements. Advances in Space Research, 2018.

[2] O. Gassot, A. Herique, W. Fa, J. Du, and W. Kofman. Ultra-wideband sar tomography on asteroids. Radio Science, 56(8), 2021.

[3] A. Dufaure, C. Eyraud, L.-I. Sorsa, Y. O. Yusuf, S. Pursiainen, and J.-M. Geffrin. Imaging of the internal structure of an asteroid analogue from quasi-monostatic microwave measurement data - i. the frequency domain approach. Astronomy and Astrophysics, 674(A72), 2023.

[4] L.-I. Sorsa, Y. O. Yusuf, A. Dufaure, J.-M. Geffrin, C. Eyraud, and S. Pursiainen. Imaging of the internal structure of an asteroid analogue from quasi-monostatic microwave measurement data - ii. the time domain approach. Astronomy and Astrophysics, 674(A73), 2023.

[5] M.S. Haynes, I. Fenni, and B.J.R. Davidsson. Inverse scattering under the born approximation using an object t-matrix and full bistatic spherical sampling geometry. IEEE Transactions on Antennas and Propagation, 72, 2024.

[6] R. Vaillon and J.-M. Geffrin. Recent advances in microwave analog to light scattering experiments. Quantitative Spectroscopy and Radiative Transfer, 146, 2014.

[7] Liisa-Ida Sorsa, Christelle Eyraud, Alain H´ erique, Mika Takala, Sampsa Pursiainen, and Jean-Michel Geffrin. Complex-structured 3d-printed wireframes as asteroid analogues for tomographic microwave radar measurements. Materials and Design, 198, 2021.

How to cite: Eyraud, C., Dufaure, A., Oluwatoki Yusuf, Y., Sorsa, L.-I., Henry, G., Pursiainen, S., and Geffrin, J.-M.: Imaging of the Inner Structure of an asteroid analogue from lab-Measurements with frequency analysis, EPSC-DPS Joint Meeting 2025, Helsinki, Finland, 7–13 Sep 2025, EPSC-DPS2025-708, https://doi.org/10.5194/epsc-dps2025-708, 2025.

Multi-component asteroid systems can be defined as collections of several distinct components, each of which may be a rubble pile body itself. There are a number of clear examples of these systems that have been observed, including binary and triple asteroids, contact binaries, asteroid pairs and clusters, and any asteroid system that has distinct components which may themselves be rubble piles. Current observations indicate that almost 50% of small, rubble pile asteroids are multi-component systems, thus these form an essential aspect of the asteroid population and their formation circumstances and evolution remain a largely open question. Of specific interest is how the different components interact with each other and form the observed asteroid population. It can be shown that for kilometric-scale and smaller bodies that such separated components can rest on each other without undergoing large-scale shape failure (Meyer & Scheeres, ApJL 963:L14, 2024), thus indicating that the components of contact binaries can themselves be rubble piles. This opens up the analysis of these bodies as few-component systems where these components can orbit each other, rest on each other, and even undergo slow collisions while still maintaining their distinct components. 

In this work we leverage these observations to analyze how the formation and evolution of such multi-component systems can be viewed in a consistent framework. To do this we leverage recent theoretical advances and analysis tools reported in (Scheeres, CMDA 135:35, 2023) and (Scheeres, Icarus  436:116563, 2025) to present a unified approach to modeling and constraining the formation and evolution of multi-component systems. These models enable us to evaluate the conditions for a system to form a contact binary or orbital binary at formation, conditions under which a system can eject a component to become an asteroid pair or cluster, pathways for a system to collapse into a contact binary, implications of exogenous forces, and the overall pathways that these systems can follow. 

These mechanical analyses are based on modeling the components as semi-rigid bodies and tracking the total angular momentum and energy of the system, both orbital and rotational, and the relative mass distributions between the components. Both analytical and numerical simulation approaches can be used. Based on fundamental celestial mechanics constraints, we can delineate the different energetically stable configurations that a multi-component system can have as a function of its total angular momentum. Thus, if a system is spun up or down due to YORP, the possible configurations of the system will change with the changing angular momentum. If a multi-component system reaches a fission spin limit, which generally occurs before surface shedding of material, its subsequent evolution will be largely dictated by the relative masses of the different components, and can lead to the creation of an asteroid pair and a slowly rotating primary, settle into a binary system, or can reconfigure its components and evolve further. The theory can provide a clear overarching approach to the analysis of outcomes, which can help inform our interpretation of the asteroidal bodies that we observe from Earth or Space-based observing platforms.  

This talk will apply this methodology to illustrate the possible evolution of several different example systems, and also address the limitations of this modeling approach.  

How to cite: Scheeres, D.: Mechanics of multi-component asteroid systems, EPSC-DPS Joint Meeting 2025, Helsinki, Finland, 7–13 Sep 2025, EPSC-DPS2025-201, https://doi.org/10.5194/epsc-dps2025-201, 2025.

