The Double Asteroid Redirection Test (DART): Planetary Defense Investigations and Requirements

The DART project is a descendant of ESA's Don Quijote mission concept (Wolters et al. 2011). In the Don Quijote concept, a rendezvous spacecraft would arrive at the target asteroid to perform initial reconnaissance observations, and a kinetic impactor would arrive while the rendezvous spacecraft remained nearby. Following the impact, the rendezvous spacecraft would assess the results. The costliness of a two-spacecraft mission prevented Don Quijote from being considered further by ESA. It was later recognized that targeting the secondary member of an eclipsing binary asteroid system would allow the kinetic impactor experiment to be conducted with a single spacecraft through comparison of the secondary's orbit before and after the kinetic impact. This could be done via photometric light-curve measurements of the target system from Earth-based facilities by monitoring the timing of mutual events (occultations and eclipses by the system primary and secondary of one another) before and after the experiment (Pravec et al. 2006).

Roughly 60 binary near-Earth asteroids (NEAs) have been detected by radar, approximately 50 of which were known when study of the DART concept was begun (Margot et al. 2015). The accessibility of mission targets is often measured in "ΔV," which is related to the energy needed to reach an object. Didymos has a ΔV that makes it among the most accessible of these 60 NEA binaries. However, accessibility alone is not the sole discriminator of suitability. Binary targets with lower ΔV than Didymos have secondaries too large to be measurably deflected by the spacecraft masses under consideration, are poorly characterized in terms of physical and/or orbital properties, do not make close approaches to Earth for several decades in the future, are noneclipsing as seen from Earth for large stretches of their orbit, or have some combination of all of these factors. Didymos stands out as a well-characterized (De Léon et al. 2006; Pravec et al. 2006; Scheirich & Pravec 2009; Dunn et al. 2013; Naidu et al. 2020a), accessible asteroid binary system with an orbit conducive to measuring orbit changes via light-curve measurements, to which an efficient, affordable kinetic impactor demonstration mission can be sent, and from which meaningful results can be extracted without waiting decades for a suitable opportunity.

Using Didymos as the DART target system has an additional benefit. Analysis of the visible–near-IR reflectance spectrum of Didymos by Dunn et al. (2013) shows that its composition is consistent with the L/LL chondrites, the composition of the most common meteorite falls. Separate observations of the components of asteroid binaries of comparable size to the Didymos system have not been possible thus far, but leading models of asteroid binary formation predict that satellites form from material sourced from their primaries and should have similar if not identical compositions (Margot et al. 2015; Walsh & Jacobson 2015). One of the end states of tidal evolution in asteroid binary systems is the formation of an "asteroid pair," in which two objects share very similar heliocentric orbits without evidence of a collisional family (Vokrouhlický & Nesvorný 2008). Measurements of pairs show very similar spectral properties (Moskovitz 2012; Wolters et al. 2014; Pravec et al. 2019), consistent with the expectation that components of binary systems have similar compositions. Moreover, Pravec et al. (2006) found from analysis of depths of mutual events in binary near-Earth asteroids that albedos of both components of a binary NEA are the same or similar to within 20%. These findings give us confidence that Dimorphos's composition is very likely to also be L/LL chondrite. Thus, not only is the Didymos system the best choice for mission design and engineering reasons, but its components are also representative of likely potential impactors. Finally, Dimorphos, at roughly 165 m diameter, is close to (but above) the minimum size (140 m) for an object to be defined as a potentially hazardous asteroid (PHA). Given the nature of asteroid size–frequency distributions, smaller objects are far more numerous than larger ones, and therefore Dimorphos is of a typical size for the most common PHAs. Taken all together, these factors mean that the experimental results will be applicable to a large number of possible planetary defense scenarios.

Although DART is managed within NASA's Science Mission Directorate, as a planetary defense mission it differs from typical science missions such as those selected via the competitive Discovery or New Frontiers processes. Rather than a Science Team, DART has an "Investigation Team," reflecting the focus of the mission on the applied science of planetary defense. Nevertheless, the goals of DART involve scientific measurements, the studies carried out by the Investigation Team use typical scientific processes, and many of the planetary defense goals are aligned with fundamental science questions.

Like all missions, DART has a set of level 1 (L1) requirements that must be met in order for the mission to be considered a success. The four L1 requirements are listed below in their official forms, with the fourth requirement having two parts:

• 1.  
  DART-1. DART shall intercept the secondary member of the binary asteroid (65803) Didymos as a kinetic impactor spacecraft during its 2022 September–October close approach to Earth.
• 2.  
  DART-2. The DART impact on the secondary member of the Didymos system shall cause at least a 73 s change in the binary orbital period.
• 3.  
  DART-3. The DART project shall characterize the binary orbit with sufficient accuracy by obtaining ground-based observations of the Didymos system before and after spacecraft impact to measure the change in the binary orbital period to within 7.3 s (1σ confidence).
• 4.  
  DART-4A. The DART project shall use the velocity change imparted to the target to obtain a measure of the momentum transfer enhancement parameter referred to as "Beta" (β) using the best available estimate of the mass of Didymos B.
• 5.  
  DART-4B. The DART project shall obtain data, in collaboration with ground-based observations and data from another spacecraft (if available), to constrain the location and surface characteristics of the spacecraft impact site and to allow the estimation of the dynamical changes in the Didymos system resulting from the DART impact and the coupling between the body rotation and the orbit.

