Wada et al. Progress in Earth and Planetary Science
https://doi.org/10.1186/s40645-018-0237-y(2018) 5:82

Progress in Earth andPlanetary Science

REVIEW

Open AccessAsteroid Ryugu before the Hayabusa2
encounter
Koji Wada1*, Matthias Grott2, Patrick Michel3, Kevin J. Walsh4, Antonella M. Barucci5, Jens Biele6, Jürgen Blum7,
Carolyn M. Ernst8, Jan Thimo Grundmann9, Bastian Gundlach7, Axel Hagermann10, Maximilian Hamm2,
Martin Jutzi11, Myung-Jin Kim12, Ekkehard Kührt2, Lucille Le Corre13, Guy Libourel3, Roy Lichtenheldt14,
Alessandro Maturilli2, Scott R. Messenger15, Tatsuhiro Michikami16, Hideaki Miyamoto17, Stefano Mottola2,
Thomas Müller18, Akiko M. Nakamura19, Larry R. Nittler20, Kazunori Ogawa19, Tatsuaki Okada21, Ernesto Palomba22,
Naoya Sakatani21, Stefan E. Schröder2, Hiroki Senshu1, Driss Takir23, Michael E. Zolensky15 and International Regolith
Science Group (IRSG) in Hayabusa2 project

Abstract
Asteroid (162173) Ryugu is the target object of Hayabusa2, an asteroid exploration and sample return mission led by
Japan Aerospace Exploration Agency (JAXA). Ground-based observations indicate that Ryugu is a C-type near-Earthasteroid with a diameter of less than 1 km, but the knowledge of its detailed properties is very limited priorto Hayabusa2 observation. This paper summarizes our best understanding of the physical and dynamical
properties of Ryugu based on ground-based remote sensing and theoretical modeling before the Hayabusa2’s
arrival at the asteroid. This information is used to construct a design reference model of the asteroid that isused for the formulation of mission operation plans in advance of asteroid arrival. Particular attention is given
to the surface properties of Ryugu that are relevant to sample acquisition. This reference model helps readers
to appropriately interpret the data that will be directly obtained by Hayabusa2 and promotes scientific studies
not only for Ryugu itself and other small bodies but also for the solar system evolution that small bodies
shed light on.
Keywords: Hayabusa2, Ryugu, Asteroids, Regolith, Physical properties

Introduction
Asteroids and comets are relicts of the early stages of solar
system evolution. They contain materials and structures
which are relatively primitive compared to those composing the planets and thus provide a window into the earliest
stages of planet formation. Investigation of various properties of small bodies thus provides the crucial knowledge
needed to understand the origin and evolution of the solar
system. The asteroid (162173) Ryugu is a C-typenear-Earth asteroid (NEA) with a diameter of less than
1 km. It is the target of Hayabusa2, the second asteroid
sample return mission led by the Japan Aerospace Exploration Agency (JAXA) (Tsuda et al. 2013). Ryugu will offer a* Correspondence: wada@perc.it-chiba.ac.jp
1
Planetary Exploration Research Center, Chiba Institute of Technology,
Tsudanuma 2-17-1, Narashino, Chiba 275-0016, Japan
Full list of author information is available at the end of the article

great opportunity to understand the present status and theevolutionary history of volatile-rich primitive materials inthe solar system (Watanabe et al. 2017). This expectation
is supported by the fact that Hayabusa, the previous andfirst asteroid exploration and sample return mission by
JAXA, acquired substantial data from remote sensing
observations and the returned particles of the S-type NEA(25143) Itokawa (e.g., Fujiwara et al. 2006; Miyamoto et al.
2007; Nagao et al. 2011; Nakamura et al. 2011; Yoshikawa
et al. 2015). Although small bodies are full of treasures,
only a limited number have been visited by other rendezvous spacecraft so far, such as asteroid (433) Eros (e.g.,Cheng 2002) and comet 67P/Churyumov-Gerasimenko(e.g., Sierks et al. 2015). C-type (and related B-type) asteroids are considered to be the most primitive bodies in the
inner solar system as they are inferred to be relatively richin volatile materials like water and organics. The only

© The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to
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Wada et al. Progress in Earth and Planetary Science(2018) 5:82

C-type asteroid visited by a spacecraft so far is the main
belt asteroid (253) Mathilde, but it was a flyby observationand full global mapping images were not obtained(Thomas et al. 1999). Thus, we do not have yet any
detailed information on the most primitive types of asteroids, other than laboratory analysis of primitive meteorites,
but the specific sources or origins of these are unknown.
Hayabusa2 arrives at Ryugu at the end of June 2018
and will stay around Ryugu for 1 year and a half (Tsudaet al. 2013; Watanabe et al. 2017). In addition, the NASAasteroid sample return mission OSIRIS-REx will arrive
at a B-type asteroid (101955) Bennu (~ 500 m in diameter) in August of the same year (Lauretta et al. 2017).
These will be the first volatile-rich asteroids for which
we will obtain high-resolution images of nearly theentire surface and will provide critical insight as towhether observed characteristics of boulders, craters,
and surface roughness (in addition to other properties
discussed elsewhere in this paper) are representative ofsimilarly sized, primitive asteroids.
Since Ryugu has never been visited before, the limited
information before Hayabusa2’s arrival should be
reviewed and appropriately set out in order to guidethe Hayabusa2 mission toward success. For this purpose, the International Regolith Science Group (IRSG)
was organized as a branch of the Interdisciplinary Science Team in the Hayabusa2 project. In this paper, aproduct of an IRSG activity, we review the information
about Ryugu before the encounter of Hayabusa2. We
focus especially on the properties of the surface regolithlayer, i.e., its global properties including surface
geological features (“Global properties” section), its
thermophysical properties (“Regolith thermophysicalproperties” section), and its mechanical properties(“Regolith mechanical properties” section). The information described in each section falls into three categories in terms of our present knowledge: themeasured data obtained so far, the properties directly
derived/deduced from the present data with basic physics, and the predicted properties. As a whole, this paper
provides a reference model of Ryugu’s regolith with thecategorized data/properties. This model will be usefulfor Hayabusa2 operations such as landing site selection
and touchdown operations as well as for interpretingand understanding data that will be obtained by the remote sensing observations of Hayabusa2 and by the
analysis of samples returned from the asteroid. One
might have a question about an expiration date of thispaper after the end of the Hayabusa2 mission. The reference model proposed in this paper, however, will keep
its validity even after we have a lot of observational dataon Ryugu because the model offers a clear example, ina well-organized form, of what information we candraw about unexplored asteroids and other small

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bodies and will be a useful guide for future missions
planning to visit small, unexplored bodies.
Hayabusa2 carries a suite of instruments for scientificobservation. These include three optical navigation
cameras (ONC), consisting of a telescopic camera withseven band filters (ONC-T) and two wide field of view
cameras (ONC-W1 and W2), a near-infrared spectrometer (NIRS3), a thermal infrared imager (TIR), and alight detection and ranging (LIDAR) instrument. The
surface of Ryugu will be investigated with these instruments. For example, global and local mapping of topography, such as craters and boulders, will be carried out
by ONC imaging (Kameda et al. 2017). The spectroscopic properties of the surface will be revealed by
ONC-T and NIRS3 observations, e.g., for detection of
hydrated minerals (Kameda et al. 2015; Iwata et al.
2017). The thermophysical properties such as the thermal inertia derived from the surface temperature distribution will be explored by TIR observations, and thesewill help to estimate the particle size and the porosityof the regolith layer (Okada et al. 2017; Arai et al. 2017;
Takita et al. 2017). LIDAR will be used for the albedo
observation and dust detection around Ryugu, in
addition to measuring the distance between the Hayabusa2 spacecraft and Ryugu’s surface (Namiki et al.
2014; Mizuno et al. 2017; Yamada et al. 2017; Senshu
et al. 2017). Two landers (rovers) are also carried by
Hayabusa2, called MINERVA-II and MASCOT. In particular, MASCOT, developed by the German Aerospace
Centre (DLR) in collaboration with the Centre Nationald’Etudes Spatiales (CNES), has several instruments forscientific investigation on the surface (Ho et al. 2017): a
camera with illumination unit (MasCam, Jaumann et al.
2017), a near- to mid-infrared spectromicroscope(MicrOmega, Bibring et al. 2017), a multi-channel radiometer (MARA, Grott et al. 2017), and a magnetometer(MasMag, Herčík et al. 2017). The close observation of
the regolith surface by each of MASCOT’s instruments
will provide “ground truth” of the remote sensing dataobtained by the Hayabusa2 spacecraft, such as the particle size distribution, mineral composition, and thermal inertia. In addition to the above remote sensing
data, the mechanical properties of the regolith layer will
be investigated by an impact experiment carried out
with the so-called Small Carry-on Impactor (SCI) andin situ observation with a deployable camera (DCAM3)(Saiki et al. 2017; Arakawa et al. 2017; Ogawa et al.
2017; Ishibashi et al. 2017; Sawada et al. 2017). If the
trajectory of MASCOT during its descent and after rebound on the surface is traceable, its analysis can also
be used to estimate the mechanical properties of theregolith layer (e.g., Thuillet et al. 2018). After the endof the mission at Ryugu, and with the benefit of analyses of the returned samples, the reference model built

Wada et al. Progress in Earth and Planetary Science(2018) 5:82

in this paper will be fully checked and refined, and ourknowledge of small bodies in the solar system will beconsiderably improved.

Review
Global properties

Here, the global properties of Ryugu are presented
along with the best knowledge of the uncertainties in
the measurements. The described properties provide
essential inputs for mission planning in advance of
Ryugu’s arrival. In particular, the design reference
mission requires precise knowledge of Ryugu’s orbit
and dynamical state, size and shape, and near-surface
spectral reflectance properties.
Measured quantities

Orbital properties The observations used for orbit determination of Ryugu date from 1986 and include 725
astrometric reports included in the JPL-Horizons database (from 16 May 2017). The derived orbit, computedby JPL, is listed in Table 1. Ryugu’s perihelion (q) of
0.963 AU and aphelion (Q) of 1.416 AU classify it as an
Apollo-type near-Earth object. Its Earth minimum orbit
intersection distance (MOID) of 0.00111549 AU isamong the smallest values for asteroids larger than
100 m (JPL/SSD).
Numerical modeling of NEA orbital evolution indicates that Ryugu originated in the inner asteroid belt.
According to a model by Bottke et al. (2002), Ryugu is
statistically most likely to have followed the ν6 secularresonance pathway from the main asteroid belt(Campins et al. 2013). This pathway marks the innerboundary of the main asteroid belt at ~ 2.1 AU and is
the most efficient way to deliver bodies into near-Earthspace, accounting for most of those that reach very
Earth-like orbits characterized by low-MOID values andlow delta-V space mission trajectories. Several models
suggest that Ryugu likely originated in the inner main
Table 1 Summary of important orbital and global properties.
The orbital data are taken from JPL’s SSD website (NASA’s Jet
Propulsion Laboratory Solar Systems Dynamics Group HORIZONS at http://ssd.jpl.nasa.gov/). Rotation period is fromnumerous references (Kim et al. 2013; Müller et al. 2017; Pernaet al. 2017)
Eccentricity

0.190225753 ± 4.1 × 10-8

Semi-major axis (AU)1.1896008220 ± 3.3 × 10-9

Inclination (°)

