Momentum transfer from the DART mission kinetic impact on asteroid Dimorphos

This work addresses a central planetary defence question: how much momentum is transferred to a small body by a spacecraft kinetic impact, relative to the spacecraft’s incident momentum. The DART mission impacted Dimorphos, the secondary in the Didymos binary, to validate kinetic impact as a deflection technique. The key objective is to determine the momentum enhancement factor β, which quantifies the ratio of imparted momentum to the impactor’s momentum along the net ejecta momentum direction. By estimating the impact-induced change in Dimorphos’s along-track orbital velocity from the observed change in binary orbit period, and combining this with the impact geometry and ejecta direction, the study derives β and evaluates the effectiveness of kinetic impact for asteroid deflection.

Prior theoretical, numerical and experimental studies have explored momentum transfer in asteroid impacts and generally predict β values between about 1 and 6. Analytical scaling relations and simulations have highlighted the roles of target material properties (cohesion, porosity, friction) and impact conditions in determining ejecta and momentum transfer. Laboratory hypervelocity impact experiments on rock and meteoritic analogs and numerical models for DART-like scenarios support the possibility of β > 1 due to ejecta recoil. However, multiple combinations of mechanical properties can produce similar β, underscoring the need for in situ constraints and post-impact observations to better infer target properties.

The study computes β using a dynamics-informed Monte Carlo framework coupled to a full two-body problem (F2BP) numerical integrator. Key steps: 1) Parameter sampling: 100,000 Monte Carlo realizations sample uncertainties in the triaxial ellipsoidal shapes of Didymos and Dimorphos, Dimorphos’s pre-impact orbit semimajor axis and pre- and post-impact periods (with covariance), Dimorphos’s bulk density (uniformly between 1,500–3,300 kg m−3), and the net ejecta momentum direction E (assigned from observations with a conservative ±15° uncertainty). DART’s mass and impact velocity and Didymos’s pole orientation are treated as fixed due to negligible uncertainties. 2) Dynamical solution: For each realization, a secant-search iteratively finds Didymos’s density that reproduces the sampled pre-impact period given the sampled shapes and separation, and a second secant-search finds the along-track Δv required to match the sampled post-impact period. The General Use Binary Asteroid Simulator (GUBAS) propagates coupled rotational–orbital dynamics including second-order gravity terms appropriate for the tight binary. Average orbital periods are measured over 30 days to capture spin–orbit coupling effects. Convergence targets exceed observational precision by 10×. Tests with fourth-order gravity (≈4,000 runs) yield consistent Δv within uncertainties, justifying second-order gravity for the main analysis. 3) Ejecta direction: The ejecta cone axis, inferred from Hubble Space Telescope and LICIACube imaging, provides the net ejecta momentum direction E pointing to RA ≈ 138°, Dec ≈ +13°, with ±15° uncertainty. 4) β estimation: Using the computed along-track Δv, Dimorphos’s mass (from sampled volume and density), and E, β is computed from the momentum balance formulation that references the ejecta momentum direction. Assumptions include near-synchronous pre-impact rotation of Dimorphos and a nearly circular orbit, instantaneous momentum transfer, and neglect of minor effects such as small impact torque on rotation and reshaping/mass loss, which are below current period measurement uncertainties.

- The along-track component of Dimorphos’s velocity change due to DART is Δvt = −2.70 ± 0.10 mm s−1 (1σ), consistent with the observed binary orbit period decrease of 33.0 ± 1.0 minutes (3σ). - The net ejecta momentum direction is toward RA ≈ 138°, Dec ≈ +13°. - The momentum enhancement factor β depends on Dimorphos’s bulk density: across 1,500–3,300 kg m−3, the mean β spans ≈2.2 to 4.9; overall β lies between ≈1.9 and 5.5 within 3σ. - For an assumed Dimorphos density of 2,400 kg m−3 (equal to the system density), β = 3.61 ± 0.19 (1σ) in the main Monte Carlo fit; equivalently reported as β = 3.6+0.13−0.10 (1σ). - β > 2 indicates ejecta recoil contributed more momentum than the spacecraft’s incident momentum, demonstrating high deflection efficiency for the DART impact.

The derived Δvt and β demonstrate that kinetic impact can yield momentum transfer substantially exceeding the incident spacecraft momentum due to ejecta recoil. These findings directly validate the effectiveness of kinetic impact for planetary defense at realistic scales. A β around 3–4 implies that, compared with a no-ejecta case (β = 1), a given impactor can deflect an asteroid with less warning time or enable deflection of larger bodies for the same warning time. The dependence of β on assumed bulk density highlights the current uncertainty in Dimorphos’s mass, emphasizing the importance of post-mission characterization. Although simulations and laboratory experiments predicted β in the observed range, the in situ determination provides the first full-scale confirmation. Future integration of the β estimate with impact site geology and ejecta morphology will refine interpretations of Dimorphos’s material properties, and ESA’s Hera mission measurements (mass and orbital state) will substantially improve β precision and reduce model degeneracies.

This study provides the first full-scale determination of momentum transfer from a spacecraft kinetic impact on an asteroid, quantifying the along-track velocity change and the momentum enhancement factor β for Dimorphos. The results show Δvt ≈ −2.70 mm s−1 and β ≈ 3.6 (for ρ ≈ 2,400 kg m−3), indicating ejecta-driven momentum significantly amplified the deflection beyond the impactor’s incident momentum. The work establishes kinetic impact as a highly effective deflection technique and delivers a methodology that couples observed orbital changes with detailed dynamics and ejecta geometry. Future research will refine β with Hera’s mass and orbital measurements, integrate geological constraints from DART and ejecta observations, and explore target property dependencies and higher-order dynamical effects to enhance predictive capability for planetary defense missions.

- Dimorphos’s bulk density is unmeasured and treated as an independent variable; β depends sensitively on this assumption. - The net ejecta momentum direction is inferred from imaging with an assumed ±15° uncertainty; non-uniform momentum distribution in the ejecta cone could bias E. - Shape models are approximated as triaxial ellipsoids with uniform density; internal heterogeneity and higher-order gravity terms are not fully captured (higher-order terms tested on a smaller sample show negligible impact within current uncertainties). - Assumptions include near-synchronous pre-impact rotation and nearly circular orbit; small deviations are possible but considered minor. - Momentum transfer is assumed instantaneous; small torques from off-center impact and effects from reshaping/mass loss are neglected as they are below current period measurement precision. - The β estimate is derived from along-track Δv component only; full 3D Δv is not directly constrained. - Post-impact orbit uncertainties (≈1 minute) and model simplifications will persist until Hera provides improved system characterization.