Note that changes to the "binary orbital period" mentioned in the requirements refer to changes in the orbit of the secondary around the primary, not the orbit of the binary system around the Sun. Also note that the threshold DART mission fulfills L1 requirements 1 through 4A, and the addition of requirement 4B constitutes the baseline DART mission.

The studies carried out by the Investigation Team and described in the following sections are designed to ensure that the L1 requirements are met by characterizing the Didymos system via observations and simulations prior to, during, and after the impact period. Five working groups (WGs) have been defined within the Investigation Team, with a charge to coordinate and carry out work in Impact, Observations, Dynamics, Proximity Imaging, and Ejecta as they relate to the DART mission and the L1 requirements, as well as additional relevant work beyond what is strictly required, but that can extract additional value from the DART mission (Table 1). The tasks in Table 1 are further described below.

Save for imagery used for terminal guidance and to characterize the impact site, the data required to meet the L1 requirements can or must be acquired via astronomical measurements of the Didymos system. Because the components will not be optically resolved from one another save perhaps at close Earth approach in 2022 by the most capable adaptive optics systems, the following discussion uses values for both components combined. Figure 3 shows the observability of Didymos between 2020 and 2023 in terms of its solar elongation and brightness. Didymos reached a peak V magnitude (V) brightness of approximately 18.9 on 2021 February 18 and reached opposition 2 days later. It was well placed for northern hemisphere observatories during the 2020–2021 apparition. After spring of 2021, Didymos will be poorly placed for Earth-based observations until the DART impact apparition of 2022. The current best-fit solution for Dimorphos's orbit period, natural change in that orbit period, and system standard gravitational parameter (GM) is presented in Table 3. The small but nonzero natural change in orbit period is consistent with, and interpreted as, being due to the binary YORP torque (BYORP; Cúk & Burns 2005; Cùk & Nesvorny` 2010), caused by unbalanced thermal emission in binary systems, which would lead to an additional change in Dimorphos's mean anomaly proportional to the square of time.

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Table 3. Current Solutions for Dimorphos Orbit Period

Parameter	Value
Period (hr)	11.921 628 7 ± 0.0000031
$\dot{n}$ (deg yr−2)	0.13 ± 0.03
GM (m3 s −2)	37.036

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The Investigation Team is conducting light-curve observations, using both guaranteed telescope access supported by the DART project and the standard competitive proposal process, to ensure meeting the DART-1 and DART-2 requirements.

Our current knowledge of the nature of the Didymos system is captured in the "DRA." The DRA currently has 43 fundamental and derived physical and orbital parameters to serve as a basis for common input to Investigation Team simulations and studies (see Appendix A). The DRA was originally implemented as a text document but has been adapted to be an online database that can be queried by DART team member applications throughout the mission. The DRA is to be updated as appropriate with each observing season, with the final pre-DART impact version scheduled to be complete in 2021 September, and post-impact DRA updates scheduled for release in 2022 October, November, and December, with release of the final post-impact DRA scheduled for 2023 April. Team members have access to the current DRA via the project Science Operations Center. The current DRA at the time of this writing is included as Tables A1–A6 in Appendix A. Later versions will similarly be included in future publications by project team members.

As with DART-1 and DART-2, telescopic measurements of Didymos's light curve will be used to meet the DART-3 requirement. As seen in Figure 3, Didymos will brighten throughout the first 9 months of 2022. On 2022 July 1 Didymos's V magnitude becomes brighter than 19.0, where it will remain until 2023 February 18, well after DART's kinetic impact. Didymos will reach a local maximum in solar elongation of 155° on 2022 August 18, after which solar elongation will decrease. It will reach a maximum brightness of V magnitude 14.4 on 2022 September 26–27. It will continue to draw closer to Earth for several days after reaching maximum brightness, with a closest approach distance of 0.071 24 au (10.66 × 10⁶ km) on 2022 October 4. However, because of Didymos's increasing phase angle in the days before close Earth approach, its brightness decreases despite the decreasing distance.

Didymos remains at solar elongations of approximately 100°–130° between 2022 September 22 and December 5, spanning the pre- and post-impact period, and during which period its brightness remains at V magnitude <16.2. During that span, it moves from a mid-southern decl. of −35° (well placed for southern hemisphere observatories, nonideal for Hawaii, and difficult from other northern hemisphere observatories) to a decl. of +22° (well placed for northern hemisphere observatories, less ideal for southern hemisphere observatories). Figure 4 shows the number of hours per night Didymos is observable and the minimum air mass it reaches for different observatories on selected dates over 2022–2023. The interplay of Didymos's east–west and north–south motions across the sky, its changing solar elongation, and the seasonally changing lengths of nighttime in different locations lead to the detailed behavior of the specific curves in Figure 4.

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The properties of interest to the Investigation Team include not only the binary orbit period and semimajor axis but also its other Keplerian orbital elements. Unlike the measurements that will constrain BYORP, the measurements that constrain or determine the inclination, eccentricity, etc., are not required to ensure that DART impacts Dimorphos and therefore are of lower priority.

As noted above, Didymos's position in the sky changes throughout the impact apparition, with northern and southern hemisphere observatories having different ideal observing times. To account for this, and as mentioned in Section 2, the DART project plans to support telescopes in both hemispheres that are operated by US-based institutions (Figure 4), covering a range of sizes: the Baade and Swope telescopes at Las Campanas Observatory in the south, Magdalena Ridge Observatory and the Lowell Discovery Telescope (LDT) at Lowell Observatory in the north, and the Las Cumbres Observatory network in both hemispheres, including a site in Hawaii.