5.8837424 ± 4.0 × 10-6

Period (day)473.9148422 ± 2.0 × 10-6

Perihelion (AU)0.963308109 ± 4.8 × 10-8

Aphelion (AU)1.4158935346 ± 4.0 × 10-9

Rotation period (h)7.625 ± 0.003

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asteroid belt, between ~ 2.1 and 2.5 AU, and reachedν6 by inward Yarkovsky drift (Campins et al. 2013,
Walsh et al. 2013, Bottke et al. 2015).
Working from the scenario of an inner main belt
origin for Ryugu, it is possible to seek relationships withknown asteroid families. Campins et al. (2013)
suggested that the spectral taxonomy of Ryugu preventsa solid match with known families, while Bottke et al.
(2015) studied the dynamical possibilities of delivery
from either the New Polana or Eulalia families. This
work found that Ryugu was more likely to have originated from the ~ 1 Gyr old New Polana family that iscentered at 2.42 AU. Surveys of these two families invisible and near-infrared wavelengths find no significant
differences between them, leaving Ryugu’s origin uncertain (Pinilla-Alonso et al. 2016; de León et al. 2016).
Size, shape, and spin The reference Ryugu shape model
was reconstructed from the inversion of optical andthermal infrared data by Müller et al. (2017). Because of
the small amplitude of the obtained light curves and low
quality of the optical light curves, the inversion did notlead to a unique solution for the pole, shape, and period.
Formally, there were different sets of these parametersthat fit the available data equally well. However, after acareful analysis, Müller et al. (2017) concluded that themost likely pole direction in ecliptic coordinates islambda = 310–340° and beta = − 40° ± 15°. The corresponding shape model is roughly spherical with avolume-equivalent diameter of 850–880 m (see Fig. 1).
Ryugu has a rotation period of approximately 7.625 ±0.003 (Kim et al. 2013; 7.63 h with no uncertainties in
Perna et al. (2017). Müller et al. (2017) provided more
possible values for the sidereal rotation period (7.6300,
7.6311, 7.6326 h), but from the analysis of the new datafrom Very Large Telescope (VLT) (Perna et al. 2017)and other observatories (Kim et al. 2016), the sidereal
rotation period of 7.6326 h is preferred (Durech, pers.
comm.). As shown in Fig. 2, the light curve has an asymmetric behavior with two different maxima and minima.
The asymmetric trend of the light curve is connected toeither the irregular shape or variations in albedo.
Phase function As discussed in Le Corre et al. (2018),
the spherical albedo and phase integral of Ryugu are useful quantities for deriving the bolometric Bond albedo
map. These quantities allow us to make temperature prediction across the surface of this asteroid during landingsite selection events of the Hayabusa2 mission. These
quantities can also be useful to calculate Ryugu’s thermal
inertia and constrain the Yarkovsky effect.
Le Corre et al. (2018) used ground-based photometricdata of Ryugu, which were compiled by Ishiguro et al.
(2014) and references therein, to constrain the averageWada et al. Progress in Earth and Planetary Science(2018) 5:82

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Fig. 1 Best fit shape model for Ryugu. Image taken from Müller et al. 2017disk-resolved brightness across Ryugu’s surface. The
radiance factor (RADF) is the ratio of the bidirectionalreflectance of a surface to that of a perfectly diffuse surface illuminated at the incident angle i = 0 (Hapke 2012).
Reflectance, rLS(i, e, α), is directly related to RADF(i, e,α) or [I/ℱ](i, e, α) as described in:½I=ℱ  ði; e; αÞ ¼ RADFði; e; αÞ ¼ πr LS ði; e; αÞ;ð1Þwhere i, e, and α being the incidence angle, the emission
angle, and the phase angle, respectively. I is the radianceand has units of W m−2 nm−1 sr−1. To dispel confusion,
the value J = πℱ is the collimated light (irradiance) andhas units of W m−2 nm−1.

Under the assumption that the photometric propertiesof the surface are well described by a Lommel-Seeliger
law, we can write:½I=ℱ  ði; e; αÞ ¼

wo μo f ðαÞ
;
4 μo þ μð2Þ

wowhere μο = cos(i), μ = cos(e), ALS = 4π
is the LommelSeeliger albedo, f(α) is the phase function, and wo is theaverage particle single scattering albedo. We approximate
the phase function with an exponential-polynomial func2
3
tion of the form f(α) =eβαþγα þδα (Takir et al. 2015), thecoefficients of which β, γ, and δ are fitted to the data.

Fig. 2 Composite lightcurve of Ryugu, as observed at the Very Large Telescope of the European Southern Observatory (ESO-VLT) on 12 Jul. 2016
by Perna et al. (2017). The rotational phase corresponds to a synodic period of 7.63 h. The zero phase time corresponds to 57,581.0 MJD

Wada et al. Progress in Earth and Planetary Science(2018) 5:82

Figure 3 shows Lommel-Seeliger models that capture
low and high phase angle behavior and the scatter in themoderate phase angle ground-based observations ofIshiguro et al. (2014). Le Corre et al. (2018) computed
models for nominal, maximum, and minimum predictedbrightness of Ryugu at 550 nm (Table 2). Although thisphotometric model fitted the disk-integrated data of
Ryugu well, it may not be an appropriate model for thisasteroid’s disk-resolved data especially at larger phaseangles (> 100°) (e.g., Schröder et al. 2017). This
Lommel-Seeliger model is a preliminary model and canbe updated when the spacecraft arrives at Ryugu.
Table 3 includes the albedo quantities of Ryugu, computed with the Lommel-Seeliger model, and the quantities
computed by Ishiguro et al. (2014). The two sets ofquantities are consistent with each other.
Spectral properties Ryugu is a primitive Apollo NEA
classified as a C-type asteroid. At present, there are eightground-based spectroscopic observations of this asteroid, three of which extend toward the near-IR (Table 4).
In nearly all the observations, the spectrum is featureless, with a slight reddening in the IR and a slight UV.
The best meteorite spectral counterpart is a heated CM

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Table 2 Lommel-Seeliger functions that predict [I/ℱ] (i, e, α)(reflectance) of Ryugu at 550 nm. ALS is Lommel-Seeliger Albedo
2
3
and f(α) = eβαþγα þδα . Table from Le Corre et al. (2018)
ALS
Nominal

0.027

β

γ
−2

− 4.14 × 10

−2

δ
−4

19.16 × 10−7−4

3.22 × 10

Maximum

0.030− 3.99 × 10

3.27 × 10

22.15 × 10−7

Minimum

0.024− 4.46 × 10−2

3.77 × 10−4

21.33 × 10−7chondrite or possibly a CI chondrite (Tonui et al. 2014);
however, this comparison is complicated by the poorly
known effects of space weathering on Ryugu.
The spectral analysis by Vilas (2008) at visible
wavelengths showed a feature at 0.7 μm attributed to
the Fe2+- > Fe3+ charge transfer transition in oxidized
phyllosilicates. This feature has not been detected inany other observations of Ryugu, and the author suggested a spatial heterogeneity in the asteroid surface
composition, as already observed in other main-beltC-type asteroid spectra (see Rivkin et al. 2002).
The observations by Lazzaro et al. (2013) in the 0.4–
0.85 μm spectral range covered 70% of Ryugu’s surface
and showed an almost uniform C-type featurelessspectrum, with no direct evidence of hydration features.

Fig. 3 The reduced V magnitude of Ryugu as a function of phase angle predicted by the Lommel-Seeliger model is shown compared with theground-based measurements of Ishiguro et al. (2014) and references therein. Shown are the minimum (red dots), maximum (blue dashes), andnominal (black solid line) models. Our minimum and maximum models do not include the Mathilde data; however, our nominal model does.
Reflectance rLS is in units of sr−1. Figure from Le Corre et al. (2018)

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Table 3 Albedo quantities of Ryugu computed using theLommel-Seeliger model and by Ishiguro et al. (2014). pv is thegeometric albedo, q is the phase integral, and AB is thespherical Bond albedo. Table from Le Corre et al. (2018)

values, which could be indicative of a heterogeneous surface; however, the visible observations by Moskovitz
et al. (2013) reported a homogenous and flat spectrum
in different observations of Ryugu, suggesting thatpossible heterogeneities should be constrained to 5% of
the entire asteroid surface. This work proposed that
Ryugu was best represented by a thermally alteredsample of the Murchison (CM2) meteorite and by thethermally metamorphosed CI chondrite Yamato 86029.
The most recent work by Perna et al. (2017) confirms
all the previous observations with a slight UV drop-off
and a featureless/flat spectrum in both the visible andnear-IR (Fig. 4). Le Corre et al. (2018) observed Ryugu
during its close flyby of the Earth in July 2016. Their
spectrum differs from those presented in Moskovitz
et al. (2013) and Perna et al. (2017), with a stronger
red spectral slope shortward of 1.6 μm. However, likethe previous observations, Ryugu’s spectrum does notshow any well-defined absorption bands. Le Correet al. (2018) suggested the possible presence of two
broad absorption bands centered around 1 and 2.2 μm
in their data. They proposed that if both are present,
these bands could be indicative of a CO or CV
chondrite-like composition. These meteorites are typically too bright to match Ryugu’s reflectance and would
require darkening effects of space weathering to provide
a match to the asteroid (Le Corre et al. 2018). Theseauthors used curve fitting techniques to confirm that
CM chondrites remain the best match. They also
found two small asteroids with very similar spectra (showing a pronounced red slope) to Ryugu: NEA (85275) 1994
LY and Mars-crossing asteroid (316720) 1998 BE7. In
addition, this work showed that the newly observed

Wada et al. Progress in Earth and Planetary Science

pv

q

AB

Lommel-Seeliger

0:042þ0:005−0:004

0:34þ0:01−0:01

þ0:001
0:014−0:001

Ishiguro et al. (2014)

0:047þ0:003−0:003

0:32þ0:03−0:03

þ0:002
0:014−0:002

Few variations have been observed at wavelengths
shorter than 0.5 μm, which lie in a UV drop-off as foundin previous observations (Binzel et al. 2001). The UV
drop-off is a common spectral feature of asteroids whosetaxonomy is associated with carbonaceous chondrites,
particularly for G and F asteroid classes (Tholen andBarucci 1989) or Cg in the Bus-DeMeo system (Bus andBinzel 2002; DeMeo et al. 2009). This spectral behavior
was investigated and widely discussed by Hiroi et al.
(1996, 2003) and Cloutis et al. (2012). These authors
noticed decreased reflectance in the UV after heating or
laser bombardment processing to simulate micrometeorite bombardment. These hypervelocity impacts cause
localized melting and the production of spherical glassy
droplets. The slight UV drop-off observed in different
regions of Ryugu’s surface could thus be explained by
the effect of heterogeneous processing due to space
weathering and/or episodes of substantial heating via,
presumably, closer perihelion passages.
The IR observations by Abe et al. (2008) and
Pinilla-Alonso et al. (2013) show a featureless/flat
spectrum and confirm that Ryugu is a C-type asteroid inline with all the other observations. A very slight positive
slope is observed. The two studies derive different slope

Table 4 Spectroscopic observations of asteroid Ryugu since its discovery in 2001. Spectral and compositional characteristics are listedReference

Spectralinterval (μm)

Taxonomy type
(T = Tholen;
BD = Bus-De Meo)

Meteoritical counterpart

Spectral characteristics

Binzel et al. 2001

0.4–0.9

Cg (BD)N.A.

UV drop-off: red (0.4–0.65 μm); flat
(0.65–0.9 μm)

Vilas 2008

0.42–0.93

C (T)

CM2

Band at 0.7 μm; flat with very weakband at 0.6 μm

Abe et al. 2008

0.4–2.4

C

N.A.

Flat and featureless spectral slope(0.85–2.2 μm) 0.89 ± 0.03%/1000 Å

Lazzaro et al. 2013

0.4–0.85

C

N.A.

Flat and featureless UV drop-off(< 0.45 μm)

Pinilla-Alonso et al. 2013

0.85–2.2

C

N.A.

