494
Arakawa, M. et al., (2020), Artificial impact crater formed on the asteroid
495
162173 Ryugu in The gravity-dominated regime, Science 368, Issue
496
6486, pp. 67-71.
497
498
499
Burns, J. A. (1978). The dynamical evolution and origin of the martian
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500
dynamical environment of Phobos and Deimos, Icarus 47(2), 220-233.
501
Dobrovolskis, A.R., Joseph A. Burns, (1980), Life near the Roche limit:
502
Behavior of ejecta from satellites close to planets. Icarus 42(3),
503
422-441.
504
Geissler, P., Jean-Marc Petit, Daniel D. Durda, Richard Greenberg, William
505
Bottke, Michael Nolan, Jeffrey Moore, (1996), Erosion and Ejecta
506
Reaccretion on 243 Ida and Its Moon. Icarus 120(1), 140-157.
507
Hirabayashi, M. et al. (2019), The Western Bulge of 162173 Ryugu Formed
508
as a Result of a Rotationally Driven Deformation Process. The
509
Astrophysical Journal Letters 874, Number 1.
510
511
512
513
514
515
Hirata, Naoyuki et al. (2020), The spatial distribution of craters on Ryugu,
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516
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517
abstract #2658 presented at 50th LPSC, Houston, Texas, 18-22 March.
518
Noguchi, R. et al. (2020), Crater depth-to-diameter ratios on asteroid 162173
519
520
521
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Icarus 148(1), 12-20.
522
Scheeres, D. J., D.D. Durda, and P.E. Geissler, (2002), The Fate of Asteroid
523
Ejecta, in Asteroid III (Eds. William F. Bottke et al.), University of
Arizona Press, Tucson.
524
525
Shor, V. A. (1975), The motions of the Martian satellites, Celestial mechanics
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526
527
Sugita, S. et al. (2019) The geomorphology, color, and thermal properties of
Ryugu: Implications for parent-body processes. Science 364, 272-275.
528
529
Thomas, P.C., (1998), Ejecta Emplacement on the Martian Satellites. Icarus
131(1), 78-106.
530
531
Thomas, P.C., J. Veverka, M. S. Robinson and S. Murchie, (2001), Shoemaker
532
crater as the source of most ejecta blocks on the asteroid 433 Eros.
533
Nature 413, 394–396.
534
Veverka, J., P. Helfenstein, P. Lee, P. Thomas, A. McEwen, M. Belton, K.
535
Klaasen, T.V. Johnson, J. Granahan, F. Fanale, P. Geissler, J.W. Head
536
III, (1996), Ida and Dactyl: Spectral Reflectance and Color Variations.
537
Icarus 120(1), 66-76.
538
Walsh, Kevin J., Derek C. Richardson, and Patrick Michel (2008), Rotational
breakup as the origin of small binary asteroids, Nature 454, 188–191.
539
540
Watanabe, S. et al. (2019), Hayabusa2 arrives at the carbonaceous asteroid
541
162173 Ryugu—A spinning top–shaped rubble pile. Science 364,
542
268-272.
543
544
545
Table 1. The 7 named craters on Ryugu and their basic data from Hirata et al.
546
(2020).
Name
Lat.
Lon. (°E)
D (m)
CL*1
Urashima
-7.19
92.99
290
Cendrillon
28.34
353.68
224
II
Kolobok
-0.70
330.28
221
II
Momotaro
-14.83
51.20
183
Kintaro
0.42
157.84
154
II
Brabo
3.24
229.95
142
Kibidango
-31.50
47.26
131
Classification shown in Hirata et al.; CL I means circular depression with
547
*1
548
rim and II circular depression without rim.
549
550
551
Table 2. Scaling parameters used in ejecta model, based on Housen and
Holsapple, (2011).
No.*
C1
C2
C3
C4
C5
C6
C7
C8
Reg.**
0.55
0.55
0.46
0.41
0.41
0.45
0.40
0.35
0.2
0.3
0.3
0.3
0.3
0.5
0.3
0.32
1.5
1.50
0.18
0.55
0.55
1.00
0.55
0.60
0.68
0.59
0.59
0.8
1.1
0.38
0.40
0.81
1.5
1.0
1.0
1.3
1.3
1.3
1.0
1.0
0.5
0.5
0.3
0.3
0.3
0.3
0.3
0.2
1000
3000
2600
1600
1510
1500
1500
1200
30
0.45
4×10-3
2×10-3
𝝆𝝆𝒕𝒕
𝝁𝝁
𝒌𝒌
𝑪𝑪𝟏𝟏
𝑯𝑯𝟏𝟏
𝑯𝑯𝟐𝟐
𝒏𝒏𝟐𝟐
𝒑𝒑
(kg/m3)
𝒀𝒀
(MPa)
552
* Scaling parameters for Water (C1), Rock (C2), weakly cemented basalt (C3), sand (C4
553
and C5), glass micro-spheres (C6), sand/fly ash mixture (C7), and perlite/sand mixture
554
(C8).
