Momentum transfer from the DART mission kinetic impact on asteroid Dimorphos

Abstract

The NASA Double Asteroid Redirection Test (DART) mission performed a kinetic impact on asteroid Dimorphos, the satellite of the binary asteroid (65803) Didymos, at 23:14 UTC on 26 September 2022 as a planetary defence test¹. DART was the first hypervelocity impact experiment on an asteroid at size and velocity scales relevant to planetary defence, intended to validate kinetic impact as a means of asteroid deflection. Here we report a determination of the momentum transferred to an asteroid by kinetic impact. On the basis of the change in the binary orbit period², we find an instantaneous reduction in Dimorphos's along-track orbital velocity component of 2.70 ± 0.10 mm s^-1, indicating enhanced momentum transfer due to recoil from ejecta streams produced by the impact^3,4. For a Dimorphos bulk density range of 1,500 to 3,300 kg m^-3, we find that the expected value of the momentum enhancement factor, β, ranges between 2.2 and 4.9, depending on the mass of Dimorphos. If Dimorphos and Didymos are assumed to have equal densities of 2,400 kg m^-3, [Formula: see text]. These β values indicate that substantially more momentum was transferred to Dimorphos from the escaping impact ejecta than was incident with DART. Therefore, the DART kinetic impact was highly effective in deflecting the asteroid Dimorphos.

Fig. 1. Schematic of the DART impact geometry on Dimorphos.

The pre-impact orbit is shown with a solid line around Didymos. The dashed line sketches the orbit change due to the impact. Orbits are drawn roughly to scale. The positive pole direction of Didymos is $\hat{\mathbf{h}}$ (pointing down in the bottom panel). DART’s incident direction is $\hat{\mathbf{U}}$, the net ejecta momentum direction is $\hat{\mathbf{E}}$ (which points to a right ascension (RA) and declination (Dec) of 138° and +13°, respectively), and the direction of Dimorphos’s orbital motion, referred to as the along-track direction, is ${\hat{\mathbf{e}}}_{\mathrm{T}}$. The relative positions of the Sun and the Earth are also indicated. The upper panel shows the view from Didymos’s negative pole direction, whereas the lower panel provides a perspective view. Scale bar, 1 km.

Fig. 2. Probability distribution of Δv_T, the along-track component of the change in Dimorphos’s velocity induced by DART’s impact, generated by our Monte Carlo analysis that samples over input parameter uncertainties.

The histogram consists of 100,000 Monte Carlo samples and is normalized to an area of unity. A Gaussian fit to the distribution indicates a mean Δv_T of −2.70 mm s⁻¹ with a standard deviation of 0.10 mm s⁻¹.

Fig. 3. β as a function of Dimorphos’s bulk density ρ_B, from the dynamical Monte Carlo analysis.

Individual samples are plotted as points, whereas the linear fit for the mean β is plotted as the solid line and the dotted lines show the 1σ confidence interval. The colour bar indicates the mass of Dimorphos corresponding to each Monte Carlo sample, which is determined by bulk density and the volume. The density range shown corresponds to the 3σ range of the Didymos system density, whereas the shaded region highlights the 1σ range. If the density of Dimorphos were 2,400 kg m⁻³, the densities of Didymos and Dimorphos would be the same as the system density, and β = ${3.61}_{-0.25}^{+0.19}$ (1σ). For context, the densities of three other S-type near-Earth asteroids are in the range shown: 433 Eros at 2,670 ± 30 kg m⁻³; 25143 Itokawa at 1,900 ± 130 kg m⁻³ and 66391 Moshup at 1,970 ± 240 kg m⁻³.

Extended Data Fig. 1. Outline of algorithm used to calculate β.

The Monte Carlo variables are outlined by dashed lines and are defined as follows: pre-impact orbit period P_pre; pre-impact orbit semimajor axis a_pre; Didymos ellipsoid extents A_x, A_y, A_z; Dimorphos ellipsoid extents B_x, B_y, B_z; Dimorphos density ρ_B; post-impact orbit period P_post; and net ejecta momentum direction $\hat{E}$. First, a secant algorithm iterates Didymos density ρ_A to match P_pre. Next, another secant algorithm iterates the along-track change in Dimorphos’s velocity Δv_T to match P_post. Finally, M is calculated using the ellipsoid extents and density of Dimorphos, and then combined with Δv_T and $\hat{E}$ to calculate β.

Extended Data Fig. 2. Ejecta cone orientation lies in the swaths of sky (black lines) defined by HST and LICIACube observations.

The light-blue envelope outlines the axis position uncertainty in the direction measured in the sky plane. Red lines divide the along-plane swaths into regions that are excluded based on cone morphology in LICIACube images: 1) and 2) are excluded because the ejecta cone would point in the opposite direction from what is observed; 3) is excluded because the axis would lie too close to the sky plane; 4) is excluded because the axis would lie too close to the line-of-sight; and 5) is the expected region for the axis orientation. The yellow dot denotes the best solution (RA,Dec) = [138°,+13°] with the dark-blue envelope showing the extent of possible solutions. The red square is the direction of the incoming DART trajectory [128°,+18°] and the green triangle shows Dimorphos’s velocity vector [134°,+5°]. The LICIACube swath is defined for the +175 s image shown in Extended Data Fig. 3.

Extended Data Fig. 3. Two LICIACube LUKE images showing the ejecta morphology that were used to reduce the possible axis orientation solutions.

The left panel shows an approach observation, 156 s after impact, with the ejecta in front of and partially obscuring Dimorphos. The right panel shows the ejecta morphology after close approach, 175 s after impact, with Dimorphos silhouetted against the ejecta cone. The images show the red channel from frames LICIACUBE_LUKE_L2_1664234220_00005_01 and LICIACUBE_LUKE_L2_1664234239_01003_01. The bright object in the upper corner of each image is Didymos.