Featureless spectral slope (0.85–2.2 μm)
0.37 ± 0.28%/1000 Å

Sugita et al. 2013

0.47–0.8

163 Erigone family

CM (heated Murchison)

Flat and featurelessMoskovitz et al. 2013

0.44–0.94

C (BD)CM (heated Murchison) CI (Y-86029)

Spectrally flat

Perna et al. 2017

0.35–2.15

C (BD)

heated Murchison CM unusual/heated CI

Featureless UV drop-off (< 0.45 μm);
spectral slope (0.5–0.8 μm)

Le Corre et al. 2018

0.8–2.4

C

CM2 carbonaceous chondrites, Mighei(grain size < 40 μm) and ALH83100(grain size < 100 μm)

Near-perfect match with NEA (85275)
1994 LY and Mars-crossing asteroid(316720) 1998 BE7Wada et al. Progress in Earth and Planetary Science(2018) 5:82

Fig. 4 The featureless/flatness nature of the Ryugu spectrum isevident in this series of three Vis-IR spectra. Superimposed are thespectra of thermally altered samples of the CM carbonaceouschondrite Murchison, in red (heated at 900 °C) and in cyan andgreen (heated at 1000 °C) (from Perna et al. 2017)

spectrum of main belt asteroid (302) Clarissa, suggested
as a possible source family for Ryugu (Campins et al.
2013), does not match their spectrum of Ryugu. It is
however a closer match with the spectrum from
Moskovitz et al. (2013).
Derived quantities

Determining the composition of Ryugu by remote spectroscopic observations requires accounting for viewing
geometry and modeling of the asteroid’s surface properties. Reflectance properties of asteroids may differ fromlaboratory analogs due to grain size, phase angle, andspace weathering (Binzel et al. 2015; Sanchez et al. 2012;
Reddy et al. 2012). Laboratory spectral measurements ofmeteorites relevant to Ryugu can improve the interpretation of future hyperspectral observations obtained by
Hayabusa2 NIRS3 instrument by linking absorption
bands to a well-characterized mineralogical composition.
Here, we summarize various authors’ interpretations of
their Ryugu spectra, most of which are included inTable 4 (see Le Corre et al. 2018 for a lengthy discussionof spectral interpretations of Ryugu).
Composition Generally, ground-based observations ofasteroid Ryugu show a featureless spectrum, with aslight reddening in the near-IR and with a slight
drop-off in the UV range. Based on laboratory data, thebest available meteoritic spectral analogs are, to firstorder, a heated CM or possibly CI chondrites. However,a list of possible surface analogs for Ryugu should contain at least components of CM and CI meteorites (e.g.,
Murchison, Orgueil, Jbilet Winselwan, Y82182, Y86029,
and so on), plus a suite of serpentines, saponite, phyllosilicates, magnetite, sulfates, sulfides, pyroxenes, andcarbonates.

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Laboratory measurements of reflectance spectra of aseries of 23 carbonaceous chondrites belonging to the CM
and CR groups were obtained between 0.3 and 100 μm in
support of the efforts to be able to interpret and relatemeasurements of the surface of Ryugu (Beck et al. 2018).
The major results are (i) the presence of 0.7 and 0.9 μm
features correlated to the amount of phyllosilicates(confirming previous work such as Vilas and Sykes 1996);(ii) reporting for the first time of the presence of 0.7 and0.9 μm features in spectra of a CR chondrites (Grosvenor
Mountains 95577), these data suggest that Cgh-type asteroids (which make up about 1/3 of the main-belt C-type
asteroids) could be the parent bodies of CM but also ofsome CR chondrites; (iii) the presence of a goethite-like
3 μm band for some CR chondrites (Beck et al. 2018).
Predicted quantities

Moving from derived quantities, where measured properties are used to derive new values for the properties of
Ryugu, here, we use the best evidence regarding Ryugu to
predict properties for which there are no measurements ofany kind. This section will often rely on the knowledge
gained from previous explorations and general estimatesfor C-type and NEAs. Some are explained in depth, notably
block sizes, due to the importance they could have for mission operations planning regarding spacecraft safety.
Satellites, dust, and the local environment There are
no directly observed, or inferred, satellites at Ryugu, so
this feature, along with dust floating around the asteroid,
has fallen into the “predicted” category of this work. Whatwould drive a prediction of the existence of a satellite? Satellites among NEAs are common—it is expected that 15%of the population have satellites on relatively close orbits(Walsh and Jacobson 2015; Margot et al. 2015). However,nearly all NEAs with satellites are very rapidly rotating,typically near the critical rotation rate of ~ 2.2 h, andnearly all have small lightcurve amplitudes, and whereavailable, their shapes are often found to be “top-shapes”
or nearly spherical with equatorial bulges. Given that
small bodies can be spun up or down by the
Yarkovsky-O’Keefe-Radzievskii-Paddack effect (YORP),
but this is highly uncertain, the current spin rate of Ryugu
certainly does not indicate that it was ever a rapid rotatorin the past, but at first glance, there is no strong indicationthat Ryugu will have a satellite or significant floating dust.
Boulders, craters, and surface roughness Safely delivering the spacecraft to the asteroid surface and effectively obtaining a sample are mission critical events that
require careful evaluation of the asteroid surface properties. The distribution and abundance of boulders andcraters pose the greatest risk to spacecraft flight thatmust be carried out autonomously. The surface roughness(2018) 5:82

Wada et al. Progress in Earth and Planetary Science

Page 8 of 30

or regolith grain size distribution is irrelevant to safety but
critical to the ability to successfully obtain a sample. Here,
we summarize spacecraft observations of asteroids thatprovide useful guidance for what we can expect upon arrival to asteroid Ryugu.
Asteroid Itokawa is similar in size (535 m × 294 m ×
209 m; Demura et al. 2006) to Ryugu (~ 900 m), but significant differences in geological features are expected.
Returned sample analyses confirmed that S-type asteroid
Itokawa is composed of an ordinary chondrite-like material, whereas C-type asteroid Ryugu is likely to be morevolatile-rich and weaker. It is already known that
Itokawa and Ryugu have strikingly differing shapes.
Itokawa is highly elongated and appears to be a rubble
pile composed of fragments from the catastrophic disruption of a larger body (Michel and Richardson 2013).
In contrast, Ryugu is roughly spherical, but its evolutionary history is not yet known.
The only C-type asteroid that has been previously visitedby spacecraft is the main belt asteroid Mathilde—a significantly larger asteroid at ~ 53 km mean diameter (Thomas
et al. 1999). The best images obtained during the NEAR
flyby of Mathilde were 160 m/pixel (Thomas et al. 1999).
At this scale, Ryugu would be only a few pixels across, sothese images do not offer much insight into what to expect
on Ryugu’s surface. Several other asteroids (S-types Eros,(243) Ida, (951) Gaspra, (2867) Steins, (4179) Toutatis,(5535) Annefrank; Q-type (9969) Braille; M-type (21)Lutetia) and other small bodies (Phobos, Deimos, several
comets, and moons of Saturn) have been imaged by spacecraft and provide some constraints as to what to expectfrom Ryugu; however, of those bodies, only Eros, Phobos,
Toutatis, and 67P/Churyumov-Gerasimenko (67P) wereimaged at scales sufficient to resolve small boulders, andonly Eros, Phobos (highest resolution images only
available in one area), and 67P have been imaged globally.
The size of Eros, the size and celestial location of Phobos,
and the cometary composition/nature of 67P all posecomplications for using these bodies as analogs to Ryugu.
At a larger scale, images of Ida and Gaspra lookbroadly similar to those of Eros, perhaps indicating that
Eros is representative of an S-type asteroid of its size.
Aside from Itokawa, Steins (5.3 km mean diameter) andToutatis (3 km mean diameter) are the asteroids thathave been observed by spacecraft that are closest in size
(both are larger) to Ryugu but have a different taxonomic
type; the best global Steins images have a ~ 160 m pixel
scale, again insufficient to give much insight into Ryugu.
The Toutatis data are limited but have a pixel scaleof ~ 3 m. There is limited, very low-resolution data available for Annefrank and Braille. (4) Vesta and Ceres are somuch larger than Ryugu that they do not provide very
good points of comparison for what to expect.
Size frequency distribution of boulders The cumulative size-frequency distributions (SFD) of boulders on
many small bodies (where sufficient data are available)
can be fit by power laws (see Table 5). Many, though notall, of the fits to global boulder populations havepower-law exponents around − 3. The exponent of thepower-law fit depends on several factors, including thegeological context, the strength of the material, andTable 5 Small bodies for which boulder counts have been made from spacecraft images. The minimum boulder sizes measured are
directly related to the best image resolution available for a given object
Name

Mean
Spectral Min boulder Min boulder
Power lawdiameter (km) typesize of global size of regional foundcount (m)count (m)

Eros

17

S

15

0.05

− 3.2 as low as NEAR
− 2.3 locallyRodgers et al. 2016; Thomas et al. 2001

Itokawa

0.35

S

6

0.1

− 3.1
Hayabusa− 3.5
as low as − 1.7
or as high as− 4.1 locally

Mazrouei et al. 2014; Michikami et al. 2008;
Noviello et al. 2014; Rodgers et al. 2016
Tancredi et al. 2015

Toutatis

2.9

S

n/a

10

− 4.4 locally

Chang’e 2

Jiang et al. 2015; Huang et al. 2013

Lutetia

99

M

n/a

60

− 5.0

RosettaKüppers et al. 2012; Sierks et al. 2011

Ida

32

S

n/a

45

n/a

Galileo

Lee et al. 1996

Phobos

22

D

n/a

5

− 3.2

Viking MGS Ernst et al. 2015; Rodgers et al. 2016;
MEX
Thomas et al. 2000
MRO

Deimos

12

D

n/a

~4

− 3.2

Viking

Lee et al. 1986; C. Ernst, personalcommunication

Comet

7

2

− 3.6 global;
local ranges− 2.2 to − 4.0

Rosetta

Pajola et al. 2015, 2016

Churyumov- 4
Gerasimenko

DatasourceReferences

Wada et al. Progress in Earth and Planetary Science(2018) 5:82

possibly the size range of boulders. The power-law behavior of cumulative size-frequency distributions of terrestrial fragmented objects has also been observed(Turcotte 1997; see also Table 1 in Pajola et al. 2015),
with the examples listed in Pajola et al. (2015) having
exponents ranging from − 1.89 to − 3.54.
In the cases of Eros, Itokawa, and Phobos, extending
the SFD power-law fit from large, tens-of-meter-sizedblocks down to small, tens-of-centimeter-sized blocks
yields reasonable estimates of small block populations(Rodgers et al. 2016, see Fig. 5). However, the geologicalcontext of an area matters for the absolute blockdensity—if lower-resolution counts include multiple geological settings, they will not extrapolate accurately to
local areas containing only one setting (Ernst et al. 2015;
Rodgers et al. 2016), and there are some indications ofbroken power laws on Itokawa that complicate simple
extrapolations (Tancredi et al. 2015).
Radar observations of some NEAs have identified large
boulders on at least 14 NEAs (Benner et al. 2015), but
the size of the boulders identified is limited by the
resolution of the data. Toutatis provides the only
“ground truth” between radar identifications of boulders
and spacecraft images of boulders—the SNR of the radarobservations was too low to positively identify boulders
on Eros or Itokawa (Benner et al. 2015). Radar data canbe used to measure the radar scattering properties ofasteroids, which gives insight into surface cobbles of thescale of the radar wavelength (0.035 m for Goldstone,
0.126 m for Arecibo).