555
** The strength regime (S) or gravity regime (G).
556
(e)
05
0.505
0 .49
...
... ,------- - ---------,
•••
...
-2
....
crater radii
0518
(f)
0516
051'
0512
051
0.508
ca.
0.500
(1)
,? 0504
0.502
0.5
..
(C)
0,498
- -- - - - - - - - ~
' - - - --1
crater radii
(g)
Kolobok
052
('y~
\ J
. - - - - - - - - =cr:..:a::;tec:;r..:cra::cd:,:ii_ _ _ _ _--,
Brabo / \
(\
I .
0.496 ' - - -- ~ - - - - - - - - - - - '
-1
-2
-2
053
·~-2~----_-1____0 , - - - - - - - - - - - ~
Cendrillon
Kintaro
0.5
• • • L.__ _ _ _ _ _ _ _ _ _ _ _ _ ___J
(b)
0 . .5
...
,---- - - - . . , ,c~,a~e,,.r..ca,,,d,,,ii' - - - - - - - - ,
Kibidango
,,,.
.'\
0455
051
"'.
05
...
0 .435
043 ' - - - - ~ - - - - - - - - - - - '
·1
-2
0485
ra:.:dc:.ii_ _..,...._ _--,
::te::.r.:.:
,-----.----.---=crca.:::
(d) •••
f \Momotaro !
0475
041
....
~!
O45S
557
...
crater radii
... L - - - -~ - - - - -- - - - - - '
-2
-1
558
Figure 1. Observed east-west asymmetric profiles of the 7 named craters on
559
Ryugu. In each plate, left side is west, and right side is east. The profiles are
560
from the shape model of Watanabe et al. (2019). Survey lines are shown in
561
Figure 2. Note that a sharp peak at the right side of Kibidango, and two
562
sharp peaks at the right side of Kolobok are boulders.
563
30°
Topography(m)
379 - - - - - - -- 529
o-----Slope(0 )
564
60
565
Figure 2. Local simple cylindrical projection maps of the 7 named craters and
566
locations of the survey lines in Figure 1. In each location, there are three
567
plates of ONC-T images mosaic colorized by topography and geopotential
568
slope at a rotation of 7.627 h and 3.5 hour. The center and length of the lines
569
is defined as the center and twice of the diameter of each crater, respectively.
570
Topography is defined as the distance from the geometric center of Ryugu.
571
572
,._____ x - - - --+
4--------
573
R: ______,
--- - - - - - - - n2Rc - ----------,
574
Figure 3. Definition of variables in Eq. (5) in Section 2.1. Dashed line is a
575
trajectory of a particle launched at a location,𝑥𝑥.
576
-1500
Initial launch
velocity
- - 1 .18
- - 1.65
-600
(a)
(b)
·1000
West
East
-550
-500
'<
~o
-500
2-
500
-450
1000
1500
1500
1000
500
-500
= 10000 h
-1000
-400
-1500
100
50
(m)
-1500
-50
=10000 h
-100
- - 2.14
- - 2.71
3.39
- - 4.24
5.32
- - 6.73
8.62
- - 11 .2
14.9
- - 20.4
- - 29.0
- - 43.1
68.7
120
- - 687
1200
3738
(cm/s)
(m)
-600
(c)
(d)
·1000
-550
-500
'<
-500
500
-450
1000
1500
1500
1000
500
-1500
-500
=7.627 h
·1000
-400
-1500
100
50
(m)
-50
=7.627 h
-100
x(m)
-600
(e)
·1000
-550
-500
'<
-500
500
-450
1000
577
1500
1500
1000
500
-500
=5.0 h
-1000
-400
-1500
100
50
-50
=5.0 h
-100
578
Figure 4. The trajectories of a particle launched from a 50m-radius crater to
579
the west and east, when 𝑇𝑇 =10000, 7.627, and 5.0 hours. The xy-plane
580
581
582
corresponds to the equatorial plane of Ryugu. Although we calculate
trajectories of 𝑁𝑁1 × 𝑁𝑁2 = 36,000,000 ejecta particles in order to obtain
Figs. 7, 9-11, a part of them is shown in this figure. The velocities of the
583
trajectories correspond to the initial lunch velocities of ejecta particles
584
launched from the initial launch position,𝑥𝑥, in increments of one-twentieth of
585
the crater rim radius.
