Flavia Saveriano

The impact of the Double Asteroid Redirection Test (DART) spacecraft on Dimorphos in 2022 provided the first controlled kinetic-impact experiment on an asteroid and enabled observations of the resulting ejecta environment [1]. The observed momentum transfer [1, 2] and ejecta evolution highlighted the importance of understanding the complex dynamics governing debris transport in binary asteroid systems. In particular, the diversity in ejecta particle sizes produces a wide range of dynamical behaviours, from rapidly escaping micrometre dust to larger boulders primarily influenced by the mutual gravity of the Didymos-Dimorphos system. With ESA’s Hera mission scheduled to arrive at the system in late 2026 [3], understanding the long-term evolution of post-impact ejecta has become increasingly relevant.In this work, we investigate the possibility of ejecta capture within co-orbital tadpole regions surrounding the equilateral equilibrium points of the post-impact Didymos-Dimorphos system, extending previous studies of ejecta capture in binary asteroid environments [4]. The Circular Restricted Three-Body Problem (CRTBP) [5] with parameters representative of the Didymos binary system is employed to study the dynamics near the L4 and L5 equilibrium regions. Families of periodic tadpole orbits [6] are computed through differential correction and continuation methods [7], and their stability and surrounding dynamical environment are analysed using Poincaré maps. Figure 1 shows representative families of bounded tadpole trajectories around both equilateral equilibrium regions up to nondimensional amplitudes of approximately 0.6 [nd], selected to visualize the transition from near-linear librational motion to increasingly nonlinear co-orbital configurations approaching the horseshoe-transition domain. The surrounding dynamical structure is consistent with KAM-type behaviour [8], indicating the persistence of locally bounded motion in the vicinity of the tadpole families.To investigate whether DART ejecta can access these regions, multiple trajectories are propagated from the Dimorphos surface at the impact location over a range of ejection velocities and geometries representative of DART-generated debris. The simulations show that a subset of ejecta trajectories naturally enters the tadpole regions surrounding both L4 and L5, where capture and sustained librational motion can occur before eventual escape or re-impact.Preliminary long-term integrations indicate that some ejecta trajectories may remain confined within the co-orbital regions for extended durations. These results suggest that resonant co-orbital motion may contribute to the long-term evolution of debris in the Didymos system and provide a dynamical framework for understanding ejecta transport and confinement in binary asteroids, with potential relevance for interpreting the debris environment to be encountered by Hera.Future work will extend this analysis beyond the idealized CRTBP by incorporating additional perturbations relevant to the Didymos-Dimorphos environment, including solar radiation pressure with a double-eclipse shadowing, third-body perturbations, and irregular gravity fields represented by polyhedral models of both primaries. While these perturbations break the idealized CRTBP geometry, the periodic tadpole solutions computed here provide suitable initial guesses for identifying surviving bounded trajectories in the perturbed system.Figure 1: Families of periodic tadpole trajectories around the L4 and L5 equilibrium regions of Didymos-Dimorphos system in the CRTBP. The colour bar represents the Jacobi constant, illustrating the nonlinear growth and deformation of the co-orbital families with increasing amplitude up to 0.6 [nd].References[1] Li, Jian-Yang, et al. "Ejecta from the DART-produced active asteroid Dimorphos." Nature 616.7957 (2023): 452-456.[2] Ferrari, Fabio, et al. "Morphology of ejecta features from the impact on asteroid Dimorphos." Nature communications 16.1 (2025): 1601.[3] Michel, Patrick, et al. "The ESA Hera mission: detailed characterization of the DART impact outcome and of the binary asteroid (65803) Didymos." The planetary science journal 3.7 (2022): 160.[4] Fu, Xiaoyu, et al. "Orbital Capture of Ejecta into Periodic Orbits around Binary Asteroid (65803) Didymos." The Planetary Science Journal 6.7 (2025): 174.[5] Szebehely, Victor, and E. Grebenikov. "Theory of Orbits-The Restricted Problem of Three Bodies." Soviet Astronomy, Vol. 13, p. 364 13 (1969): 364.[6] Murray, Carl D., and Stanley F. Dermott. Solar system dynamics. Cambridge university press, 1999.[7] Munoz-Almaraz, Francisco J., et al. "Continuation of periodic orbits in conservative and Hamiltonian systems." Physica D: Nonlinear Phenomena 181.1-2 (2003): 1-38.[8] Arnold, Vladimir I. "Small denominators and problems of stability of motion in classical and celestial mechanics." Russian Mathematical Surveys 18.6 (1963): 85-191.