Fig. 5 Figure taken from Rodgers et al. (2016) showing the size
frequency distribution of the blocks measured on Eros, Itokawa,Phobos, and comet 67P/Churyumov-Gerasimenko (see Rodgers et al.
2016, Fig. 1)

Page 9 of 30

If there were radar data that suggest either a numberof boulders or cobbles, an average size distribution ofboulders for the asteroid could be estimated by assuming a − 3 power-law exponent. The actual distribution ofboulders will be influenced by factors such as their origin and the geopotential of Ryugu. Ponds full ofcentimeter-sized pebbles are found on Itokawa at
geopotential lows, and most boulders are located inother regions of the asteroid (Fujiwara et al. 2006; Saito
et al. 2006). If this distribution is typical of a small
asteroid, Ryugu should have concentrations of finermaterial (ponds) near the geopotential lows, and boulders will be found at higher geopotentials. Generally, thelowest potential for an asteroid of Ryugu’s shape is
expected to be found at or near the equator; the shapeand density of the asteroid will affect the location ofthese geopotential lows.
If the boulders are sourced from the craters, as with
Eros (Thomas et al. 2001), they are likely to be distributed
around the craters as ejecta would fall on the irregularly
shaped body. On the other hand, they may preferentiallysettle in the equatorial or near-equatorial regions.
Shapes of boulders The aspect ratios of boulders on
Itokawa > 6 m in diameter were measured by Mazrouei
et al. (2014), who found that most boulders in this size
range were elongated, with b/a ratios of 0.7 (a, b, and c
are triaxial dimensions of the boulders, defined to bea ≥ b ≥ c). It was not possible to measure the third dimension of most boulders in the Hayabusa AMICA images. Similar b/a ratios (0.62–0.68) were found by
Michikami et al. (2010) and found to peak near 0.7 in
Tancredi et al. (2015). The c/a ratio was measured for
21 boulders, the mean was 0.46 (Michikami et al. 2016).
A compilation of fragment dimensions from several laboratory experiments is shown in Table 6. Although themeasurements assume an ellipsoidal shape, the fragments are actually irregular in shape. It is not known
whether the aspect ratio of rocks on a C-type asteroid
would be different from those seen on Itokawa or in thestrong-rock experiments of Table 6. Also unknown isthe magnitude of the influence of thermal degradation
on boulder fragmentation.
Craters Itokawa has a small number of identified impact
craters, especially small ones (Hirata et al. 2009). Given
its similar size to Itokawa, Ryugu may also not exhibit
many craters. Eros, Phobos, Ida, and Gaspra all have numerous craters; on Eros, seismic shaking is suggested tohave acted to erase many small (< 100 m diameter) craters (Chapman et al. 2002; Thomas and Robinson 2005);
craters of 100 m size would be of significant size
compared to Ryugu. These observations imply that
Eros has a global loose regolith as deep as 100 m

Wada et al. Progress in Earth and Planetary Science(2018) 5:82

Page 10 of 30

Table 6 Compilation of fragment ratios b/a and c/a from several publications in the literature. Dimensions are defined to bea≥b≥c
Reference

TargetFujiwara et al. 1978

BasaltCapaccioni et al. 1986

BasaltConcrete

Projectile

Impact velocity (km/s)

b/a

c/a

Polycarbonate cylinders

2.6 and 3.7

0.73

0.50

Aluminum spheres

8.8 and 9.7

0.7

0.5

Durda et al. 2015

BasaltAluminum spheres

3.9–5.8

0.72 ± 0.13

0.39 ± 0.13

Michikami et al. 2016

BasaltNylon spheres

1.6–7.1

0.74

0.5 (catastrophic disruption)
0.2 (impact cratering)(Robinson et al. 2002). Eros’s relatively flat topography(< 55% of the surface is steeper than 30°) may also be
explained by a thick global regolith (Zuber et al.
2000). Craters are more apparent on Toutatis than on
Itokawa (Huang et al. 2013), with different densities ofcraters seen on the different lobes of the asteroid(Zou et al. 2014). As Ryugu is intermediate in size between Itokawa and Toutatis, it might be expected tohave more craters per unit area than Itokawa but
fewer than Toutatis. Since the size of regolith particles
on Ryugu is expected to be similar to that on Itokawa(see the “Regolith thermophysical properties” section),
steep cratered topography is not expected on Ryugu
as well as on Itokawa. However, the different composition of Ryugu could affect the size of craters and theregolith depth and structure.
Meter-scale surface roughness Here, surface roughness
at the meter-scale is described, to be distinguished fromthe smaller-scale roughness that is a parameter in thermophysical model fitting routines, or roughness in terms ofvery fine scale regolith grains—both are discussed in later
sections. The surface roughness of Itokawa and Eros has
been measured by rendezvous spacecraft laser altimeters.
Itokawa’s two major regions, the highlands and lowlands,
have different surface roughnesses that are obvious evenin the images. The roughest parts of the asteroid correspond to those with more boulders, which correspond toregions of higher geopotential (Barnouin-Jha et al. 2008).
It is thought that finer materials may move to regions oflower geopotential and cover up larger boulders, creating
a smoother (less rough) region. These areas arethought to correspond to areas with the thickest (fine)regolith. Over baselines of 8–50 m, the highlands of
Itokawa are 2.3 ± 0.4 m rougher than the MUSES-C
region (Barnouin-Jha et al. 2008); this difference may
correspond to the expected regolith depth in this area.
Alternatively, it is possible that large boulders are segregated to higher geopotential through the granularphysics phenomena known as the Brazil nut effect,
whereby under the action of various shaking processes,
segregation occurs with larger bodies moving upwardin the geopotential (Tancredi et al. 2015).

The highlands of Itokawa are at a baseline of 20 m—
rougher than Eros—and the lowlands of Itokawa are significantly smoother than Eros (with the possible exceptionof Eros’ ponds) (Barnouin-Jha et al. 2008). The surface
roughness of Itokawa does not exhibit self-affine over theexamined baselines (Barnouin-Jha et al. 2008).
On Eros, the surface roughness is self-affine over twoorders of magnitude of baseline (~ 4–200 m), suggesting
similar processes control the surface properties overthese scales (Cheng et al. 2002). The corresponding
Hurst exponents lie between 0.81 and 0.91 (Cheng et al.
2002). There are regional variations in surface roughnessof Eros; smaller roughness values are found where more
regolith is thought to have accumulated, and higher
values are found along the crater walls and grooves(Susorney and Barnouin 2016).
There is a strong dependence of radar circularpolarization ratio with asteroid class, suggesting a
relationship between roughness at the centimeter- to
decimeter-scale and composition (Benner et al. 2008).
However, the mean ratios for S- and C-type NEAs areindistinguishable, perhaps indicating similar average surface properties for these populations (Benner et al. 2008).
Regolith thermophysical properties

Regolith thermophysical properties govern the exchangeof radiative energy between the asteroid and its environment, and knowledge of these parameters is needed to
calculate the surface and subsurface temperatures. While
the surface energy balance is governed by insolation andregolith thermal inertia, heat diffusion governs temperatures in the subsurface. Heat is conducted to the subsurface according to:


∂T
∂
∂T
ρcp
¼
k
;
∂t
∂z
∂z

ð3Þ

where ρ is regolith density, cp is specific heat capacity, T
is temperature, t is time, z is depth, and k is thermal
conductivity. Equation (3) is a second-order differential
equation, which can be solved by prescribing two
boundary conditions: One is usually given by zero heat
flux from the interior, while the other is usually given inWada et al. Progress in Earth and Planetary Science(2018) 5:82

terms of the surface energy balance. For periodic insolation forcing, the surface energy balance takes theconvenient form:rﬃﬃﬃπ ∂T 
;σ SB ϵT ¼ ð1−AÞS þ I
P ∂z0 z0 ¼0
4

ð4Þ

where σSB is the Stefan-Boltzmann constant, ϵ is the surface emissivity, A is the Bond albedo, S is the total solar
radiative flux including scattered radiation, P is theperiod of the forcing, and z' =pz/de is the depth normalﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ized to the skin depth d e ¼ kP=ρcp π . In Eq. (4), allmaterial parameters have been absorbed in the single
thermal inertia parameter I, which is defined as:
I¼

pﬃﬃﬃﬃﬃﬃﬃﬃﬃ
kρcp :

ð5Þ

It is worth noting that Eq. (5) is only valid at the surface and provided that thermal conductivity is constant,which is not strictly true (see below). However, thermal
inertia is a convenient way to describe the reaction of
surface temperatures to insolation changes, and it is thus
widely used. In addition, lack of data usually does notallow different parameters to be disentangled, although
recent studies indicate that the radiometrically measured
thermal inertia changes with heliocentric distance for anindividual object (Rozitis et al. 2017; Marsset et al.
2017). Nevertheless, temperature dependence of thermal
conductivity can have a significant influence when interpreting conductivity in terms of regolith grain size (e.g.,
Opeil et al. 2012; Gundlach and Blum 2013; Piqueux
and Christensen 2011; Sakatani et al. 2017), and thermal
inertia is therefore generally interpreted at a representative
surface temperature (e.g., Müller et al. 2017; Gundlach
and Blum 2013). In addition, care must be taken whenconverting thermal inertia to material parameters likethermal conductivity, since different combinations ofmaterial parameters govern the temperature at the surface(thermal inertia) and in the subsurface (thermal diffusivity).
There is evidence for regolith layering in terms ofthermal conductivity from remote sensing data of main
belt asteroids (MBA), and Harris and Drube (2016)
argue that thermal inertia typically increases significantly
as a function of thermal skin depth for these bodies.
This effect may be caused by the fact that for slowly
rotating asteroids surface temperature and thus surface
thermal inertia is influenced by deeper layers than forfast rotators, and thus for slow rotators, they probe
regolith material parameters to a greater depth. The
observed increase of surface thermal inertia as a function of skin depth can thus be interpreted as thermal
conductivity increasing as a function of depth, and it
should therefore be kept in mind that a similar layering
may be present on Ryugu.

Page 11 of 30

Measured quantities

Thermal inertia and albedo Relevant thermal observations of Ryugu are summarized in Müller et al. (2017)and include the following: SUBARU-COMICS, multiple
N-band (Aug 2007), AKARI IRC 15/24 μm photometry(May 2007), Herschel-PACS, 70/160 μm photometry(Apr 2013), Spitzer-IRS spectrum (5–38 μm) (May 2008),
Spitzer-IRAC 3.6/4.5 μm two-epoch thermal light curves(Feb/May 2013), Spitzer-IRAC 3.6/4.5 μm multiple-epoch
point-and-shoot sequence (Jan-May 2013), and new datafrom NEOWISE at 4.6 μm (Sep 2016; J. Masiero, priv.
comm.)A thermal inertia of 150 to 300 J m−2 s−1/2 K−1 is required to explain the available rich data set of thermal
measurements over a wide phase angle and wavelength
range. The corresponding maximum surface temperatures
are in the range of ~ 320 to 375 K (rhelio = 1.00–1.41 AU
for our observational thermal data set), with Tmax ~ 350 K
at the object’s semi-major axis distance (a = 1.18 AU).
The corresponding shape model is very spherical withthe volume-equivalent diameter 850–880 m (compare“Global properties” section). The surface has thermal inertia of 150–300 J m−2 s−1/2 K−1, and the roughness is small
with the rms of surface slopes < 0.1, which means thesurface appears very smooth in the radiometric context(connected to a very low width-to-depth ratio in the modeled spherical crater segments on Ryugu’s surface). The reference model of Müller et al. (2017) has the pole direction(340°, − 40°), the volume-equivalent diameter 865 m,
surface thermal inertia 200 J m−2 s−1/2 K−1, low surface
roughness with rms of surface slopes 0.05, geometricV-band albedo 0.049, infrared emissivity 0.9, and rotation
period 7.63109 h (compare “Global properties” section).
These are consistent with other estimates independently
conducted by Yu et al. (2014). Geometric albedo, phase
integral, and the spherical bond albedo have already been
discussed in the “Global properties” section, and the values
presented there are compatible with the estimates fromthermophyiscal models, which yield geometric V-band albedos of approximately 0.042 to 0.055. Using a phase integralof q = 0.29 + 0.684G, where G = 0.13 ± 0.02 is the slope parameter as derived from V-band observations (Ishiguro et al.
2014), the bond albedo can be calculated using A = qpV.
The uncertainty in G translates into an uncertainty in thephase integral q (Bowell 1989) and combined with a 5%
accuracy of the q − G relation (Muinonen et al. 2010) abond albedo of A = 0.019 ± 0.003 for the full admissible
thermal inertia and roughness range is obtained.
Derived quantities