3.2.1. Photometry

If the minimum requirement for orbital period change (73 s) is met, the length of Dimorphos's period will differ from the unperturbed case by roughly 0.17%, and every orbit Dimorphos will accrue an additional 0.17% difference in mutual event timings due to this change. While 73 s is the minimum required change, the specifics of the DART impact lead us to suspect that a 5-to-10-minute change is more likely, if still a conservative expectation (Cheng et al. 2018). A 7-minute change in period corresponds to a 1% change relative to the unperturbed period, etc. Figure 5 schematically shows how the change in orbit period caused by the DART impact will accrue in Didymos's light curve, with only the mutual events shown and the variation due to the rotation of Didymos removed, and neglecting effects due to changing viewing angles between the Sun, the fixed stars, the observer, and the Didymos system. After 15 orbits (roughly 7 days after the impact), the 73 s period change results in a timing offset of the mutual events from the unperturbed case by approximately 18 minutes, with the 7-minute orbit period change accruing a 1.7 hr offset. Note that Figure 5 assumes a leading-hemisphere impact that shortens the orbit period of Dimorphos. A trailing-hemisphere impact that lengthens the orbit period of Dimorphos will have similar offsets, but with mutual events later than the unperturbed case.

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In practice, it is unlikely that a very short campaign on any telescope can reach the 7.3 s uncertainty required of the measurement of the new orbit period. However, a relatively short campaign should be able to obtain the minimally required data: the photometric data used to discover Dimorphos (Pravec et al. 2006) spanned 13.2 days in 2003 November–December, with analysis by Scheirich & Pravec (2009) resulting in a precision of +14/−22 s (3σ). These data were taken from four different observatories with aperture sizes ranging from 0.35 to 1.5 m. Note that this 3σ uncertainty is roughly comparable to the required 7.3 s 1σ uncertainty for DART-3.

The Investigation Team has been using as guidelines for usable data a cadence of ∼3 minutes between images, with signal-to-noise ratio (S/N) of >50 (and S/N > 100 preferable). If S/N > 100 can be met with exposure times <2 minutes, improved S/N is preferred to a faster imaging cadence. Online exposure time calculators (for instance, the one hosted by the Las Cumbres Observatory: https://exposure-time-calculator.lco.global/) show that S/N ∼ 100 can be reached on a 1 m telescope in 120 s integrations for objects at V = 17.5 at air mass 1.3 and a quarter-moon phase, with S/N ∼ 50 reachable in the same conditions for V = 18.4. Didymos is brighter than V = 18.4 from 2022 mid-July to 2023 February and brighter than V = 17.5 from late 2022 July to late 2023 January, though of course much of those time periods are after the impact.

During the 2003 apparition, Didymos was at V magnitude ∼12.8–13.2, roughly 1.5 mag (factor of 4) brighter than it will be shortly after the impact, and roughly 3 mag (factor of 16) brighter than it will be a month after the impact. To make up for these differences using larger apertures alone requires mirrors ∼2–4 times larger in diameter than were used at that apparition, or ∼1–6 m. The observatories to be supported by the DART project are in this size range, including the 4.3 m LDT, the 6.5 m Magellan Telescopes, and the 2.4 m Magdalena Ridge Telescope. Simulations were undertaken by Scheirich et al. (2019) assuming rms uncertainties of 0.01 mag, with the conclusion that observations of four mutual events per month (a small fraction of the ∼60 mutual events that occur each month in the Didymos system) beginning on 2022 October 15 should result in an orbital uncertainty of ±10 s (3σ) by the end of November 2022 and ±4 s by the end of 2023 January, with the 1σ L1 requirement met during November. Higher-quality photometry, as would be expected from apertures larger than 1 m aperture, and/or additional mutual event measurements will further shorten the time until the requirement is met and reduce the uncertainty of the final measurement of Dimorphos's orbit period.

While the DART project will only support a limited number of observatories, we expect astronomers around the world, particularly those involved in the Hera mission, to be interested in participating in the 2022–2023 Didymos observations. These observations will be of great use to the DART project by providing different lines of sight to the Didymos system, providing additional margin against the threat of long-term regional weather problems, and allowing for monitoring of short-term variation in ejecta cloud brightness and morphology (if present).

3.2.2. Radar

The imaging time line for DART consists of three phases (Barnouin et al. 2019b):

(1) Approach phase. This phase provides light curves at viewing geometries complementary to those obtainable by ground-based telescopes. It begins when the Didymos system is first detected by Didymos Reconnaissance & Asteroid Camera for OpNav (DRACO), about 30 days before impact. The Didymos system will not be resolved during most of this phase. Using approaches employed in previous efforts (Pravec et al. 2006; Viikinkoski et al. 2015; Weaver et al. 2016), these light curves will be used to tighten constraints on the rotation rate and shape of Didymos and the orbital period and shape of Dimorphos. The long-range images also will be used to search for additional satellites.

(2) Terminal phase. The terminal phase begins when the spacecraft initiates autonomous navigation a few hours prior to impact. During roughly the last hour of this phase, Didymos and Dimorphos can be separately resolved, and DRACO images support both autonomous navigation and asteroid characterization. By the end of this phase, images of Dimorphos will have a pixel scale of roughly 3.5 m.