Several landmark space missions have focused on characterizing small bodies and advancing planetary defense, including NASA’s DART and ESA’s Rosetta and Hera missions [4]. The DART mission successfully demonstrated kinetic impact as a viable asteroid deflection technique by altering the orbital period of Dimorphos, the smaller body in the Didymos binary asteroid system [5]. The Hera mission will follow up on this event by conducting a detailed post-impact survey of the same system. HERA includes two CubeSats, Juventas and Milani. Juventas is equipped with the low-frequency monostatic radar JuRa, which will perform the first direct probing of an asteroid’s subsurface structure. JuRa transmits a binary phase-shift keyed signal with a 20 MHz bandwidth and a 60 MHz carrier frequency, powered at 5 W. The signal wavelength is approximately 5 m in vacuum and about 2.5 m within the asteroid, assuming a relative permittivity consistent with typical porous silicate materials [4].

Electromagnetic (EM) tomography [3, 2, 1] offers a non-invasive means to investigate the internal structure of asteroids, aiming to recover spatial variations in relative permittivity and density by analyzing scattered wavefields. This study focuses on simulated monostatic radar tomography, where both transmission and reception are conducted from a single satellite platform. Special attention is given to the role of wave polarization in the accuracy of structural reconstructions. Polarization, which describes the orientation of the electric field vector, is an intrinsic property of EM waves. Neglecting it can reduce computational complexity, but may affect the fidelity of the reconstructions.

The primary objective of this research is to determine how accurately a synthetic asteroid model’s internal structure can be reconstructed without modelling polarization: a strategy that can significantly reduce computational cost. To this end, the study compares simulations of EM wave propagation and tomography using single-component (scalar) and three-component (vectorial) field models. The performance of these two alternative approaches is evaluated in terms of their ability to resolve internal voids and structural boundaries.

In this study, a numerical solution for the wavefield is found via leapfrog time-stepping [6]. The Green’s function, which characterizes the impulse response of the medium, is estimated using Tikhonov-regularized deconvolution and Born approximation [7], allowing for tractable linearization of the forward problem. Several inversion strategies are explored for reconstructing the spatial distribution of relative permittivity, including tomographic back-projection and total variation (TV) regularization.

The results present the reconstructions generated from both single- and three-component models, under noiseless and noisy signal conditions. Accuracy is quantitatively assessed using overlap metrics between the reconstructed regions and ground-truth internal features, specifically focusing on voids alone and voids with surrounding structural boundaries. For noisy simulations, Gaussian noise is added to the synthetic data, and reconstruction robustness is visualized using box plots depicting overlap quantiles. Additionally, the influence of the signal envelope is investigated in a similar fashion, providing further insight into reconstruction stability and performance. The results suggest that omitting polarization does not necessarily deteriorate the quality of the structural maps, especially in the presence of uncertainty factors, such as modelling discrepancies due to signal carrier and measurement noise.

References

[1] Jian Deng et al. “EI+ FWI method for reconstructing interior structure of asteroid using lander-to-orbiter bistatic radar system”. IEEE Transactions on Geoscience and Remote Sensing, 60 (2021), pp. 1–16.
[2] A. Dufaure et al. “Imaging of the internal structure of an asteroid analogue from quasi-monostatic microwave measurement data—I. The frequency domain approach”. Astronomy & Astrophysics, 674 (2023), A72.
[3] Mark Haynes et al. “Asteroids Inside Out: Radar Tomography”. (2020).
[4] Patrick Michel et al. “The ESA Hera Mission: Detailed Characterization of the DART Impact Outcome and of the Binary Asteroid (65803) Didymos”. The Planetary Science Journal, 3.160 (2022), pp. 1–21. doi:10.3847/PSJ/ac6f52. URL.
[5] Andrew S. Rivkin et al. “The double asteroid redirection test (DART): Planetary defense investigations and requirements”. The Planetary Science Journal, 2.5 (2021), p. 173.
[6] John B. Schneider. “Understanding the finite-difference time-domain method. School of Electrical Engineering and Computer Science, Washington State University”. URL: http://www.eecs.wsu.edu/~schneidj/ufdtd/ (2010).
[7] Liisa-Ida Sorsa et al. “A time-domain multigrid solver with higher-order Born approximation for full-wave radar tomography of a complex-shaped target”. IEEE Transactions on Computational Imaging, 6 (2020), pp. 579–590.

How to cite: Pajala, T., Tuumanen, M., Yusuf, Y. O., Koulouri, A., and Pursiainen, S.: Simulation Study for Numerical Effects of Polarized vs. Non-Polarized Signal Propagation in Radar Tomography of Asteroids, EPSC-DPS Joint Meeting 2025, Helsinki, Finland, 7–13 Sep 2025, EPSC-DPS2025-31, https://doi.org/10.5194/epsc-dps2025-31, 2025.