On 26 September 2022, NASA's DART spacecraft successfully demonstrated the deflection of a near-Earth object by intentionally impacting Dimorphos, the secondary body of the Didymos binary asteroid system. This historic event marked the first extensive observation of the post-impact dynamics ejecta from a binary asteroid system [1, 2], offering invaluable insight into the behaviour of an impact event in “active” asteroids.Post-impact observations of the system were facilitated by LICIACube, the Hubble and James Webb Space Telescopes, and ground-based observatories, thus, revealing a wide particle size distribution, with some material experiencing temporary orbital capture within the binary system [3]. Additionally, smaller millimetre-sized particles, strongly influenced by solar radiation pressure, were quickly expelled from the system, whereas larger, meter-sized particles remained in orbit for longer periods [4]. These findings highlight the complexity of the ejecta dynamics, including the potential for temporary orbital capture of larger objects.Despite these observations, a systematic probabilistic mapping [5, 6, 7] of post-impact material transfer onto Didymos remains as of yet unexplored.In view of ESA’s Hera mission, launched on October 7, 2024 [8] and due to arrive at Didymos in late 2026, an ideal opportunity arises to perform a comprehensive investigation of particle dynamics within the binary system. Hera’s arrival offers a unique chance not only to survey Didymos and its composition but also to study the long-term orbital capture and evolutionary behaviour of particles within this environment [8]. Moreover, an opportunity to track reaccreted fresh material post-impact.In this work, the dynamics of a perturbed two-body problem is used to provide the first comprehensive probability maps of ejecta re-impacting onto Didymos. The model is formulated in a Didymos-centred inertial frame, incorporating the point-mass gravity of both Didymos and Dimorphos, solar tidal acceleration computed from SPICE kernel ephemerides, eclipse-modulated solar radiation pressure, and third-body solar gravity.In implementing this model, the surface of Dimorphos is discretised into nodes, each launching massless particles at a grid of ejection speeds and five distinct elevation angles (15, 30, 45, 60, and 75 degrees) [6]. Trajectories are integrated utilising a variable-step Adams-Bashforth-Moulton scheme. This study adapts and expands the probabilistic ejecta-transfer methodology previously developed by Chappaz et al. [6] for Mars and its moons, specifically tailoring it to the Didymos-Dimorphos system.From these simulations, the resulting transfer-efficiency maps quantify both the global mass-exchange fraction for the complete DART ejecta population and illustrate how variations in angle and ejection speed shape surface-contamination patterns on Didymos.Unlike Langner et al. [9], who investigated only specific subsets of boulder sizes and velocities using a shock-physics and N-body pipeline to characterize individual re-impact trajectories, this study adopts a fully parametrised probabilistic approach. By covering the entire ejecta parameter space, this research produces high-resolution probability and contamination maps and detailed quantitative estimates of mass transfer. Additionally, the current analysis considers a broader spectrum of perturbations, whereas Langner et al. [9] restrict their model to MacCullagh gravity with minimal solar and tidal effects. Future extensions of this work, if feasible, will incorporate modelling of higher-order gravitational effects, further improving the study’s depth and accuracy.In conclusion, this systematic probabilistic survey contributes to the understanding of ejecta dynamics, enhancing secondary-ejecta hazard assessments for the spacecraft operations, directly supporting ESA's Hera mission objectives, facilitating safer navigation and more effective scientific interpretation of remote-sensing data from the post-impact Didymos environment. AcknowledgementsDr Stefania Soldini was supported by the Medical Research Council UKRI-FLF grant number MR/W009498/1. References[1] J.-Y. Li, M. Hirabayashi, T. L. Farnham, et al, Ejecta from the dart-produced active asteroid dimorphos, Nature 616 (2023) 452–456.[2] A. Graykowski, R. A. Lambert, F. Marchis, et al, Light curves and colours of the ejecta from dimorphos after the dart impact, Nature 616 (2023) 461–464.[3] E. G. Fahnestock, A. F. Cheng, S. Ivanovski, et al, Pre-encounter predictions of dart impact ejecta behavior and observability, The Planetary Science Journal 3 (2022) 206.[4] F. Ferrari, S. D. Raducan, S. Soldini, M. Jutzi, Ejecta formation, early collisional processes, and dynamical evolution after the dart impact on dimorphos, The Planetary Science Journal 3 (2022) 177.[5] D. J. Kessler, Derivation of the collision probability between orbiting objects: The lifetimes of jupiter’s outer moons, Icarus 48 (1981) 39–48.[6] L. Chappaz, H. J. Melosh, M. Vaquero, K. C. Howell, Transfer of impact ejecta material from the surface of mars to phobos and deimos, Astrobiology 13 (2013) 963–980.[7] E. J. Opik, Collision probabilities with the planets and the distribution of interplanetary matter, Proceedings of the Royal Irish Academy. Section A : Mathematical and Phisical Sciences 54 (1951) 165–199.[8] X. Fu, S. Soldini, F. Saveriano, Orbital capture of the dart impact ejecta around the didymos binary asteroid system.[9] K. Langner, E. Martellato, R. Luther, F. Marzari, A. Rossi, Secondary impact debris in the didymos system: what could be observed by hera?, arXiv preprint arXiv:2503.08158 (2025).

The successful impact of the Double Asteroid Redirection Test (DART) spacecraft on Dimorphos enabled the first-ever extensive observation of a postimpact ejecta tail from a binary asteroid system. Studying the ejecta can provide insights into impact physics and asteroid composition and inform future asteroid missions. In this research, the orbital capture of the impact ejecta around the Didymos binary asteroid system is investigated. The ejecta dynamics are described using an augmented bicircular restricted four-body model, which incorporates the binary’s irregular gravity field and solar radiation pressure (SRP) acceleration. Typical periodic orbit (PO) families, including planar Lyapunov and terminator orbits, are selected as the candidates for capture analysis. The candidate POs are perturbed and backward-propagated using the invariant manifold theory, and eligible trajectories intersecting the asteroids’ surfaces are recorded. The ejecta characteristics of different POs are summarized from three principal aspects: ejection location, ejection velocity, and ejection angle. The influence of two critical factors is qualitatively assessed, including the geometry of the asteroids in the binary system and the strength of SRP acceleration. Lastly, the likelihood for the ejecta from the DART impact being transferred to candidate POs is assessed.