(3) Final phase. The final phase comprises the last 4 minutes of the DART mission. In the current baseline plan with an impact velocity of 6.6 km s⁻¹, at 15 s prior to impact, DRACO will image Dimorphos with a pixel scale ≤50 cm. Higher spatial resolution data will continue to be acquired in the final seconds of the mission. Planned real-time DSN coverage enables downlink of the images acquired up to 7 s before impact (which will have 23 cm pixel scale in the baseline trajectory), and possibly including even higher-resolution images acquired during the final 7 s prior to impact. Because the impact velocity depends on the actual launch date, the time at which these pixel scales are met could shift by 1–2 s in either direction.

Images from DRACO will provide the main data sets for a shape model for Dimorphos and impact-site images with a spatial resolution of 66 cm pixel⁻¹ or better (Figure 7). These data will be augmented by Earth-based light-curve data to develop a shape model of Dimorphos using stereophotoclinometry (Gaskell et al. 2008; Barnouin et al. 2020). Imaging along the incoming path for DART does not provide much opportunity for stereo or illumination variation, or for seeing more than half of the surface; nonetheless, initial modeling done by Barnouin et al. (2019b) demonstrates that volume uncertainties of 22% can be achieved from simulations of DART approach imagery using the shape of Itokawa, without any input from LICIACube or other non-DRACO sources (Figure 8). Bodies that are more symmetrical than Itokawa would yield smaller uncertainties. Inclusion of LICIACube data will provide stereo imagery and limb measurements that will not otherwise be available and will further improve the uncertainty on a volume estimate (and thus Dimorphos's mass estimate), but the exact amount is dependent on the shape of Dimorphos. A suite of simulations are currently underway to investigate this question in more detail. The shape model developed for Dimorphos will then be used, along with density estimates based on compositional analogs and a porosity estimate based on other asteroidal satellites (Section 5.2, Table 4), to provide an estimate of its mass and an associated uncertainty.

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Obtaining a measure of β, even in a simplified, idealized case, requires a measure of the mass of Dimorphos. While it is a goal of the Hera mission to make a measure of that mass to better than 10% in 2027 (Michel et al. 2018), the DART investigation will initially rely on a mass estimate based on the density of compositional analogs and the shape of Dimorphos.

The spectrum of the Didymos system was first reported by Binzel et al. (2004), who classified it as an Xk-class object based on 0.5–1.0 μm spectroscopy. Observations to 2.5 μm were made by de Léon et al. (2006), showing the presence of 1 and 2 μm silicate absorptions typical of S-complex asteroids. Dunn et al. (2013) analyzed the spectrum of Didymos and found it to be most consistent with an L/LL-chondrite composition. Theoretical and observational evidence suggests that asteroid satellites should share the same composition as their primaries (Margot et al. 2015), and therefore we expect Dimorphos to have the same composition as Didymos (Section 1.1). The Dunn et al. analysis, which supersedes that of a simple taxonomic classification, suggests that the components of the Didymos system would have a density of 3520–3580 kg m⁻³ if neither component has any porosity (Flynn et al. 2018). The mutual orbit period of Dimorphos and the sizes of the system components give a density for the system of 2170 ± 350 kg m⁻³ and an implied porosity of 38% ± 6% (Naidu et al. 2020a), though the size difference between Didymos and Dimorphos (derived from the depth of dimming during mutual events and independently constrained by radar measurements) suggests that >95% of the mass resides in Didymos, and this density is most accurately thought of as a density for that object alone. There are few asteroid systems with available densities for both primary and secondary, and situations where the secondary is denser and where it is less dense both exist (Ostro et al. 2006; Naidu et al. 2015), though recent work on the light curve of (66391) Moshup suggests that its satellite Squannit may be significantly larger (and thus less dense) than the results from radar measurements (Scheirich et al. 2021). Geophysical limits on the density of Dimorphos can be calculated: the fact that it is in its current orbit without being tidally disrupted sets a minimum density if it is cohesionless. However, Zhang et al. (2017) found that Didymos is spinning faster than the critical limit for its nominal density, concluding that it probably has surface cohesion, which might imply that Dimorphos also has cohesion. The fact that no reflex motion in Didymos was seen in the 2003 radar measurements sets a maximum mass, and the fact that the compositional analog cannot have negative porosity sets a maximum density limit. Table 4 presents density constraints for Dimorphos that can be used to constrain its likely mass value.

The momentum transfer efficiency, β, is defined as the ratio of the change in the asteroid momentum to the momentum of the impacting spacecraft, in the direction perpendicular to the asteroid's surface at the point of impact. Appendix B explains the background of this definition (for more detailed discussion, see, e.g., Jutzi & Michel 2014; Scheeres et al. 2015) and also lays out the mathematical formalism for how β will be determined from DART data. Figure 6 shows schematically the possible outcomes of the DART kinetic impact and how they correspond to different values of β. A purely inelastic collision where all of the spacecraft momentum and energy are simply absorbed by the asteroid corresponds to β = 1. An increased momentum change due to the recoil from ejecta blown back along the spacecraft trajectory corresponds to β > 1, and a decreased momentum change caused by material spalled off from the opposite side of the asteroid, albeit unlikely, would correspond to β < 1.