Thermal conductivity The thermal conductivity ofparticulate media is known to be very low in a vacuumWada et al. Progress in Earth and Planetary Science(2018) 5:82

because the weak contacts between particles act as highthermal resistance points for heat conduction, andcontributions of heat transfer by gas are absent (e.g.,
Fountain and West 1970). In fact, thermal conductivityof the lunar regolith was estimated to be less than
0.03 W m−1 K−1 even at depths below 50 cm based on theanalyses of Apollo Heat Flow Experiment data (Langseth
et al. 1976; Grott et al. 2010), and much lower values are
expected at shallower depth. Accordingly, the thermal
conductivity of Ryugu’s surface is also expected to be very
low if it is covered by regolith or small particles.
The thermal conductivity of the top surface layer can beconstrained using Eq. (5) if the thermal inertia is assumed
to be known from, for example, ground-based observations. For Ryugu, using the estimated typical value of
200 J m−2 K−1 s−1/2 (Müller et al. 2017) and assuming abulk density of ρ = 1100–1500 kg m−3 (typically
1270 kg m−3) as well as a specific heat capacity cp of
758 J kg−1 K−1 at 300 K (as an averaged temperature ofdaytime on Ryugu), thermal conductivity is constrained tobe 0.020 < k < 0.108 W m−1 K−1, with a most likely valueof k = 0.042 W m−1 K−1. However, it is worth pointing out
again that this estimate is only valid if density, specificheat capacity, and thermal conductivity are constant as afunction of depth and time, which will in general not hold.
Rather, on the actual Ryugu, these parameters may have
depth-directional distributions and will vary with time dueto the diurnal temperature variations.
Thermal conductivity of regolith-like powders is acomplicated function of parameters, such as grain size,
porosity, temperature, and particle surface energy, thelatter being a measure for the attractive surface force
acting between solids in close proximity (Johnson et al.
1971), and different models have been proposed for thisproblem (e.g., Halajian and Reichman 1969; Hütter et al.
2008; Gundlach and Blum 2012). Here, we use the integrated model by Sakatani et al. (2017) that was developed based on experimental studies. Under vacuum
conditions, effective thermal conductivity is given by thesum of “solid conductivity” originating from thermal
conduction through inter-particle contacts and “radiative
conductivity” originating from thermal radiation throughvoid spaces between the particles, and it is given by:
k ¼ k solid þ k rad :ð6Þ

The solid part of the conductivity ksolid can be modeled as
serial and parallel connections of heat paths around thecontact areas between spheres and it may be expressed as:
k solid ¼

4rc
k m ð1−ϕ ÞCξ ;
π2
Rp

ð7Þ

where km is the thermal conductivity of the bulk material, ϕ is the porosity, C is the coordination number, rc is

Page 12 of 30

the radius of the contacts area between two spheres, Rp
is the radius of the grains, and ξ is a coefficient that represents a reduction of contact heat conductance due tosurface roughness on the grains; ξ = 1 if particles are perfectly smooth spheres, and comparison with experimental data showed that ξ ≤ 1 for natural samples including
spherical glass beads. The coordination number may be
expressed as a function of porosity, and according toSuzuki et al. (1980), it is given by:
C¼

2:812ð1−ϕ Þ−1=3 ;f2 1þ f2

ð8Þ

where f = 0.07318 + 2.193ϕ − 3.357ϕ2 + 3.194ϕ3. The contact radius rc between two spheres depends on the force
with which the particles are pressed together as well as
their elastic parameters, and under the micro-gravity environment of Ryugu surface energy γ, and thus, van der
Waals forces will dominate the solid conductivity contribution. Contact radius rc may be expressed as:
93
8sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2ﬃ= 1=3
2 <
3
ð
1−ν
Þ
3
3
5 ;
rc ¼ 4F þ πγRp þ 3πγRp F þ
πγRp
;
4E :
2
2
2

ð9Þ
where ν is Poisson’s ratio, E is Young’s modulus, F is theexternal compressive force on the particle, and γ is thesurface energy (Johnson et al. 1971). F is given as thecompressional stress σ divided by the number of grains
per unit cross-sectional area, and
2πR2p
σ:F ¼ pﬃﬃﬃ
6ð1−ϕ Þð10Þ

On planetary surfaces, the compressional stress iscaused by the self-weight according to σ = ρm(1 − ϕ)gz
with ρm being the bulk density of the grain, g gravitational acceleration, and z depth, but on Ryugu, this contribution will be small. Overburden pressure on Ryugu is
only of the order of 0.01 Pa at a depth of 10 cm, andassuming van der Waals forces to be of the order of
0.075 N/m times Rp (Kiuchi and Nakamura 2014); thelatter will dominate F for particle sizes smaller than 1 m(compare Eq. (10)). On the other hand, the overall contribution of the solid conductivity to the total conductivity will be small for typical NEAs with thermal inertia I
larger than 100 J m−2 K−1 s−1/2 when compared to theradiative contribution, and radiative conductivity will
dominate (see below).
The radiative part of the conductivity may be modeledby approximating the particle layers as multiple infinitely
thin parallel slabs. Then, radiative conductivity may be
written as:

Wada et al. Progress in Earth and Planetary Sciencek rad ¼4ϵ
σ SB LT 3 ;2−ϵ(2018) 5:82

ð11Þ

where ϵ is the grain surface’s thermal emissivity, σSB is
the Stefan-Boltzmann constant, T is temperature, and L
is the effective radiative distance between the slabs.
Thus, L is proportional to the geometrical clearance ortypical pore length between the grains, and in a homogeneous packing of equal-sized spheres, the geometricalpore length can be expressed in terms of grain size andporosity (Piqueux and Christensen 2009). Additionally,
introducing a factor ζ to scale the geometrical length tothe effective one, L is given by:


ϕ 1=3
L¼2ζ
Rp :
ð12Þ
1−ϕ
Comparison with experimental data for glass beads
showed that ζ increases with decreasing grain size,
which may be caused by a number of effects: First,
the assumption of independent scatterers may break
down, or a change of the scattering characteristics
may take place for particles smaller than the thermal
wavelength, resulting in more forward scattering. Further, radiative transfer may be enhanced across gaps
smaller than the thermal wavelength (Rousseau et al.
2009), or there may be bias in the experimentally derived ksolid. The latter may be due to the fact that thetemperature dependence of krad is not exactly T 3 dueto the coupling between solid and radiative heattransfer (Singh and Kaviany 1994); thus, an extrapolation of measured data to 0 K for determining ksolid
may not be perfect.
A potential shortcoming of the above theory is thatnatural regolith does not consist of monodispersed
spherical particles. However, laboratory measurementsof the thermal conductivity of lunar regolith analog
material (Sakatani et al. 2018) show that measured
thermal conductivity is in close agreement with theory if the median particle size (in the volume fraction
sense) is used in the above equations. This is due tothe fact that (a) the solid conduction only weakly depends on particle size and (b) the average pore size is
close to the one calculated with the median radiususing Eq. (12).
Another simplifying assumption made above is thespherical particle shape, while natural regolith is generally both non-spherical and angular. The deviation fromthe ideal shape can be measured by quantities called
sphericity and angularity, and both shape indicators may
influence the contact radii in the solid conduction
contribution in complicated ways. However, their main
contribution on thermal conductivity is to change
regolith porosity, which is sufficiently described by the
median particle radius. Thus, the current best estimate

Page 13 of 30

for determining ζ is an empirical relation derived fromthe experimental results of Sakatani et al. (2018) for a
lunar regolith simulant, and it is given by:ζ ¼ 0:68 þ

7:6  10−5
;
Rp

ð13Þ

where Rp is in units of meter. In the above model,
Thermal conductivity of the regolith depends mainlyon the particle size and porosity, and ranges for thesetwo parameters can be estimated if thermal inertia or
effective thermal conductivity is known. Figure 6
shows a thermal inertia contour plot as a function ofparticle size and porosity. For thermal inertia valuesof I = 150–300 J m−2 K−1 s−1/2 as derived from remotesensing observations (Müller et al. 2017), a typicalparticle size for the Ryugu regolith can be estimatedto be 3–30 mm, with 6–10 mm being the most likely.
For such large grain sizes, the radiative conductivity
is dominant over the solid conductivity even at low
temperatures. For example, assuming a particle diameter of 3 mm and a temperature of 150 K, the solid
contribution to thermal conductivity is of the orderof 5∙10−4 W m−1 K−1, whereas the radiative part islarger than 3∙10−3 W m−1 K−1. Therefore, the uncertainty of assumed parameters in the solid conductivity
model, such as Young’s modulus and surface energy,
does not affect the grain size estimation. On theother hand, porosity cannot be effectively constrained
because a major part of heat flow is made by theradiative heat transfer in this particle size range.
Radiative thermal conductivity increases while theheat capacity decreases with porosity; therefore, thisbalance of both parameters makes thermal inertia
nearly constant for various porosities.
For a verification of the determined grain size, acomparison with the thermal model developed byGundlach and Blum (2013) can be made. This modelis based on the same physical concept as the calculations described above, however deviates in some details. Basically, these differences are (i) the formulationof the network heat conductivity, (ii) the descriptionof the radiative thermal transport process, and (iii)
the irregularity parameter measured by different calibration measurements. A derivation of the regolithgrain radius based on the Gundlach and Blum (2013)
formulations yields radii ranging between 1.1 and2.5 mm (for volume filling factors between 0.1 and0.6). Thus, both models agree rather well, with theGundlach and Blum (2013) model having slightly
smaller sizes, which provides confidence in the grain
size determination from thermal inertia measurementsof planetary surfaces.

(2018) 5:82

Wada et al. Progress in Earth and Planetary Science

0.80

Page 14 of 30

30

0.75
0.70
30
Porosity

0.65

30
30

0.60
50
0.55
0.50 50
50

0.45
0.40

-2

10

10

150 200

50

50

300

500

80
-1

0

10
Particle Diameter (mm)

1

10

2

10

Fig. 6 Contour plot of thermal inertia (in units of J m−2 s−1/2 K−1) as a function of particle diameter and porosity. The gray-filled region indicates
the thermal inertia range estimated for Ryugu by ground-based observations (Müller et al. 2017). The regolith parameters assumed in thecalculation are cp = 758 J kg−1 K−1, T = 300 K, ρm = 3110 kg m−3, km = 0.0021 T + 1.19 W m−1 K−1, γ = 0.032 J m−2, ν = 0.25, E = 78 GPa, ϵ = 1.0,

ξ = 0.12, z = 0.01 m, and g = 1.8 × 10–4 m s−2, respectively. γ and ξ were optimized for experimental data of lunar regolith simulant JSC-1A(Sakatani et al. 2018)





350−T
;
cp ¼ 4184∙ 0:2029 þ 0:0383 1− exp100

Predicted properties

Regolith heat capacity The specific heat capacity ofrocks and soils at low temperatures has been studied forlunar samples (Robie et al. 1970; Fujii and Osako 1973;
Hemingway et al. 1973; Opeil et al. 2012), and a strong
temperature dependence has been found. The suite ofmaterials studied includes particulate material such as
lunar fines and soils, but brecciated lunar rocks as wellas basalts have also been studied. The best fit to thelunar soils data is given by Hemingway et al. (1973), andthe specific heat capacity can be approximated as:
cp ¼ −23:173 þ 2:127T þ 1:5009∙10−2 T 2−7:3699∙10−5 T 3 þ 9:6552∙10−8 T 4 ;ð14Þ
where cp is the specific heat capacity in units of J kg−1 K−1and T is temperature in K. This best-fitting formula isaccurate to within 2% down to temperatures of 200 K
and to within 6% down to temperatures of 90 K. At
higher temperatures, the expression

ð15Þ
by Wechsler et al. (1972) may be used (also see Ledlow
et al. (1992), Stebbins et al. (1984), and Schreiner et al.
(2016)). The fit to the data is shown along with the data
in Fig. 7 and extends to temperatures of up to 350 K, asappropriate for Ryugu. The extrapolation applicable athigher temperatures is shown as a dashed line.
Measurements on lunar material are in good agreementwith measurements performed by Winter and Saari (1969)
using other geological materials as well as measurements ofthe specific heat capacity of meteorites performed by
Yomogida and Matsui (1983) as well as Consolmagno et al.
(2013). It may be worth noting that a trend exists with respect to the iron content of the considered samples, with
low iron corresponding to high heat capacity (Yomogida
and Matsui 1983). While heat capacity thus shows a strong
temperature dependence, this is only relevant if the nearsurface regolith layer is considered. At depths below a few
skin depths, perturbations rapidly decay such that theWada et al. Progress in Earth and Planetary Science(2018) 5:82