586
-1500
-600
-1000
·550
-500
'<
-500
~O
2-
500
-450
1000
T = 3.5 h
1500
1500
1000
500
·500
·1000
T = 3.5 h
-400
·1500
100
50
(m)
·1500
-50
·100
Initial lau nch
velocity
- - 1.18
- - 1.65
- - 2.14
- - 2.71
3.39
- - 4.24
5.32
- - 6.73
8.62
- - 11.2
14.9
- - 20.4
- - 29.0
- - 43.1
68.7
120
- - 687
1200
3738
(cm/s)
(m)
·600
·1000
·550
·500
'<
·500
500
-450
1000
T = 3.0 h
587
1500
1500
1000
500
-500
-1000
·400
-1500
100
50
·SO
·100
588
Figure 5. The trajectories of a particle launched from the 50m-radius crater
589
to the west and east, when 𝑇𝑇=3.5 and 3.0 hours.
590
(a) T=10000h
90
Initial launch
vel ocity (cm/s)
10
60
30
·30
·10
-60
1.18
1.65
2.14
2.71
3.39
·90
30
60
90
(b) T=7.627h
1 20 150 180
210
240
270
300 330
360
140
160
150
170
180
190
200
Long1tude(E)
LOOg1tude(E)
90
60
10
30
·30
-60
4.24
5.32
6.7 3
8.62
11.2
14.9
20.4
29.0
- - Crater rim
-10
·90
30
60
90
(c) T=S.0h
120 150 180
210
140
240 270 300 330 360
150
160
Long1tude(E)
170
180
190
200
Long1tude(E)
90
.,'
10
60
30
·30
:(Q)
f-~
·60
-10
·90
30
60
90
(d) T=3.5h
1 20 150 180
210
240
270
300 330
360
140
150
160
Long1tude(E)
170
180
190
200
180
190
200
180
190
200
Long1tude(E)
90
10
60
30
·30
-10
-60
·90
30
60
90
(e) T=3.0h
1 20 150 180
210
240 270 300 330 360
140
150
160
Long1tude(E)
170
Loog1tude(E)
90
60
10
30
-30
-10
·60
-90
30
60
90
120 150 180
210
Long1tude(E)
591
240 270 300 330 360
140
150
160
170
Loog1tude(E)
592
Figure 6. The landing locations of particles launched from a crater with a
593
radius of 50m at the equator as a function of initial launch velocity of ejecta
594
particles.
(a) T=10000h
90
Initial launch
Azimuth
10
60
East
NE
Nouth
NW
West
SW
South
SE
30
-30
-60
· 10
-90
30
60
90
120 150
180
210
240
270
300 330
140
360
150
160
Long1tude(E)
(b) T=7.627h
170
180
190
200
- - Crater rim
Long1tude(E)
90
60
10
30
-8
-8
-30
'\:,
-60
-10
-90
30
60
90
120
(c) T=5.0h
150
180 210
240
270
300
330
140
360
150
160
Long1tude(E)
170
180
190
200
180
190
200
180
190
200
180
190
200
Long1tude(E)
90
60
10
30
-8
-8
-30
-10
·60
30
60
90
1 20 150 180
(d) T=3.5h
210
240
270
300
330
360
140
150
160
Long1tude(E)
170
Long1tude(E)
90
10
60
30
-8
-8
il
'.l
·30
-10
·60
·90
30
60
90
1 20 150 180
(e) T=3.0h
210
240
270
300 330
360
140
150
160
170
Long1tude(E)
Long1tude(E)
90
60
10
30
-8
-8
-30
-60
-10
-90
30
60
90
120
150
180 210
Long1tude(E)
595
240
270
300
330
360
140
150
160
170
Long1tude(E)
596
Figure 7. The landing locations of particles launched from a crater with a
597
radius of 50m at the equator as a function of initial launch direction of ejecta
598
particles.