An exact equation for β, developed in Appendix B, is

$$\begin{eqnarray}&&\beta =\frac{\frac{M}{{m}_{{sc}}}{\rm{\Delta }}{V}_{T}-{{\boldsymbol{V}}}_{{\infty }_{\perp n}}\bullet {\hat{{\boldsymbol{e}}}}_{T}+{V}_{{\infty }_{n}}{\boldsymbol{\epsilon }}\bullet {\hat{{\boldsymbol{e}}}}_{T}}{{V}_{{\infty }_{n}}(\hat{{\boldsymbol{n}}}+{\boldsymbol{\epsilon }})\bullet {\hat{{\boldsymbol{e}}}}_{T}},\end{eqnarray} \tag{ 1 }$$

where M is the target mass, m_sc is the kinetic impactor (spacecraft) mass, ${\hat{{\boldsymbol{e}}}}_{T}$ is the unit vector in the direction of the satellite orbital velocity at impact, ΔV_T is the component of the satellite's velocity change in the direction of ${\hat{{\boldsymbol{e}}}}_{T},\hat{{\boldsymbol{n}}}$ is the surface normal vector at the impact site, ${V}_{{\infty }_{n}}$ is the component of impactor velocity in the direction of the surface normal, ${{\boldsymbol{V}}}_{{\infty }_{\perp n}}$ is the component of impactor velocity orthogonal to the surface normal (that is, along the surface), and is an offset vector between the surface normal direction and the ejecta momentum vector.

The inputs to Equation (1) can be separated into three categories, each the focus of a different working group: (1) estimate of tangential (along-track) change in orbital speed (ΔV_T : Observations Working Group); (2) estimate of Dimorphos shape and mass and impact location and surface normal at impact location (M and $\hat{{\boldsymbol{n}}}$: Proximity Imaging Working Group); and (3) estimate of off-normal component of ejecta momentum ( : Impact Working Group). The other variables in Equation (1) are m_sc , ${\hat{{\boldsymbol{e}}}}_{T}$, and the components of V _∞. The DART spacecraft team will provide initial inputs of the spacecraft trajectory and system to the Investigation Team as a whole within a week after impact. In particular, the true anomaly of Dimorphos at the time of impact, which provides ${\hat{{\boldsymbol{e}}}}_{T}$, will be determined by the Navigation Team in conjunction with the Proximity Imaging Working Group, using DRACO images.

• 1.  
  Estimate of tangential change in orbital speed (ΔV_T ). As discussed for DART-3, the Observations Working Group will determine the change in the orbital period of Dimorphos that results from the DART impact. The period change determination will provide the change in velocity to Dimorphos as a result of the DART impact to use in the determination of β, as further detailed in Equation (5) of Appendix A. The final determination of the period change will use all available data from the 2022–2023 Didymos observing period and will be available by 2023 April. However, preliminary estimations of the period change will be available earlier for DART team use, starting at roughly 2 weeks after impact.Determining the change in orbit period is, besides an independent L1 requirement, a key input to the determination of β discussed in the following sections. Dimorphos travels around Didymos at an average speed of 174.2 mm s⁻¹ (using the current DRA values). We expect a change of semimajor axis of roughly 10 m, with exact values dependent on the arrival mass of DART and the mass of Dimorphos. This estimate assumes a completely inelastic collision (β = 1) but assumes that DART's entry angle is 15° relative to Dimorphos's orbit plane. Those changes would lead to a new average speed of 173.5 mm s⁻¹ and a ΔV of roughly 0.7 mm s⁻¹. A 7.3 s uncertainty (1ρ) is roughly 1.4% of the nominal period change, so we do not expect uncertainties in the orbit period to be a significant contributor to uncertainties in β.
• 2.  
  Estimate of Dimorphos shape ( M and $\widehat{{\boldsymbol{n}}}$). As discussed in the previous section, spacecraft images will be used to produce a shape model of Dimorphos. The Proximity Imaging Working Group will produce an initial version of the shape model along with a volume determination within a month after the DART impact. This volume estimate will be used along with assumptions for the density of Dimorphos (Table 4) to estimate the mass of Dimorphos. Using spacecraft images, the local tilts and geology of the impact location will be determined to provide an estimate of the surface normal of the DART impact location, though information beyond determining the shape of Dimorphos is considered part of the efforts to achieve L1 DART-4B. It is expected that determination of the impact location and development of the Dimorphos shape model will occur in tandem. The surface area over which $\hat{{\boldsymbol{n}}}$ is determined should be roughly that of the DART spacecraft (Barnouin et al. 2019a), and work is underway to determine the extent to which the solar panels affect DART's effective surface area (Owen et al. 2019). DRACO images will be able to support calculation of surface normals for length scales of roughly 1 m and larger, finer than will be necessary for these purposes.
• 3.  
  Estimate of off-normal direction of ejecta momentum ( ). Ejecta formation and evolution have a profound influence on the value of β. The amount and trajectory of ejecta generated following impact depends nonlinearly on, e.g., impact incidence angle, target material properties, surface block distribution and frequency, and object shape. High-fidelity impact simulations provide information about the mass and velocity distributions for the ejecta, from which the ejecta motion can be determined. The Impact Working Group is performing suites of high-fidelity impact simulations to provide constraints on the magnitude of various unknowns (e.g., material properties, impact angle, block distribution) on ejecta generation and material trajectories (e.g., Stickle et al. 2015, 2017, 2020; Syal et al. 2016; Raducan et al. 2019, 2020; Rainey et al. 2020). These simulations utilize a variety of different standard impact hydrocodes (e.g., Stickle et al. 2020). In general practice, impact modelers on the Investigation Team simulate the DART impact in a plane containing the spacecraft momentum vector and the surface normal ( V _∞ and $\widehat{{\boldsymbol{n}}}$), with an assumption that the net ejecta momentum vector is coplanar. This assumption reduces the problem to a 2D calculation and allows consistency between simulations despite the fact that topography at the impact location is not known prior to receiving approach images, and thus the actual incidence angle with respect to the surface normal is uncertain. Focused 3D modeling by the Investigation Team will test this assumption in realistic DART impact cases. Both sets of simulations will be used to estimate the direction of the ejecta momentum vector in the actual DART impact and determine the difference between this direction and the surface normal $\widehat{{\boldsymbol{n}}}$, denoted as .

