Momentum transfer from the DART mission kinetic impact on asteroid Dimorphos

The Double Asteroid Redirection Test (DART) mission, a NASA-led planetary defense initiative, successfully performed the first-ever hypervelocity kinetic impact on an asteroid. The target was Dimorphos, a smaller asteroid orbiting the larger asteroid Didymos. This experiment aimed to validate the kinetic impactor technique as a viable method for deflecting potentially hazardous asteroids that might pose a threat to Earth in the future. The ability to predict the effectiveness of such an impact is crucial for planning future planetary defense strategies. Understanding how much momentum is transferred from the impactor to the target asteroid is a critical component of this prediction. Previous theoretical models and laboratory experiments had predicted a range of momentum enhancement factors, but the actual value in a real-world scenario remained uncertain. The DART mission provided the opportunity to experimentally measure this factor for the first time under conditions relevant to planetary defense, filling a significant gap in our understanding of asteroid deflection techniques. This experimental validation is crucial for refining current deflection models and informing future mission designs for the mitigation of asteroid impact threats.

Prior to the DART mission, several studies had explored the theoretical aspects and potential effectiveness of kinetic impactors for planetary defense. These studies used computational models and laboratory experiments to simulate hypervelocity impacts and estimate the momentum transferred to the target body. However, the results often varied significantly due to the range of possible material properties and impact conditions. Factors like the target asteroid's composition, strength, and porosity, as well as the impactor's velocity and mass, all played a crucial role in the outcome of the impact, making predictions challenging. Some studies suggested a momentum enhancement factor (β) greater than 1, indicating that the ejecta produced by the impact contributed significantly to the momentum transfer to the target. Others had explored the relationship between β and various asteroid properties, such as density and strength, but real-world data to validate these relationships was lacking. The DART mission aimed to resolve some of this uncertainty by providing data from a full-scale test on a real asteroid.

The study utilized data from the DART mission, including observations of Dimorphos's pre-and post-impact orbit. The change in orbital period was a key measurement used to determine the along-track component of the change in Dimorphos's velocity (Δv). A Monte Carlo approach was employed to account for the uncertainties associated with several parameters. The parameters considered were: the shapes of Didymos and Dimorphos (modeled as triaxial ellipsoids), Dimorphos's bulk density, the pre-impact orbital parameters, and the direction of the net ejecta momentum (Ê). A wide range of values for these parameters was sampled randomly within their uncertainties. For each sample, the General Use Binary Asteroid Simulator (GUBAS), a full two-body problem code, was used to numerically determine Δv. This code accounted for the non-spherical shapes of the asteroids and their close proximity. The momentum enhancement factor (β) was then calculated using equation (2) presented in the paper, which relates β to Δv, the mass of Dimorphos (M), the mass and velocity of DART (m and U), and the direction of the net ejecta momentum (Ê). The direction of Ê was estimated from observations of the ejecta plume by the Hubble Space Telescope and the LICIACube spacecraft. This process yielded a distribution of β values, allowing for statistical analysis of the results, The authors employed a technique to estimate the axis of the ejecta cone geometry using Hubble and LICIACube data. The uncertainty in the direction of Ê was also incorporated into the Monte Carlo analysis. The mass of Dimorphos was derived from the sampled ellipsoidal shape parameters and the sampled bulk density. The authors used a secant search algorithm in conjunction with GUBAS to determine the density of Didymos needed to reproduce the pre-impact orbital period for each Monte Carlo sample. Then they used a second secant search algorithm to calculate Δv needed to achieve the post-impact period. Second-order dynamics were utilized in the GUBAS simulations, validated by a smaller batch of fourth-order simulations showing negligible differences. The authors justified using a near synchronous rotation for Dimorphos due to the observed orbital drift, radar constraints, and models for tidal dissipation in binary asteroids, Higher order effects, like reshaping due to the impact, were considered negligible given the current uncertainties on measurements.

The analysis revealed that the along-track component of the change in Dimorphos's velocity was Δv = -2.70 ± 0.10 mm s⁻¹. This value, derived from the observed 33.0 ± 1.0 min reduction in the binary orbit period and the Monte Carlo analysis of the various uncertainties, represents a significant change in Dimorphos's orbital velocity induced by the impact. The momentum enhancement factor (β) is a key result. The study found that β was significantly greater than 1, indicating that ejecta recoil significantly contributed to the overall momentum transferred to Dimorphos. For a Dimorphos bulk density ranging from 1,500 to 3,300 kg m⁻³, the mean β values ranged between 2.2 and 4.9. For a nominal Dimorphos density of 2,400 kg m⁻³ (assuming similar density for Dimorphos and Didymos), β was found to be 3.61 ± 0.19 (1σ). This result confirms that a substantial portion of the momentum transferred to Dimorphos originated from the escaping ejecta, highlighting the importance of considering this effect in future planetary defense strategies. The findings show that the momentum transfer to the asteroid substantially exceeded the impactor's incident momentum, thus highlighting the increased effectiveness of the kinetic impact method due to ejecta recoil.

The findings demonstrate the effectiveness of the kinetic impactor technique for asteroid deflection, The significant momentum enhancement factor (β > 1) suggests that ejecta play a crucial role in the overall momentum transfer to the target asteroid. This has important implications for future planetary defense strategies, implying that kinetic impactors could be more effective than previously estimated. The results are consistent with earlier numerical simulations and laboratory experiments, although the specific value of β depends on the target asteroid's properties. The large range of β values reflects the uncertainty in Dimorphos's bulk density, which was not directly measured by the DART mission. The study highlights the need for future missions, such as ESA's Hera mission, to obtain more precise measurements of the asteroid's properties to refine the models of kinetic impact deflection. The observed value of β has implications for mission design. If a β value of greater than two holds true for a wide range of asteroids, this means a kinetic impactor of a given size could deflect an asteroid with less warning time or a larger asteroid with the same warning time. Future research should focus on refining estimates of β by incorporating additional constraints from the DART impact site geology and ejecta observations, These will help improve the understanding of Dimorphos's material properties and the momentum transfer process.

The DART mission successfully demonstrated the effectiveness of kinetic impact for asteroid deflection. The momentum transfer to Dimorphos significantly exceeded the incident momentum of the DART spacecraft, primarily due to the recoil from the ejecta plume. The momentum enhancement factor (β) was found to be significantly greater than 1, Future missions, like the ESA's Hera mission, will provide further data to refine the estimates of β and to better characterize the properties of Dimorphos. This research strengthens the case for kinetic impactors as a viable planetary defense strategy.

The primary limitation of the study is the uncertainty in Dimorphos's bulk density, which significantly affected the range of calculated β values. The assumption of instantaneous momentum transfer is a simplification of the complex impact process. The use of ellipsoidal shapes for Didymos and Dimorphos is an approximation, and more detailed shape models might provide more accurate results in future studies. Additionally, higher-order effects like reshaping due to the impact and mass loss from ejecta, though deemed negligible within the current margins of error, might be important to address in future iterations as the uncertainties in data improve.