599
,l
(a)
90
T=10000h
60
30
-1
.,
-2
-3
-30
-5
-6
-60
10'(rn)
30
60
90
120
150 180 210 240 270
Longitude(E}
300
30
60
90
120
150 180 210 240 270
Longitude(E}
300 330 360
30
60
90
120
150 180 210 240 270
300 330 360
(b)
90
T=7.627h
60
;r
·1
-2
.3
330 360
30
.5
·60
10'(rn)
·90
(c)
90
T=5.0h
60
-1
-2
.3
"8
i_,
30
.5
·60
-6
10'(rn)
LOOgitude(E}
(d)
90
T=3.5h
60
'l"
-1
.,
~ 0
-2
.3
.30
-60
10'(rn)
(e)
30
60
90
120
150 180 210 240 270
Longitude(E}
300
30
60
90
120
150 180 210 240 270
Longitude(E)
300 330 360
90
T=3.0 h
330 360
60
'j"
-1
-2
.3
Io
.5
-60
-6
600
1o'(rn)
.,
...J
-30
.90
601
Figure 8. The global distribution of ejecta thickness launched from a
602
50m-radius crater at the equator.
603
(a)
10
7.627h
5,0h
3,5h
3.0h
:E
0,1
t-
"'
tl
0.01
0 .001
150
(b)
160
170
180
190
200
210
LOngitude(E)
10
3.
3.4h
3.3h
3.2h
3.lh
3,0h
..
:E
0.1
t-
"'
tl
,!I!.
0.01
0 .001
604
605
606
607
150
160
170
180
190
200
210
Longitude(E)
Figure 9. The west-east profile of the ejecta thickness near the crater at the
equator.
Cl
C2
C3
C4
C6
C7
C8
(a) T = 3.5 h
10
(/)
C6
C7
C8
(/)
(/)
(/)
Q)
Q)
C:
C:
{)
{)
Cl
C2
C3
C4
(b) T = 3.4 h
10
0.1
ro
t5
0.1
ro
t5
Q)
Q)
w0.01
w0.01
0.001
0.001
·3
·2
·1
·3
·2
·1
crater radii
crater radii
Cl
C2
C3
C4
C6
C7
C8
(c) T = 3.3 h
10
(/)
(/)
C3
C4
C6
C7
C8
(/)
Q)
Q)
C:
C2
10
(/)
C:
-""
.:£
.S1
Cl
(d) T = 3.2 h
.S1
0.1
ro
t5
0.1
ro
t5
Q)
Q)
w0.01
w0.01
0.001
0.001
·3
·2
·1
·3
·2
·1
crater radii
Cl
C2
C3
C4
C6
C7
C8
(e) T = 3.1 h
10
(/)
(/)
Cl
C2
C3
C4
10
C6
C7
C8
(/)
(/)
Q)
Q)
C:
C:
-""
{)
{)
crater radii
0.1
Q)
0.1
~Q)
w0.01
w0.01
---608
609
610
611
612
613
614
0.001
0.001
.3
·2
·1
.3
·2
·1
Figure 10. The comparison of model results in the 8 sets of scaling
parameters in Table 2. It shows that the west-east profile of the ejecta
thickness near the crater along the equator as a function of the rotation
period between 3.5h and 3.0 h.
(a)
90
LAT=30
60
10-1
-2
-3
30
QI
"O
_J
-4
·30
-5
-6
-60
10x(m)
30
(b)
LAT=60
10-1
-2
-3
-4
-5
-6
60
90
120
150 180 210
240
270
300 330 360
240
270
300 330 360
Longitude(E)
90
60
30
QI
"O
1i
_J
·30
-60
10x(m)
30
60
90
120
150 180 210
Longitude(E)
(c)
10
LAT=O
LAT=30
LAT=60
original
::l
QI
-l3
:c
0.1
I-
"'
t:l
fil
0.01
0.001
-3
615
616
617
618
619
620
621
622
623
624
-2
-1
crater radii
Figure 11. (a) The global ejecta thickness of a 50m-radius crater formed at
30°N, 180°W when 𝑇𝑇 =3.0 hours. (b) The global ejecta thickness of a
50m-radius crater formed at 60°N, 180°W when 𝑇𝑇 =3.0 hours. (c) The
comparison of the west-east profile of the ejecta thickness near the crater
formed at the equator, 30°N, and 60°N when 𝑇𝑇=3.0 hours. The horizontal
axis is scaled at 1 crater radius (50 meter).