Figure 9 shows the parameters in Equation (1) that are related to the surface geometry. Additional inputs that will aid in the interpretation of β come from tasks conducted in primary support of the DART-4B requirement and are discussed in Section 6.

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Dynamical modeling of the Didymos system informed by available observations (Section 3.1) indicates that there is sensitivity to unknown pre-impact details such as the precise orientation of the primary at a given time (Agrusa et al. 2020). This uncertainty precludes knowing the exact dynamical state of the system prior to impact, although it is assumed that the system will be in or near a relaxed configuration—meaning a near-circular orbit with the secondary long axis nearly aligned with the orbit radial vector and nearly in the equatorial plane of the primary. The impact will excite modes relative to this relaxed state that may be either measurable or inferable based on improved knowledge of the system provided by DRACO and LICIACube (and later Hera). Notably, the difference between the new orbit and spin periods combined with the excited radial oscillations will result in libration of the secondary long-axis orientation around the orbit radial vector in proportion to β (Agrusa et al. 2021). It is possible that the libration could be detectable in light-curve and radar data (Naidu & Margot 2015; Pravec et al. 2016), but it should be readily measurable by Hera, along with a lower limit on the damping timescale. We note that the libration amplitude is also sensitive to the currently poorly constrained shape of the secondary. The orbital radial oscillations will range between 1% and 8% of the mean body separation—for β between 1 and 5, respectively—and corresponding out-of-plane oscillations in the orbit will increase the orbital inclination by between 01 and 05, but these motions will not likely be measurable prior to Hera. Note that variation in these results is expected for off-nominal impact velocities/masses, or impact circumstances yielded by launch dates later in the launch period.

If ejecta from Dimorphos impact Didymos, causing landslides or shape deformation, there is a small chance that the gravity perturbation on the orbit of Dimorphos driven by this event may be large enough to be observed in light curves by ground-based telescopes. This event would also change Didymos's spin period, which is key information for separating an orbit change due to the reshaping of Didymos from the one directly caused by the DART impact onto Dimorphos. The required 7.3 s measurement precision for the orbit period (requirement DART-3) will also allow measurement of any change of Didymos's spin period to the same precision, which corresponds to the period change expected if Didymos's short axis length changed by ∼1 m (Hirabayashi et al. 2019). The photometric measurement uncertainty may be improved to be <0.1 s by the end of 2023 April (Pravec & Scheirich 2018). That spin period change would be equivalent to reshaping of ∼1 cm along the short axis. We also note that ground-based observations could characterize Didymos's surface modification by comparing the surface albedo and/or color before and after the impact. Such measurements would significantly help assess Didymos's reshaping and Dimorphos's orbital behavior. Using current DRA values (Section 3.1), we estimate that the upper limit of the timescale of surface mass movement on the primary is ∼40 minutes. Ejecta moving faster than 1 m s⁻¹ will be gone 20 minutes after the DART impact, and most of the remaining ejecta mass will collide with either Didymos or Dimorphos within 17 days (Yu et al. 2017; Section 6.2). This implies that any dynamical effect will be complete within the post-impact observing window of ground-based telescopes, which lasts more than 6 months after the DART impact, into 2023 March.

Both rigid-body and rubble-pile modeling of the Didymos system using the improved shape models and dynamical configuration knowledge obtained just prior to impact will lead to refined estimates of the pre-impact circumstances and, when coupled with the β measurement (DART-4A) and other observables, estimates of the post-impact configuration. A suite of simulation outcomes consistent with observational constraints for plausible ranges of remaining free parameters will be continually updated before and after impact. The goal will be to find the set of dynamical parameters that most closely match the data. This will help constrain remaining free parameters (perhaps secondary mass, porosity, bulk density, etc.) and possibly improve the accuracy or equivalently reduce the uncertainty of the β estimate.

The DART impact is expected to liberate a large amount of surface material from Dimorphos as ejecta. Studies of the ejecta provide the opportunity to make an estimate of β if the ejecta momentum can be measured sufficiently well. LICIACube will have a flyby distance of 55 km, and its imagery, with a best resolution of 1.4 m pixel⁻¹ (Dotto et al. 2021), will be used to determine near-field ejecta properties. LICIACube objectives include multiple images at times and phase angles to allow measurement of ejecta, with an emphasis on measuring ejecta moving at <5 m s⁻¹ (Dotto et al. 2021). The LICIAcube images are designed to follow plume evolution in the first 300 s with both the Liciacube Explorer Imaging for Asteroid (LEIA) and Liciacube Unit Key Explorer (LUKE) cameras. With this sequence the dynamical characteristics and speed distribution within the plume can be retrieved. Given the timing of the LICIACube flyby (currently planned for 165 s after the DART impact; Dotto et al. 2021), opportunities for plume imagery may be expected both inbound and outbound for LICIACube.

Cheng et al. (2020) developed an ejecta model relevant to the DART impact into Dimorphos and discussed how imagery can be used to extract information about the impact conditions from the ejecta plume, including using measurements of the plume axis and asymmetry to estimate the ejecta momentum direction. Ejecta mass and velocity distributions can be constrained from the plume optical depth profile and evolution, which can then be tied to physical properties like strength and porosity. The Small Carry-on Impactor (SCI) experiment done by the Hayabusa2 team was analyzed using data from the Deployable Camera (DCAM3) in a similar fashion (Wada et al. 2021), and members of the Hayabusa2 team are also part of the international DART team to lend their experience.