Page 15 of 30

Fig. 7 Specific heat capacity of lunar samples 14,163,186 (fines > 1 mm, blue circles), 15,301,20 (soil, red triangles), 60,601,31 (soil, green squares),and 15,555,159 (basalt, cyan left triangles) as a function of temperature together with the best fitting curve (solid line) as well as an extrapolation
for temperatures beyond 350 K (dashed line). Data and fit from Hemingway et al. (1973), extrapolation from Ledlow et al. (1992)

regolith can be assumed isothermal for the purpose ofdetermining its heat capacity. Evaluated at a representative
average daytime surface temperature of 300 K, a valueof cp = 758 J kg−1 K−1 is obtained by evaluating Eq. (14).
Surface temperatures, thermal gradients, and thermal
fatigue The thermal evolution of Ryugu is simulated bysolving Eq. (3) numerically. In general, the input flux atthe surface is not only the heat flux from the sun but also
the sum of the heat radiation from the other surface area
(Rozitis and Green 2011; Davidsson and Rickman 2014;
Davidsson et al. 2015). However, Ryugu is predicted to bea round-shaped body from ground-based observations.
Thus, hereafter, for simplicity, it is assumed that thesurface is convex, and areas to be calculated do notreceive heat radiation from other areas.
It is to be noted that the thermal emissivity is notneeded to be the complement of the surface albedo because the peak wavelength of the solar radiation is in therange of the visible light while that of the thermalradiation from the surface of an asteroid is around or
longer than 10 μm. Thus, the thermal emissivity and thealbedo are independent parameters. We adopt 0.019 forthe albedo and 0.90 for the emissivity of the surface of
Ryugu as nominal values. Hereafter, we will show theequilibrium temperature evolution as a function of local
time, which is obtained after 100 asteroid rotations at a
fixed solar distance and a sub-solar latitude. The difference between the equilibrium temperature distribution
and a full numerical simulation taking into account theorbit of the body around the sun is less than a few K.
Figure 8 shows the evolution of equilibrium surface
temperature as a function of local time with a constantthermal inertia (left panel, thermal inertia equal to
200 J m−2 s−1/2 K−1) but various local latitudes, andconstant local latitude (right panel, 0°) but various
thermal inertias. In these numerical simulations, we
adopt a solar distance of 1.2 AU and the sub-solar

Wada et al. Progress in Earth and Planetary Science(2018) 5:82

Page 16 of 30

Fig. 8 Surface temperature change as a function of local time for various latitudes (left) and thermal inertia (right). The sub-solar latitude isassumed to be 0 (equator)

latitude of 0° (equator) for simplicity. As shown in Fig. 8,
surface temperature changes with solar direction anddecreases almost linearly during night time. Both the
maximum and minimum temperatures decrease withlatitude for a constant thermal inertia. The local time of
the maximum temperature is achieved after noon, andthe degree of phase shift relative to the noon is almost
the same for each latitude. On the other hand, as shownin the right panel of Fig. 8, the local time of the maximum temperature becomes later with thermal inertia.
The phase shift is a diagnostic parameter to estimate thethermal inertia from the surface temperature distribution obtained by the instrument TIR (Takita et al. 2017).
The maximum temperature decreases with thermal
inertia and the minimum temperature increases withthermal inertia because subsurface temperatures are kept

warmer for larger thermal conductivities. It is to be
noted that the total thermal radiation from the surface
must balance with the solar influx in the equilibrium
state. Thus, the decrease of maximum temperature issmaller than the increase of minimum temperature since
the thermal radiation is proportional to the fourth powerof the temperature.
Figure 9 shows results similar to Fig. 8, but for aspin axis tilted by 30°. In this case, the duration of
day and night depends on the latitude. As a result, themaximum temperature is not needed to be obtained at
the latitude identical to the sub-solar latitude. For thecase with a thermal inertia of 1000 J m−2 s−1/2 K−1,
the maximum temperature is obtained at the latitudeof 45°. Despite the change of the length of day time,
the shift of the local time of peak temperature isFig. 9 Left: similar to Fig. 8, but for a case with sub-solar latitude of 30, i.e., a tilted spin axis. Left: the thermal inertia is 200 J m−2 s−1/2 K−1. Right:
thermal inertia is 1000 J m−2 s−1/2 K−1

Wada et al. Progress in Earth and Planetary Science(2018) 5:82

independent of the latitude. These results are similar
to those obtained by Müller et al. (2017), who calculated the maximum surface temperatures in the rangeof 320 to 375 K by considering the derived object
properties and heliocentric distances of 1.00–1.41 AU.
At the object’s semi-major axis distance of 1.18 AU,
Müller et al. (2017) find a reference maximum
temperature of 350 K.
Delbo et al. (2014) suggested that thermal fatigue could
be the driver of regolith formation on asteroids with perihelion distances of less than 2.5 AU, including NEAs suchas Ryugu. Thermal fatigue describes the breakdown of larger boulders due to thermal stress. The regolith is exposedto large temperature differences between night and day
time temperatures causing large temperature gradientsand therefore stress in the material leading to crack formation and propagation. Delbo et al. (2014) estimated that
thermal fatigue erodes the surfaces of NEAs like Ryugu
several orders of magnitude faster than erosion caused by
micrometeoroids. Consequently, studying the temperature
gradient at the surface might be essential for understanding the evolution of the surface of Ryugu. Figure 10 represents the evolution of the temperature gradient justbeneath the surface as a function of the local time andlatitude. The thermal inertia and the sub-solar latitude areassumed to be 1000 J m−2 s−1/2 K−1 and 0°, respectively.
We adopted a larger thermal inertia than the nominal
value of Ryugu because dust creation due to the thermal
fatigue takes place at the surface of consolidated boulders
or monolithic rocks. As shown in Fig. 10, the maximum
temperature gradient is achieved before noon. The absolute value of the thermal gradient is larger for lower
latitude. This is simply because the larger thermal spatial

Page 17 of 30

gradient is obtained at the time when the maximum temporal gradient of the surface temperature is achieved. In
fact, as shown in the right panel of Fig. 8, the maximum
temporal gradient at the surface is achieved before noon.
The maximum thermal spatial gradient becomes larger
for smaller thermal inertia. On the other hand, the negative maximum temperature gradient is achieved at sunset.
After sunset, the temperature gradient becomes smaller
because the underground temperature distribution is
alleviated during night time. The right-hand panel ofFig. 10 is similar to the left one but uses a spin axis
tilted by 30°. In this case, the maximum thermal gradientis achieved not only at the sub-solar latitude but also at
the sub-solar latitude and the equator. Thus, the determination of location at which the maximum temperature
gradient is achieved is not straightforward (Hamm et al.
2019). It is to be noted that the integration of thermal
gradient through a day should be zero in the equilibrium
state if the thermal conductivity is independent of
temperature.
We assumed above that the surface of Ryugu issmooth. If the roughness of the surface is taken into account, the apparent temperature distribution changes
depending on the degree of roughness (Rozitis andGreen 2011; Davidsson and Rickman 2014, Davidsson
et al. 2015). The temperature of a slope is especiallyaffected at dawn and dusk. A wall of a valley observed
at a low phase angle will have a much higher
temperature than the horizontal, surrounding surface.
Contrarily, when observing a wall against the sun, it
will be much colder than its surroundings. In addition
to the case of concave areas such as craters, the absorption of radiation could raise the temperature of theFig. 10 Thermal gradient just beneath the surface as a function of local time. Left: sub-solar latitude of 0°. Right: sub-solar latitude of 30°. The
negative maximum of the thermal gradient is achieved at sunset while the positive maximum of the thermal gradient is achieved justbefore noonWada et al. Progress in Earth and Planetary Science(2018) 5:82

bottom area of the concavity depending on its size andshape. Moreover, we must point out that the bondalbedo of a rough surface changes with solar incident
angle (Senshu et al. in preparation). These effects need
to be taken into account when analyzing the apparent
temperature distribution obtained by the Hayabusa2
TIR instrument.
Regolith mechanical properties
Measured quantities

There are no directly measured quantities of the mechanical properties of the regolith on Ryugu, as for any asteroidthat has not been visited by a spacecraft. Therefore, theonly quantities that can be determined must be derived
from current data or rely on pure assumptions.
Derived quantities

The only quantity that can be derived from observations
is the dominant grain size, based on the measurement of
the thermal inertia of the asteroid (see the previous
section). The grain shape can also be derived from theonly asteroid from which regolith particles have been

Page 18 of 30

returned, i.e., the asteroid Itokawa. However, we notethat Itokawa belongs to the S taxonomic class, and its
composition is thus very different from that expected for
Ryugu. This probably also means that its mechanicalproperties are different, and therefore, how regolith isgenerated on this body, as well as its properties, arelikely to be different too. But since this is the only data
point that we have so far, we use it in this section.
Grain size As summarized previously in the “Regolith
thermophysical properties” section, a thermal inertia of 150
to 300 J m−2 s−0.5 K−1 is required to be compatible withremote sensing observations (Müller et al. 2017). Using themodel by Sakatani et al. (2016), this translates to typicalparticle diameters of 3–30 mm for Ryugu, with 6–10 mmbeing the most likely. This is consistent with, althoughslightly larger than, the results by Gundlach and Blum(2013), who obtain grain diameters of 2.2 to 5 mm.
Grain shape For the grain shape as shown in Figs. 11 and
12, we note that the mean aspect ratios of particles
returned from the asteroid Itokawa by the Hayabusa

Fig. 11 Backscattered electron (BSE) images of asteroid Itokawa regolith grains RA-QD02-0030 (a), RA-QD02-0024 (b), RA-QD02-0013 (c), and RAQD02-0027 (d) from Nakamura et al. (2011). Ol, olivine; LPx, low-Ca pyroxene; Chr, chromite; Pl, plagioclase; Tr, troilite; Tae, taeniteWada et al. Progress in Earth and Planetary Science(2018) 5:82

Page 19 of 30

Fig. 12 The 3D external shapes of Itokawa particles. a Stereogram (box size 232 μm × 232 μm × 203 μm) and b SEM micrograph of RA-QD020023. c Stereogram (box size, 112 μm × 112 μm × 93 μm) and d SEM micrograph of RA-QD02-0042

mission, b/a and c/a (a is the longest axis, b is themedium axis, c is the shortest axis) (Tsuchiyama et al.
2014), are 0.72 ± 0.13 and 0.44 ± 0.15, respectively, and aresimilar to the mean axial ratio of fragments generated inlaboratory impact experiments (a:b:c ≈ 2:√2:1 or b/a ≈0.71 and c/a ≈ 0.5). Note that the bulk density of
Itokawa samples is 3.4 g cm−3. The average porosityof Itokawa samples is 1.5%. We do not have any data
yet for a C-type asteroid like Ryugu.
Predicted quantities

Because we do not yet have any detailed image of a
C-type asteroid of Ryugu’s size and any experiment doneon such a surface allowing us to understand how it
responds to an external action, most of the information
regarding regolith mechanical properties of Ryugu are
predictions.
Regolith porosity Natural regolith is typically
non-spherical (measured by a quantity called sphericity)
and angular (measured by “angularity”). Together withthe adhesion properties, the median grain size and thesize distribution determine the porosity.
It is well known that random packings of monosizedcoarse spheres have a porosity of 0.363 (dense) to 0.42
(loose packing). Adhesion increases the porosity, to thelimit of 1; the decisive parameter is the granular Bond
number Bo = Fvdw/Fg, i.e., the ratio of van der Waals
forces and weight acting on a grain (Kiuchi andNakamura 2014). If the particles are polydisperse, theporosity tends to decrease with the width of the size
distribution (the smaller particles filling up the voids ofthe larger particles). Finally, non-spherical grains tend toincrease the porosity compared to packings consisting of
spherical grains.
A well-known packing theory which can be used forpredictions is described in Zou et al. (2011). Here, theequation expressing the “initial porosity” as a functionof grain size has to be generalized to arbitrary gravity(instead of 1 G), and the assumption has to be madeon the increase of initial porosity due to shape effects.
Ryugu has a very low gravity so that compaction
by lithostatic pressure is not likely to play a role in
the upper meter or so. This is different from themoon: the porosity of lunar regolith (as a functionof depth) is relatively well known; it is 83% on thevery surface (Hapke and Sato 2016) and decreases
quickly to about 58% at a few centimeters and toabout 38% at a few meter depth. Apart from thevery upper surface, we see compaction by overburden pressure at work (Schräpler et al. 2015; Omura
and Nakamura 2017).