Urashima
Cendrillon
(f)
(a)
90
T=10000h
90
T=10000h
60
-1
-2
-3
-4
60
f'
30
"C
.e o
-30
-1
-2
-3
30
-4
-60
-60
-5
10'(rn)
10'(rn)
30
(bl
60
90
90
120 150 180 210
Longitude(E)
240 270
300 330 360
60
21
-1
-2
-3
-4
Jj
-2
-3
-60
-4
30
60
90
120 150 180 210
Longitude(E)
240 270 300 330 360
10'(rn)
30
60
90
120
240 270
300 330 360
30
60
90
120 150 180 210 240 270
300 330 360
30
Jj
.e o
-2
-3
-30
-30
-4
·60
·60
-5
10'(rn)
30
60
90
(d)
90
T=3. 5h
120 150 180 210
Longitude(E)
240 270
300 330 360
(i)
90
T=3.5h
60
60
30
'I"
1l
-8
.e o
-2
-3
·30
-4
-60
JJ
·30
-2
-3
-60
-4
-5
-5
-90
10'(rn)
30
60
90
120 150 180 210
240 270 300 330 360
Longitude(E)
(e)
90
T=3.0h
10'(rn)
T=3.0h
60
2-
Longitude(E)
90
60
30
30
-8
-8
.e o
.e o
Jj
-30
-2
-3
-60
-4
-5
1o'(rn)
300 330 360
-8
.11
625
120 150 180 210 240 270
Longitude(E)
60
.e o
-4
90
-60
90
(h)
T=5.0h
-8
-2
-3
60
·30
-5
-90
30
.i
30
·30
60
300 330 360
.e o
-1
120 150 180 210 240 270
Longitude(E)
-8
.e o
-4
10'(rn)
90
30
-8
90
(c)
T=5.0h
-2
-3
60
60
30
10'(rn)
30
(g)
90
T=7.627h
T=7.627h
-30
-60
-5
30
60
90
120 150 180 210
240 270 300 330 360
10'(rn)
30
60
90
120 150 180 210 240 270
300 330 360
626
Figure 12. The global ejecta thicknesses from Urashima, Cendrillon, and
627
Kolobok and Brabo craters.
628
Kolobok
Brabo
(f)
(a)
90
T=10000h
90
T=10000h
60
Jj
60
f'
30
"C
.e o
-2
-3
-4
-5
·30
-60
10x(m)
-1
-2
-3
-4
-5
30
-60
10x(m)
30
(bl
60
90
90
120 150 180 210
Longitude(E)
240 270
300 330 360
30
60
90
120 150 180 210 240 270
Longitude(E)
300 330 360
30
60
90
120 150 180 210 240 270
Longitude(E)
300 330 360
30
60
90
120 150 180 210 240 270
Longitude(E)
300 330 360
30
60
90
120 150 180 210 240 270
300 330 360
(g)
90
T=7.627h
T=7.627h
60
60
230
X -1
-2
-3
-4
Jj
-8
.e o
.e o
-30
-2
-3
-4
-5
-60
10x(m)
30
60
90
90
(c)
T=5.0h
120 150 180 210
Longitude(E)
240 270 300 330 360
10x(m)
Jj
-8
.e o
.11
-2
-3
-4
-5
-30
-60
30
60
90
(d)
90
T=3.5h
-60
120 150 180 210
Longitude(E)
240 270
300 330 360
(i)
90
T=3.5h
60
60
'I"
1 -
"ll
-2
-3
-4
-5
30
-1
X -2
-3
-4
-5
-6
10x(m)
-8
.e o
'1
·30
-60
-90
10x(m)
30
60
90
120 150 180 210
240 270 300 330 360
Longitude(E)
(e)
90
T=3.0h
-30
-60
-90
T=3.0h
60
2-
30
30
-8
629
630
631
1o'(m)
Longitude(E)
90
60
-2
-3
-4
-5
-30
10x(m)
10x(m)
.i
30
-8
.e o
-1
-60
60
30
-30
90
(h)
T=5.0h
60
-2
-3
-4
30
-8
.e o
:l
-1
-2
-3
-4
-5
-6
10x(m)
-30
-60
30
60
90
120 150 180 210
240 270 300 330 360
-8
.e o
-30
-60
30
60
90
120 150 180 210 240 270
300 330 360
Figure 13. The global ejecta thicknesses from Kolobok and Brabo craters.
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