Visualizations are being developed to generate simulated LEIA and LUKE imagery, as well as larger-scale imagery more relevant to astronomical observations, from ejecta models like those in Yu et al. (2017; Yu & Michel 2018) and Cheng et al. (2020). These involve translating the time-evolving 3D-spatial number density field into plane-of-sky appearance. At this writing, work is focusing on simple cases using spherical particles and reasonable assumptions for particle SFD and photometric properties. In the near-field, ejecta particles feel the gravitational acceleration from both binary components, positioned and oriented using the modeling of Full Two-Body Problem (F2BP) dynamical evolution of the binary itself, developed for DART-1 and DART-2 and also employed for DART-4A. Particles also feel throughout near field and far field both differential solar gravity acceleration ("solar tides") and solar radiation pressure (including Didymos and Dimorphos shadowing in the near field). Particles are propagated without tracking interparticle collisions or influencing the binary in any way, so they are essentially treated as an ensemble of test particles in the Restricted Full Three-Body Problem (RF3BP).

In order to quickly interpret data, a suite of simulated images for nominal and off-nominal cases will be rendered prior to the DART impact, along with a pipeline for generating those images from input parameters, to allow real images to be compared to the simulated cases and allow those cases that match the data most closely to be used as bases for more detailed modeling. Forward modeling of simulated images to match data returned from LICIACube and astronomical facilities (Section 6.4), with knowledge of the topography and geology near the site of DART's impact (Section 6.3), will allow estimation of particle properties that fit the evolving ejecta plume, which in turn will inform our understanding of Dimorphos's surface properties.

The imaging acquired by DRACO (prior to impact) and LICIACube (both before and after impact) will enhance understanding of the DART impact and its consequences on momentum transfer. The data collected by DART will be used by the Proximity Working Group to address several objectives:

• 1.  
  Identify the impact location. The location of the impact site and its relation to the center of figure of Dimorphos will be determined via the Dimorphos shape modeling effort supporting DART-4A. Current estimates suggest that the impact point will be known relative to the center of figure observed by the DRACO images to <50 cm; radial errors from the center of Dimorphos parallel to the DART velocity vector will be larger (<3.8 m). LICIACube images, which provide stereo parallax data, reduce the radial error; ongoing efforts are characterizing the magnitude of this error reduction.
• 2.  
  Assess the target properties. DRACO images will be used to assess the local target conditions at the impact site. Particular attention will be paid to whether the DART spacecraft impacted a block or regolith, and if any large blocks or other topography nearby may have influenced the excavation of debris from the impact. Impact simulations (Barnouin-Jha et al. 2003; Syal et al. 2016; Susorney et al. 2017) and experiments (Güttler et al. 2012; Tatsumi & Sugita 2018; Barnouin et al. 2019b), including those in situ at Ryugu (Arakawa et al. 2020; Wada et al. 2021), have shown that surface properties can have a substantial effect on the excavation process and resulting momentum transfer. LICIACube has color imaging capability via its LUKE camera, which can provide evidence of or upper limits to color variations across the surface of Dimorphos and between Dimorphos and Didymos at resolutions as fine as 4.3 m pixel⁻¹ in the nominal flyby case (Dotto et al. 2021). These data in turn provide insight into the homogeneity of these objects in terms of their composition and/or level of space weathering.
• 3.  
  Characterize the impact crater. LICIACube will attempt to image the DART impact location. If ejecta do not obscure the surface, the images will be used to characterize the DART impact crater. The Proximity Imaging Working Group will analyze the LICIACube images and, by comparison to pre-impact DRACO images, will determine some of the characteristics of the crater, including diameter, depth, and shape, with the caveat that the crater may not have completed forming when it is still resolvable by the LICIACube cameras. Evidence from the Haybusa2 Small Carry-On Impactor (SCI) experiment at Ryugu (Arakawa et al. 2020) and the Touch-And-Go event at Bennu indicates that near-cohesionless surface conditions may be possible on rubble-pile asteroids, and as a consequence very long-lived crater excavation in the weak-gravity regime may occur on Dimorphos.
• 4.  
  Characterize the ejecta. LICIACube will image the DART impact and provide constraints on the resulting ejecta, including the ejecta plume angle, and debris distribution.
• 5.  
  Refine the Didymos system properties. DRACO approach images, including light curves collected when the system is not yet resolved, will enable improved determination of Didymos system properties, such as the rotation rate and orbit of Dimorphos, as well as any updates to the Earth-based, light-curve-derived shape model. The observation geometry from DART and LICIACube on approach is different from what is easily achieved from Earth. The approach images will also help to inform dynamical modeling of the Didymos system and to understand the consequences of the DART impact.

A series of observations specifically designed to image the impact ejecta will be performed during and following the DART impact. Our primary observing mode to measure the orbit of Dimorphos uses visible-wavelength light with strict requirements on time resolution and observational uncertainty. Our ejecta observations will use longer integration times at a variety of ground- and space-based observatories with a range of wavelengths.

