Lunar and Planetary Science XLVIII (2017)
2881.pdf
INVESTIGATING THE EFFECTS OF THE ROTATION AND INTERIOR DENSITY DISTRIBUTION ON
THE SURFACE GRAVITY FIELD OF ASTEROID ITOKAWA. M. Kanamaru1 and S. Sasaki1, 1Department
of Earth and Space Science, Graduate School of Science, Osaka University (Address: 560-0043, 1-1,
Machikaneyama, Toyonaka, Osaka, Japan. E-mail: [email protected]).
Table 1. Physical characteristics of Itokawa [3][6].
Dimentions [m]
535 294 209 ( 1m)
Rotation period [hour]
12.1324 0.0001
Mass [kg]
(3.58 0.18) 1010
Bulk Density [kg/m3]
1,950 140
DensityEs1ma1on-GravityPoten1al
0.0030
NormalizedStandardDevia1onofPoten1al
Introduction: The Hayabusa spacecraft visited asteroid 25143 Itokawa and unveied its detailed surface
topography and active geological phenomena. Itokawa
surface is clearly divided into rough highlands and
smooth terrain [1]. Rough areas are covered with lots of
boulders, on the other hand, smooth terrain is covered
with centimeter-sized gravel. It is considered to be an
evidence of regolith migration by seismic shaking [2].
Fine gravel was segregated into areas of potential lows
and formed the smooth terrain. The gravity field on the
surface has a great role in formation and evolution of
surface topography.
However, the internal structure of Itokawa is still an
open question. Itokawa is considered to be a rubble-pile
object [3]. Therefore, it is possible that Itokawa has
heterogeneity inside that reflects its formation process.
Light curve observation and YORP simulation for Itokawa suggests shift of the center-of-mass (COM) by
~21m [4]. It is explained by a difference of bulk density
between two lobe, “head” and “body”.
In this study, we investigate a main factor affecting
the surface gravity field of Itokawa, internal density
distribution. We aim to make a restriction on the interior structure in terms of gravity potential and surface
slope.
Gravity Calculation: A polyhedral method is
suitable to calculate the gravity field of an irregularshaped body [5]. If we assume that a small body is a
constant-density polyhedron, we can calculate the gravitation from a 3D shape model. The gravity field on the
surface of Itokawa can be computed as a resultant force
of the gravitational force and the centrifugal force due
to the rotation at the rate of ~12 hour (Table 1). We referred to a Gaskell’s shape model (49,152 triangle surface facets) [7] and gravity simulation code developed
in Aizu Univeristy [8].
Remodeling the polyhedron model. We remodeled
the constant-density simulation so that we can calculate
the gravity field assuming denisty heterogeneity inside
the polyhedron. We generated tetrahedral meshes also
inside the body using “Netgen” mesh generator [9]. We
2,244SurfaceElements
0.0025
5,530SurfaceElements
0.0020
0.0015
0.0010
0.0005
Densityof"Head"[kg/ ]
Figure 1. We calculated the gravity potential through
the global surface of Itokawa giving different densities to the head and body. The head density of ~2,650
kg/m3 minimized the standard deviation despite resolution of shape models.
calculated the gravitation of each tetrahedral unit, based
on the polyhedral method [5], and added together contributions from all units through the Itokawa’s shape.
Each unit was given constant density according to a
density map, such as a planar division model where
density of the body part is 1,750 kg/m3 and that of the
the head part is 2,850 kg/m3 (a compressed head model,
Figure 4) [4][10].
Density Estimation: We calculated variance of
gravity potential through the surface of Itokawa as a
function of bulk density of the “head”. Density of the
remaining “body” was derived from the restriction condition of total mass. Potentiail variance was minimized
where the head density was ~2,650 kg/m3 (Figure 1).
This corresponds to a body density of ~1,800 kg/m3 and
the COM shift by ~16m toward the head.
This study implies a new evidence of internal heterogeneity for Itokawa. The mean bulk density of 1,950
kg/m3 shows Itokawa is a rubble pile object [6]. If we
assume that two lobes of Itokawa are composed of
similar LL-chondrites, the internal density variation
mentioned above corresponds to porosity widely rang-
Lunar and Planetary Science XLVIII (2017)
0.01
0.02
0.03
0.04
0.05
Constant density, 12.1324 hr period
Compressed head, 12.1324 hr period
Compressed neck, 12.1324 hr period
0.00
Fraction of Global Surface Area
0.06
Slope Distribution of Different Density Maps
0
10
20
30
Slope (degree)
40
50
Figure 2. Internal density variation caused to change
the slope distirbution. A compressed head tended to
relax steep slopes of ~30 to 40 degrees. On the other
hand, slopes increased assuming that the “neck” region was locally compressed.
Slope Distribution of Compressed−Head Model
0.06
0.05
0.04
0.03
0.02
0.01
Fraction of Global Surface Area
0.07
Compressed head, 12.1324 hr period
Compressed head, 9.0 hr period
Compressed head, 6.5 hr period
Compressed head, 5.0 hr period
Compressed head, 4.0 hr period
0.00
ing from ~15% to ~45%. The head of Itokawa is possible to have a more monolithic structure in comparion
with the remaining part.
Slope Distribution: “Slope” is defined as a separation angle between a gravity acceleration vector and a
normal vector of a surface facet. Surface slopes are
affected by internal mass distribution and a rotation
period despite use of a same shape model. Slope distribution reflects surface topography and macroscopic
roughenss and is considered to be an indicator of a
mismatch between the gravity field and the surface topography.
We investigated the responses of slope distribution
to three different density maps: a constant density model, a compressed head model and a compressed “neck”
model (Figure 2). Local compression of the “neck” part
between the head and body can explain the COM shift
by ~21m [4]. However, the compressed head model
made the gravity field in harmony with the surface topography most of three types of density distribution.
We also calculated slope distribution assuming different rotation periods other than the rate of ~12 hour.
We confirmed that faster rotation tended to make slope
distribution flatter. The surface became the flattest
when Itokawa was spinning at a rate of 5 hour. However, 4 hour period increased steep slopes in reverse
(Figure 3).
YORP spin-up/down might have a strong effect on
the Itokawa’s history of reconfiguration in hundreds of
thousand years time span [11]. We need further research of a correlation between a time scale of changing
spin state and that of erosion processes in terrain.
2881.pdf
0
10
20
30
Slope (degree)
40
50
Figure 3. We added the centrifugal force due to
faster rotation on the gravitation of the compressed
head model.
Figure 4. Itokawa’s shape is devided into the head
and the body at ~150m in the X-axis.
References: [1] Demura et al. (2006), Science, 312,
1347–1349. [2] Miyamoto et al. (2007), Science, 316,
1011–1014. [3] Fujiwara et al. (2006), Science, 312,
1330–1334. [4] Lowry et al. (2014), Astronomy & Astrophysics 562, A48. [5] Werner and Scheeres (1997),
Celestial Mechanics and Dynamical Astronomy, 65,
313–344. [6] Abe et al. (2006), Science, 312, 1344–
1347. [7] Gaskell et al. (2006), AIAA-2006-6660. [8]
Mitsuta et al. (2012), 39th COSPAR Scientific Assembly,
39, 1254. [9] Netgen Mesh Generator © 1987-2016 Tcl
Core Team. [10] Takahashi and Scheeres (2014), Icarus,
233, 179–193. [11] Scheeres et al. (2007), Icarus, 188,
425–429.