Scientific Objectives of Small Carry-on Impactor (SCI) and Deployable Camera 3 Digital (DCAM3-D): Observation of an Ejecta Curtain and a Crater Formed on the Surface of Ryugu by an Artificial High-Velocity Impact

Abstract

The Small Carry-on Impactor (SCI) equipped on Hayabusa2 was developed to produce an artificial impact crater on the primitive Near-Earth Asteroid (NEA) 162173 Ryugu (Ryugu) in order to explore the asteroid subsurface material unaffected by space weathering and thermal alteration by solar radiation. An exposed fresh surface by the impactor and/or the ejecta deposit excavated from the crater will be observed by remote sensing instruments, and a subsurface fresh sample of the asteroid will be collected there. The SCI impact experiment will be observed by a Deployable CAMera 3-D (DCAM3-D) at a distance of ∼1 km from the impact point, and the time evolution of the ejecta curtain will be observed by this camera to confirm the impact point on the asteroid surface. As a result of the observation of the ejecta curtain by DCAM3-D and the crater morphology by onboard cameras, the subsurface structure and the physical properties of the constituting materials will be derived from crater scaling laws. Moreover, the SCI experiment on Ryugu gives us a precious opportunity to clarify effects of microgravity on the cratering process and to validate numerical simulations and models of the cratering process.

Appendices

Appendix A: Derivation of Eq. (6)

As shown in Fig. 15, which shows a snapshot of the cross section of an ejecta curtain and the ballistic trajectories of ejecta particles composing the curtain, we consider that an ejecta particle $P_{i}$ ($i =1, 2,\ldots$) originally located on the target surface at a distance $x_{i}$ from the impact point (here we define $x_{i} < x_{i+1}$) is ejected at an angle $\theta_{i}$ measured from horizon and a speed $V_{i}$. Given that the ejection time of the ejecta particles is 0 and that ejecta particles land at a distance $X_{i}$ at time $t_{i}$ under the gravity $g$, the equations of ballistic motion give

$$\begin{aligned} &X_{i} = x_{i} + V_{i} \cos \theta_{i} t_{i}, \end{aligned}$$

(7)

$$\begin{aligned} &{-} \frac{1}{2} g t_{i}^{2} + V_{i} \sin \theta_{i} t_{i} =0. \end{aligned}$$

(8)

In impact cratering, it is natural to assume $X_{i} > X_{i+1}$ and $t_{i} > t_{i+1}$ for $x_{i} < x_{i+1}$. At time $t_{i+1}$, the particle $P_{i+1}$ has just landed while the particle $P_{i}$ has not yet landed (let its position be ($X_{ip}, Y_{ip}$) in $xy$-plane) and the base of the ejecta curtain is located at $X_{i+1}$. At this moment, the angle $\beta_{i+1}$ of the ejecta curtain is given by the angle between the segment $P_{i} P_{i+1}$ and $x$-axis and thus

$$ \tan \beta_{i+1} = \frac{Y_{ip}}{X_{ip} - X_{i+1}}. $$

(9)

From Eqs. (7) and (8), $X_{ip}$ and $Y_{ip}$ are given by

$$\begin{aligned} X_{ip} &= X_{i} - \frac{g t_{i}}{2 \tan \theta_{i}} ( t_{i} - t _{i+1} ) , \end{aligned}$$

(10)

$$\begin{aligned} Y_{ip} &= \frac{g t_{i+1}}{2} ( t_{i} - t_{i+1} ) . \end{aligned}$$

(11)

Substituting (10) and (11) into (9), we have

$$ \frac{t_{i}}{\tan \theta_{i}} + \frac{t_{i+1}}{\tan \beta_{i+1}} = \frac{2 \Delta X_{i}}{g\Delta t_{i}}, $$

(12)

where $\Delta X_{i} = X_{i} - X_{i+1}$ and $\Delta t_{i} = t_{i} - t _{i+1}$. Here let $\Delta t_{i} \rightarrow 0$, then $t_{i} \rightarrow t_{i+1} =t$, $\beta_{i} \rightarrow \beta_{i+1} =\beta$, $\theta_{i} \rightarrow \theta_{i+1} =\theta$, ${\Delta X_{i}} / {\Delta t_{i}} \rightarrow {dX} / {dt= \dot{X}}$, and (12) becomes

$$ \frac{1}{\tan \theta } + \frac{1}{\tan \beta } = \frac{2 \dot{X}}{gt}. $$

(13)

This is Eq. (6) in the text, relating the ejection angle $\theta$ and the ejecta curtain angle $\beta$ using observable parameters: the horizontal proceeding speed $\dot{X}$ of the ejecta curtain, the time $t$ from the moment of impact, and the gravity $g$.

Fig. 15

Cross section of ejecta curtain in the $xy$-plane, showing parameters related to the ejecta curtain

In the above derivation of Eq. (13), we implicitly assume that the parameters related to the ejecta curtain are observed at the target surface. We can also consider a more general case in which the parameters are given by the observation at a horizon level of height $h$. In that case, Eq. (13) is extended as

$$ \biggl( 1+ \frac{2 h}{g t^{2}} \biggr) \frac{1}{\tan \theta } + \biggl( 1- \frac{2 h}{g t^{2}} \biggr) \frac{1}{\tan \beta } = \frac{2 \dot{X}}{gt}, $$

(14)

where the angle $\beta$ and the proceeding speed $\dot{X}$ of the ejecta curtain are measured at the observation level of height $h$.

Appendix B: Estimation of S/N of SCI in DCAM3-D Image

We suppose SCI is approximated by a cylinder of $\phi 30~\mbox{cm} \times \mbox{height} 15~\mbox{cm}$, wrapped with Beta-cloth with a diffusive reflectance of ∼80 %, independent of the light wavelength. We consider that the lateral surface of SCI is a uniform diffuse reflector. The specifications of the optics and the imager of DCAM3-D used in this calculation are as follows (see Ishibashi et al. 2016, in this issue, for detail). The spatial resolution is 1 m/pixel, the exposure time is 0.5 msec, the range of the wavelength transmitted through the optics is 450–700 nm, and the read-out noise of the imager is 7 electron/pixel. The parameters fixed in this calculation are the solar distance of 1.25 AU and the phase angle of the Earth-SCI-Sun of 20 degrees. Then, the free parameters we consider are the transmittance of optics that varies with the angle from the center of FOV, i.e., the position of SCI in an image, and the ensquared energy within 4 pixels. The calculated S/N of SCI image is shown in Fig. 16, in which 4-pixels binning is adopted. Note that the reflectance of SCI surface is assumed to be 50 %, not 80 %, taking into account that the full surface of SCI is not covered by Beta-cloth. Figure 16 shows that $\mbox{S/N} >5$ is realized even if the ensquared energy is only 50 % and the transmittance of optics is 22 % which corresponds to the angle from the FOV center of 50 degrees, i.e., near the corner of a DCAM3-D image.

Fig. 16

S/N of SCI image in 4-pixels binning as a function of the total transmittance of DCAM3-D optics. Each line shows S/N for each ensquared energy (EE). The angle from FOV center corresponding to the optical transmittance is also shown in the upper horizontal axis