Wada et al. Progress in Earth and Planetary Science(2018) 5:82

Given these considerations, a porosity of ~ 0.4–0.5
can be assumed for the near-surface regolith, whichcorresponds to the random loose packing of slightly
adhesive (relative to weight) centimeter-sized irregular
but roundish particles with a size distribution.
Regolith subsurface properties According to Britt andConsolmagno (2001), the materials in porous asteroids
may be sorted by the particle size. The large irregularpieces (and larger voids/fractures) may be located deeper
inside the asteroid, and the fine particle size fractions
that are observed on their surfaces are restricted to thesurface regolith zone (Fig. 13). The large interior voids/
fractures are preserved from infilling by the effects offriction on the smaller size fractions. Friction tends todominate the downward pull of gravity and prevents thefine fractions from filtering into the interior of the asteroid and infilling the large fractures and voids. Friction
may also play a role in allowing shattered asteroids tomaintain their relief features and shape by resisting the
movements of pieces within the object, in effect providing strength to non-coherent objects.
However, another mechanism, called the Brazil nut effect, may cause an opposite trend (Tancredi et al. 2012,2015; Matsumura et al. 2014; Maurel et al. 2017) andsegregate larger particles to the surface, as seen on
Itokawa. Thus, coarse gravel (1 cm or greater) may be
expected to exist on the surface overlaying fine-grainedmaterial with the fraction of fines increasing with depth.
The combination of low surface acceleration and solar

Fig. 13 Schematic of the possible structure of rubble pile asteroids.
The original reaccretion of these objects is assumed to be particle
size sorted with the largest pieces accreting first to form the core of
the object and successively smaller sizes accreting later (Michel andRichardson 2013). The finest size fractions are generated at thesurface by regolith action. These fine particles are confined to thenear-surface zone by the dominance of frictional forces (from Britt
and Consolmagno 2001)

Page 20 of 30

radiation pressure tends to strip off fine particles thathave been generated by comminution processes andleave lags of larger, harder to move materials. On theother hand, this material may experience thermal fatigue
that can turn them in smaller pieces. There is thus acompetition between various processes, and we are notyet in a position to understand which one is dominantor their respective contributions to the final product.
We would actually need at least one image of the surface
of a C-type asteroid of Ryugu’s size, which does not yet
exist, and thus, we have to wait for Hayabusa2 toprovide one.
Regolith cohesion, angle of friction, tensile strength,
and their influence on shear strength In terrestrial
environments, the shear strength of regolith is driven
by inter-grain frictional forces and rotations; however,both effects are largely affected by the level of gravity.
Thus, as gravitational forces decrease, other forces start
to govern the behavior of granular matter. With thedecrease of gravitational forces, the importance of
attractive forces like van der Waals forces rise. These
attractive forces may, like higher gravity, increase thefrictional forces by holding the grains together andhence increasing the normal pressure. Thereby, both
frictional forces and resistance torques are increased,
which in turn increase shear strength. Taking these
considerations into account, the behavior of granularmatter gets even more complex in micro-gravity (μg).
Furthermore, each particle is affected by the spin of theasteroid (particularly if it is fast) and the resulting
forces, which constantly try to separate the grains andthus break the soil.
Cohesion, friction angles, and relative density havebeen linked for the lunar regolith as shown in Fig. 14.
With an assumption of 50% porosity, the cohesion

Fig. 14 Friction angle as a function of cohesion and relative density
for the regolith on the Moon (same as Fig. 9.27 of Heiken
et al. 1991)

(2018) 5:82

should be 300 Pa, and the angle of friction about 37°.
However, this is estimated for lunar regolith with finegrains. If Ryugu’s regolith is coarser (1 mm to 1 cm
grains), then it may have lower cohesion, say 100 Pa(30% relative density) equivalent to an angle of frictionof 33°. From this, we can estimate the tensile strengthfrom the Mohr-Coulomb curve to be 1 kPa or less (seeFig. 9.26 of Heiken et al. 1991). The effect of gravity is acomplicating factor, but Kleinhans et al. (2011) haveshown that if gravity decreases, the static angle of reposeof regolith increases.
While cohesion in regolith is best known for the influence of water bridges in terrestrial environments, here
the term cohesion covers the whole range of attractive
forces. Due to the absence of water, the most important
attractive forces for μg environments are van der Waals
forces, electrostatic forces, magnetostatic forces, andself-gravity (Scheeres et al. 2010; Murdoch et al. 2015).
In a study comparing the cohesive forces to gravitational
forces in different levels of gravity, Scheeres et al. (2010)
have shown that cohesion might be one of the governing
effects for the shear strength of granular matter in
micro-gravity. Using scaling laws, the study showed thatcohesion mostly governed by van der Waals forces may
be able to be the governing force even for gravel-sizedparticles (~centimeter size) in Ryugu’s ambient gravity as
shown in Fig. 15.
The non-dimensional bond number can be expressedby the relation between the gravitational weight and thecohesional forces (Scheeres et al. 2010, see Fig. 16):
B¼

FC
:
Fg

ð16Þ

100000Force (Newtons)

11G
1 milli-G
1 micro-G
VDW for S = 1
VDW for S = 0.1
VDW for S = 0.01
Terminator ES
SRP @ 1 AU
Self gravity

1e-05

1e-10

1e-15

1e-20
1e-06

1e-05

0.00010.001
0.01
Particle Radius (meters)

0.1

1

Fig. 15 Magnitude of different forces compared to gravity as afunction of particle radius (from Scheeres et al. 2010). VDW expresses
van der Waals force, and S is the surface cleanness (S goes to 1 forclean surfaces). Ryugu’s ambient gravity is estimated of the orderof 0.25 m G

Page 21 of 30

1
B=1
B = 10B = 100
0.1

Particle Radius (meters)

Wada et al. Progress in Earth and Planetary Science

0.01

0.001

1999 KW4 Range

0.0001

1e-05

Itokawa Range

1e-06
1e-08

1e-07

Eros Range

0.01
0.001
0.0001
1e-05
1e-06
Ambient Gravitational Acceleration (Earth Gs)

0.1

1

Fig. 16 Bond numbers as a function of particle radius andgravitational acceleration (from Scheeres et al. 2010). Ryugu’s
ambient gravity is estimated of the order of 0.25 m G

For the expected gravitational level of Ryugu, Scheeres
et al. (2010) predict bond numbers of one for gain sizes
up to 10th of cm. They also state that clumping andmacroscopic cohesional behavior will be present even inregolith made of coarse sand portions. Other authors
like Durda et al. (2012) studied the likely behavior ofasteroid regolith using terrestrial laboratory simulants.
As inter-grain cohesion forces act on the grain frictionlevel, they act similarly to overburden pressure regarding
macroscopic friction and grain rolling. This may easily
be shown regarding the normal FN and tangential forces
FT on grain level:
F N ¼ F r− F C

ð17Þ

F T ¼ ð F N þ F C Þμ

ð18Þ

where Fr is the repulsive force due to contact, FC is thetotal cohesion force, and μ is the micro-scale friction
coefficient. The effect of cohesion lowers the repulsive
effect of contact forces by holding grains together,whereas this effect does not lower the effective normal
force for friction as cohesion keeps the contact in atense condition. Regarding this issue, the magnitude of
the frictional force may not only depend on the level ofgravity and the bond number but also on the loading
history. Higher loads that might have occurred in thepast will compact the material establishing a larger number of bonds at possibly larger bond areas and thus increase the total amount of contact tension. The higher
contact tension and thus micro-scale normal forces, thehigher the friction forces and hence the macro-scale
shear strength.
Given the expected angle of friction as stated above
and the expected grain shape, inter-grain friction canalso be expected to be higher than for most terrestrial

Wada et al. Progress in Earth and Planetary Science(2018) 5:82

sands. Thus, the inter-grain friction angle for a spherical surrogate particle is expected to be in the rangeof 40–50°.
Regolith bearing strength Assuming that the shape of
an interacting device with the regolith is a square ora circle, the bearing capacity or strength of the regolith is defined as σ = 1.3 × c × Nc, where 1.3 is theshape factor (corresponding to a square or a circle),c is the regolith cohesion, and Nc is the bearing
capacity factor. Assuming that cohesion is of theorder of 100 Pa and that Nc is in the range 6–20
depending on the actual angle of friction (0–33°),
then the bearing strength may be of the order of afew kPa or lower.
Whole rock properties We use as a reference theMaster’s thesis of Shigaki (2016, Kobe University) for
regolith with millimeter size range particles (Table 7);
for bigger rocks, strength scaling may apply, resulting in
weaker strength with increasing size. Note that the tensile strength measure gives similar or slightly higher
values. The compressive (unconfined) strength of sandstone is of the order of 50–100 MPa, while tensile
strength is of the order of a few MPa (Ahrens 1995).
However, the rock porosity of Ryugu may be higher(~ 40%) than the rock porosity of sandstone (~ 20%),and therefore, the compressive and tensile strengths
may be a factor 3 lower than that of sandstone, similar to Weibern tuff (Poelchau et al. 2014). This meansthat we can assume that the compressive strength
could be of the order of 15–30 MPa and the tensile
strength about 1 MPa or less.
Presence of ponds and their properties For sample return missions, very flat areas among the wide variety ofasteroid surfaces are the most sought after since they are
the safest places to touch down. As revealed by asteroid
surfaces imaged at the centimeter scale, ponds are goodcandidates (Veverka et al. 2001; Robinson et al. 2001;
Cheng et al. 2002; Miyamoto et al. 2007). Since it isTable 7 Crushing strength of various materials from Shigaki(2016)
Materials

Crushing strength (MPa)

Chondrule from Allende (CV3)7.7 ± 5.9

Chondrule from Saratov (L4)9.4 ± 6.0

Glass bead (1 mm size)

223 ± 61

Dunite (a few mm)

13.1 ± 2.6

Basalt (a few mm)

16.9 ± 2.6

Sandstone (a few mm)*

3.4 ± 1.1

*Sandstone can be considered as an upper limit for the whole rock properties
of Ryugu

Page 22 of 30

likely ponds are present on Ryugu’s surface, it is essential
to know if there is a difference between the materialpresent in the ponds and the material in other areas. Do
our chondrite samples help us solve this issue?
Some fine-grained cognate lithologies in chondrites(Figs. 17 and 18) have been inferred to be sedimentaryfeatures indicating that they sample asteroid ponds. A
cognate clast in the Vigarano CV3 chondrite, first identified by Johnson et al. (1990), appears to be a sample
from such a pond of a C-type asteroid. The clast consists
mainly of micron-sized grains of olivine, arranged intolayers with varying composition and porosity. The densest (most Fe-rich) olivine grains are in sections of layerswith the lowest bulk porosity, which appears bright in
BSE images. The most remarkable aspect of the clast is
crossbeds. Zolensky et al. (2002), Zolensky and Le(2017) proposed that this clast is formed by the processes of electrostatic grain levitation and subsequent
seismic shaking. They then described similar clasts inanother Vigarano sample, and in a section of Allende—
all CV3 chondrites, and most recently in the LL3 chondrite NWA 8330 (Zolensky and Le 2017). These clastsconsist mainly of olivine, whose compositional range isessentially identical to the host meteorite, although there
is a striking predominance of heavy, Fe-rich olivine in
the bulk clast relative to the bulk host. However, becauseof the compositional zoning within the pond deposit
layers, the top-most surface is depleted in Fe-rich,heavier olivine. Based on these observations, samples
collected from the surfaces of ponds on Ryugu will
significantly differ from the bulk asteroid by being
finer-grained and metal-poor, and silicates will be
Fe-poor. Note that Itokawa samples were also depleted from typical LL chondrites by being metal depleted. Grain sizes in Ryugu regolith probably will
extend down to the micron size, as was the case for
Itokawa.
This interpretation is however challenged by a recent
survey of Fe-rich secondary phases in CV chondrites(Ganino and Libourel 2017), which states that the phases
constituting such similar networks of veinlets formed in
reduced conditions near the iron-magnetite redox buffer
at low aSiO2 (log(aSiO2) < − 1) and moderate temperature(210–610 °C). The various lithologies in CV3 chondrites,
i.e., CV3Red, CV3OxA, and CV3OxB, including thosepresent in Figs. 17 and 18, and their diverse porosity andpermeability (MacPherson and Krot 2014) are in good
agreement with CV3 lithologies being variably alteredcrustal pieces coming from an asteroid percolated heterogeneously via a porous flow of hydrothermal fluids. Thesehot, reduced, and iron-rich fluids resemble pervasive,
Darcy flow type, supercritical hydrothermal fluids, andconsistent with textural settings of secondary phases, as
scattered patches in the CV chondrite matrices or, whenWada et al. Progress in Earth and Planetary Science(2018) 5:82