At the time of impact, the focus of our observing program will be to detect the ejecta. We will obtain infrared images from NASA's James Webb Space Telescope (JWST) with time allocated through the Guaranteed Time Observations program. While Didymos's rate of motion exceeds the tracking limit of JWST (108'' per hour) at the time of the DART impact, it drops below that limit on 2022 November 6, and observations will be made on or after that date. In addition, observations are still possible during the period in which it is moving faster than the limit, with the strategy of using the fastest tracking rate available, allowing Didymos to move across the chip. This strategy will be used for observations at the time of the impact itself. Our ability to use ground-based observatories at the time of impact depends on the time selected for impact and the location of the Didymos system relative to Earth at that time. Didymos will be in the southern hemisphere sky, and there are several locations in the southern hemisphere where a lack of telescope facilities could limit our ability to observe the impact itself. DART will support observations from Las Campanas Observatory in Chile and from Las Cumbres Observatory sites in South Africa, Australia, and/or Chile. At this writing, team members have access to additional Southern Hemisphere telescopes in Chile, South Africa, and New Zealand.

Following impact, we will obtain more observations to enable the study of the evolution of the ejecta. We will use the telescopes and observers involved in our light-curve study (DART-3) to obtain periodic images of the system. As the models indicate a growing ejecta plume and corresponding decrease in density, we expect to need longer exposure times to successfully obtain images of the ejecta. We will perform follow-up ground-based observations until the ejecta is no longer visible to our telescopes. We expect the supported observations to be made in commonly used visible-wavelength filters, since these will be used in the light-curve studies. Additionally, we are scheduled to obtain additional JWST infrared images in 2022 November. The JWST measurements at the time of impact will be made using the F164N (1.64 μm) and F323N (3.23 μm) filters, while later characterization will be done via images in those filters and spectroscopically with NIRSpec (0.6–5.3 μm) and MIRI (5–28 μm). If there is abundant ejecta in the decimeter size range, it may be detectable with radar, but that is not thought to be likely.

Little is known about the shape and material properties of Dimorphos. While initial radar observations (Naidu et al. 2020a) provide an estimate of the moonlet's size, no other resolved images or observations are available. Thus, material properties and structure must be estimated from what is known about meteorites or from other asteroids that have been visited by spacecraft. This provides additional complications to interpreting the impact simulations because a given velocity change may not arise from only one set of unique parameters. The impact simulations described in Section 5.3 cover a wide range of parameter space to reduce this uncertainty. Additional observations (e.g., shape, texture, topography, crater size, color from LICIACube) can help mitigate these uncertainties even more. Thus, additional information that may be available from, for example, LICIAcube and the Proximity Working Group (Section 6.3) and the Observations Working Group (Section 6.4) will be used if available to further refine estimates of β , ejecta mass, and predictions of the crater size.

• 1.  
  Using results from proximity imaging. Information provided by the Proximity Working Group (Section 6.3) can help constrain and refine the inputs to the impact simulations of the DART impact. Images of the impact location allow determination of the local geology (e.g., presence or absence of boulders and whether or not DART hit one), surface tilt, and surface normal ($\widehat{{\boldsymbol{n}}})$. These observations provide important setup parameters to the impact models to ensure that the components of Equation (1) and are estimated as robustly as possible. Further, while the velocity change imparted by the DART impact, as a singular measurement, will not uniquely determine material parameters such as strength or porosity, information about the ejecta cone properties and the crater size and shape, if available, can provide additional constraints (e.g., Raducan et al. 2019, 2020; Rainey et al. 2020). Information about the ejection angle and thickness of ejecta curtain, as well as how the ejecta curtain evolves in time, from LICIAcube can be used to provide information about the nature of Dimorphos's surface (Richardson et al. 2007; Schultz et al. 2007; Cheng et al. 2020). The potential availability of images of the size and morphology of the DART impact crater from LICIAcube could be used to provide additional constraints on material strength and porosity, as well as potential target structure (e.g., Raducan et al. 2020), as was done for Ryugu from images of the crater caused by their Small Carry-on Impactor (Arakawa et al. 2020; Wada et al. 2021).
• 2.  
  Change in rotational period of Didymos. The Didymos system light curve, determined by the Observations Working Group, is a combination of the rotation period of Didymos and the orbital motion of Dimorphos; therefore, the rotation period of Didymos will be measured as a by-product of determining the orbital period of Dimorphos. Models suggest that there is a very low but nonzero probability that ejecta from the DART impact striking Didymos could cause large-scale mass movement on the primary, resulting in a reshaping of Didymos and a change in its rotation period (Hirabayashi et al. 2019, Section 6.1). Because Dimorphos is so close to Didymos, such an event could potentially produce a change in Dimorphos's orbital period, and that change could be erroneously interpreted as being due to the direct momentum transfer from the DART impact. A determination of whether there is any change in Didymos's rotation period will allow an evaluation of whether this low-probability event has occurred. A preliminary determination of any change in the rotational period of Didymos will be available roughly a month after impact, and if a change is detected, the Dynamics Working Group would use the dynamical models discussed for DART-1 and DART-2 to assess the change in the orbital period of Dimorphos that was due to the change in Didymos versus that produced by the DART impact.
• 3.  
  Measurement of libration of Dimorphos. Agrusa et al. (2020) showed that the impact of DART into Dimorphos will induce free and forced librations. The amplitudes of these librations are shape dependent, and while calculations of their observability are still being made, it is expected that they will require light-curve precisions better than 0.5% in the most optimistic cases. Measurements of these librations would provide insight into the mass distribution of Dimorphos, but they are unlikely to be measured prior to the arrival of the Hera spacecraft or before the formal completion of the DART project. However, in the event that they are detected by the 2022–2023 telescopic observations, they would allow the assumption of a homogeneous mass distribution to be tested and/or corrected for Dimorphos.