Page 23 of 30

Fig. 17 Backscattered electron image of a portion of a pond deposit clast from the Vigarano CV3 chondrite. The mineralogy of the clast is mainly
olivine, with Fe-rich olivine being lighter in shade. Sedimentary beds are apparent, and light gray (Fe-olivine-rich) layers are at the bottoms of thebeds. Crossbeds are apparent

Fig. 18 Close-up on the clast in Fig. 17, showing the bottom of one bed (upper left) with a sharp contact with the top of the succeeding bed(lower right). The mineralogy of the clast is mainly olivine, with Fe-rich olivine being lighter in shade. The highest concentration of light gray, Ferich olivine is at the bottom of the bed. Insert image at lower left is a lower mag view of the same area, with the high mag area at the lower leftof the insert. Note that the grain size extends down to the micron scaleWada et al. Progress in Earth and Planetary Science(2018) 5:82

Page 24 of 30

Table 8 Properties of Ryugu, covered and discussed in the text
Global properties
Measured

Eccentricity

0.190208

Semi-major axis

1.189555

AU

Inclination

5.883556°

Period473.8878

Days

Perihelion

0.963292

AU

Aphelion

1.415819

AU

Rotation period

7.6326hPole direction in ecliptic
coordinates (lambda, beta)(310–340, − 40 ± 15)

°

Shape

Almost spherical

Volume-equivalent diameter

850–880

Phase function (Lommel-Seeliger model)

see Table 2

Geometric and bond albedos

see Table 3

Spectral typeC-type, see also Table 4

DerivedComposition (meteorite
spectral counterpart)

heated CM, CM2, or CI

Predicted

Satelliteno

Dust around Ryuguno or little

Boulders: power law
exponent of cumulative SFD−3

Crater density

more than Itokawa, less than Toutatis

Surface roughness atmeter scales

like Eros and Itokawa

OriginOriginated in the inner main asteroid belt,
between ~ 2.1 and 2.5 AU, and reachedthe ν6 by inward Yarkovsky driftm

Regolith thermophysical properties
Measured

DerivedPredicted

Thermal inertia

150–300, typically 200

J m−2 s−1/2 K−1
KMaximum surface temperature

320–375

Roughness (the rms
of surface slopes)< 0.1

Regolith thermal conductivity

0.020–0.108, most likely 0.042

W m−1 K−1

Typical particle size in diameter

3–30 most likely 6–10 (2.2–5 byGundlach and Blum 2013 model)

mm

Regolith heat capacity at 300 K

758

J kg−1 K−1Regolith emissivity

0.9Regolith thermal albedo

0.019

Regolith bulk density

1100–1500

kg m−3

Regolith mechanical properties
Predicted

Regolith porosity~ 0.4–0.5

Regolith cohesion

100

Pa

Regolith angle of friction

33°

Regolith tensile strength< 1000Pa

Inter-grain friction angle

40–50

°

Wada et al. Progress in Earth and Planetary Science(2018) 5:82

Page 25 of 30

Table 8 Properties of Ryugu, covered and discussed in the text (Continued)
Regolith bearing strength< a few 1000

Pa

Compressive strength of rock

15–30

MPa

Tensile strength of rock

<1

MPa

Presence of ponds

Possible, there are compositions being
expected to be significantly different
from that of the bulk asteroid

the fluid is channelized, as subtle veinlet networks. If thisinterpretation is correct, the permeability/porosity/cohesiveness of the unprocessed Ryugu surface, assuming CV(or CO) chondrites are relevant proxy, will depend on the
percolation of hydrothermal fluids in the Ryugu’s parent
body, and their efficiency to precipitate secondary phases,
which will in turn control the formation and evolution of
the regolith, its size distribution, and the ease of its
sampling (see the “Regolith thermophysical properties”
section).

Conclusions
We have reviewed a wide range of information about theC-type, NEA (162173) Ryugu from the point of view ofdescribing the regolith layer of Ryugu: the global properties, the thermophysical properties, and the mechanicalproperties. Each property is categorized into three types,
i.e., the measured/observed, the derived, and the predicted properties, as summarized in Table 8. This tablegives a reference model of Ryugu, especially on the surface regolith.
As a whole, this paper provides a reference model of
Ryugu’s regolith which should be extremely useful bothfor science applications until Hayabusa2’s arrival and for
Hayabusa2 operations at Ryugu. It will be checked andrefined thanks to Hayabusa2 data, and further relatedscientific studies will be promoted toward understanding
Ryugu, other small bodies, and solar system evolution.
Abbreviations
ESO-VLT: Very Large Telescope of the European Southern Observatory;
CNES: Centre National d’Etudes Spatiales; DCAM3: Deployable camera 3;
DLR: German Aerospace Centre; IRSG: International Regolith Science Group;
JAXA: Japan Aerospace Exploration Agency; LIDAR: Light detection andranging; MARA: Multi-channel radiometer; MasCam: MASCOT camera with
illumination unit; MasMag: Magnetometer; MBA: Main belt asteroids;
MicrOmega: Near- to mid-infrared spectromicroscope; MOID: Minimum orbit
intersection distance; NEA: Near-Earth asteroid; NIRS3: Near-infrared
spectrometer; ONC: Optical navigation cameras; ONC-T: Optical navigation
telescopic camera; ONC-W1 and W2: Optical navigation wide field of view
cameras 1 and 2; PSL: Planetary Science Laboratory; RADF: Radiance factor;
SCI: Small Carry-on Impactor; SFD: Cumulative size-frequency distributions;
TIR: Thermal infrared imager; VLT: Very Large Telescope; VWD: van der Waals
force; YORP: Yarkovsky-O’Keefe-Radzievskii-Paddack effect; μg: Micro-gravity
Acknowledgements
We thank two anonymous reviewers for the useful comments that improved
this paper. We are grateful to Daniel Jay Scheeres, Paul Sanchez, andChristine Hartzell for providing figures and helpful comments. This paper
is a product of IRSG in Hayabusa2 project, JAXA. The members of IRSG,

except for the authors of this manuscript, are as follows: Paul Abell,
Masahiko Arakawa, Young-Jun Choi, Harold C. Connolly Jr., Carsten
Güttler, Naru Hirata, Tra-Mi Ho, Trevor R. Ireland, Masato Kiuchi, Goro
Komatsu, Dante Lauretta, Deborah Domingue Lorin, Clara Maurel,
Tomokatsu Morota, Sho Sasaki, Hirotaka Sawada, Daniel Jay Scheeres,
Nicole Schmitz, Stephen R. Schwartz, Seiji Sugita, Shogo Tachibana,Satoshi Tanaka, Eri Tatsumi, Florian Thuillet, Yuichi Tsuda, Faith Vilas, Sei-ichiro Watanabe, Hikaru Yabuta, Hajime Yano, and Makoto Yoshikawa.
Funding
KW is supported by JSPS KAKENHI Grant Number 15K05273. PM and MAB
acknowledge financial support from the French space agency CNES. MEZ is
supported by the NASA Emerging Worlds and Hayabusa2 Participating
Scientist Programs, and the SERVII Center for Lunar Science and Exploration.
TM has received funding from the European Union’s Horizon 2020 Researchand Innovation Programme, under Grant Agreement no 687378. This material isbased partly upon work supported by NASA under Contract NNM10AA11C
issued through the New Frontiers Program. CME and DT are supported by theNASA Hayabusa2 Participating Scientist Program.
Availability of data and materials
Data sharing is not applicable to this article as no datasets were generated
or analyzed during the current study.
Authors’ contributions
KW led this study. MG, PM, and KJW proposed the topic and designed eachsection of this study. The other authors contributed to reviewing related
works, writing parts of the manuscript, and proposing some critical ideas on
this study, based on their own expertise. All authors read and approved thefinal manuscript.
Authors’ information
KW is a PI of the International Regolith Science Group (IRSG) which is abranch of the Interdisciplinary Science Team in the Hayabusa2 project. KW,
MG, PM, KJW, and HM are core members of IRSG.
Competing interests
The authors declare that they have no competing interests.

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.
Author details
1
Planetary Exploration Research Center, Chiba Institute of Technology,
Tsudanuma 2-17-1, Narashino, Chiba 275-0016, Japan. 2DLR Institute ofPlanetary Research, Rutherfordstr. 2, 12489 Berlin, Germany. 3Université Côted’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, CS
34229, 06304 Nice Cedex 4, France. 4Southwest Research Institute, Boulder,USA. 5Laboratoire d’Etudes Spatiales et d’Instrumentation en Astrophysique(LESIA), Observatoire de Paris, PSL Research University, CNRS, Université Paris
Diderot, Sorbonne Paris Cité, UPMC Université Paris 06, Sorbonne Universités,
5 Place J. Janssen, 92195 Meudon Principal Cedex, France. 6DLR RB-MSC
German Aerospace Center, 51147 Cologne, Germany. 7Institut für Geophysik
und extraterrestrische Physik, Technische Universität Braunschweig,
Mendelssohnstr. 3, 38106 Braunschweig, Germany. 8Johns Hopkins University
Applied Physics Laboratory, Laurel 20723, MD, USA. 9DLR German Aerospace
Center, Institute of Space Systems, System Engineering and Project Office,Robert-Hooke-Strasse 7, 28359 Bremen, Germany. 10Department of BiologicalWada et al. Progress in Earth and Planetary Science(2018) 5:82

and Environmental Sciences, University of Stirling, Stirling FK9 4LA, Scotland.
11
Physics Institute, University of Bern, Bern, Switzerland. 12Center for Space
Situational Awareness, Korea Astronomy and Space Science Institute, 776,
Daedeokdae-ro, Yuseong-gu, Daejeon 305-348, Republic of Korea. 13Planetary
Science Institute, 1700 East Fort Lowell, Suite 106, Tucson, AZ 85719, USA.
14
DLR Institute of System Dynamics and Control, Oberpfaffenhoffen,
Germany. 15Robert M Walker for Space Sciences, Astromaterials Research andExploration Science, NASA Johnson Space Center, Houston, TX 77058, USA.
16
Faculty of Engineering, Kindai University, Hiroshima Campus, 1 Takaya
Umenobe, Higashi-Hiroshima, Hiroshima 739-2116, Japan. 17Department of
Systems Innovation, University of Tokyo, Tokyo 113-8656, Japan. 18Max-Planck
Institute for Extraterrestrial Physics, Garching, Germany. 19Department ofPlanetology, Graduate School of Science, Kobe University, 1-1 Rokkodai,
Nada-ku, Kobe 657-8501, Japan. 20Department of Terrestrial Magnetism,
Carnegie Institution of Washington, 5241 Broad Branch Rd NW, Washington,
D.C. 20015, USA. 21Institute of Space and Astronautical Science, Japan
Aerospace Exploration Agency, Sagamihara, Japan. 22INAF, Istituto di
Astrofisica e Planetologia Spaziali, via Fosso del Cavaliere, 00133 Rome, Italy.
23
JETS/Astromaterials Research and Exploration Science, NASA Johnson
Space Center, Houston 77058, TX, USA.
Received: 25 June 2018 Accepted: 29 October 2018

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