論文紹介セミナー15分発表 2010/4/22

Houston, Texas

学会参加報告学会参加報告41st
41st Lunar
Lunar andand Planetary
Planetary Science
Science
Conference
Conference
March
March 1-5,
1-5, 2010,2010, Houston
Houston名古屋大学 D1 嶌生有理

Waterway Marriott Hotel

Topics•Planetary Atmospheres•Impacts•Planetary Igneous Processes•Planetary Differentiation•Exobiology•Cosmochemical Origins•Early Solar System

Chronology•Interplanetary Dust Particles
and Presolar/Solar Grains•Small Bodies (including
comets, asteroids, near-Earthobjects)•Outer Planets/Satellites/Rings•Differentiated Bodies•Mars Geomorphology•Martian Geochemistry•Moon•Venus•Mercury•Material Analogs (including

both physical and chemical)•Environment Analogs(including terrestrial
operationla analogs)•Planetary Mission Concepts•Instruments and Payload
Concepts•Education/Public Outreach•A New Moon
•Characterizing Near-Earth
Objects•Water in the Solar System•Other41st Lunar and Planetary Science Conference (2010)Introduction:

研究報告
1. Hypervolocity Impact Experiments on Low

The Martian surface is increasingly1357.pdf
and S2(255 K) were similar in appearance to Fig 1a,seen as aandmixtureof K)
rock/sandand near-subsurface
Introduction: The Martian surface is increasingly
S2(255weresimilarin appearance toice
Fig 1a, whereas those in S2(182 K) and S4 were like Fig. 1b.
HYPERVELOCITY
inregions those[1]. The
widespread
impacton 1b. IMPACT EXPERIMENTS ON LOW TEMPERATURE SAND:ICE TARGETS. T. B.
seen as a HYPERVELOCITY
mixture of rock/sandIMPACT
and near-subsurface
icemany whereasin S2(182
K) andwerecraters
like Fig.
1 S4
EXPERIMENTS ON LOW TEMPERATURE SAND:ICE
TARGETS. T. B. 1
Mars
therefore not allSimcox
haveofoccurredin eitherD.
R. Kent
I.rock,Wall
and M. J. Burchell1, 1School of Physical Sciences, University of Kent, Canterbury, Kent CT21
1 1
in many regionsThe
widespreadcraters
on of will
Simcox1[1].
, D. R.
I. Walland M. J.impact
Burchell, School
Physical Sciences, University
Kent, ,Canterbury,
CT2sand or pure ice, but some will have taken place inMars will 7NH,
therefore
not all have occurred in either rock,
UK (m.j.burchell@kent.ac.uk).
7NH, UK (m.j.burchell@kent.ac.uk).
or layered materials. It has been suggested [2]sand or pure ice, but some will have taken placemixturesinmixtures or layered materials. It has been suggested for[2] example that the presence of sub-surface ice layerThe ofMartiansurface isand S2(255
K) wereofsimilar
in appearance
to Fig as
1a,for example Introduction:that the presence
sub-surface
iceincreasingly
layering may explain
featuresMartiancraters suchseen as a features
mixture ofofrock/sandnear-subsurface
whereas those in S2(182 K) and S4 were like Fig. 1b.
ing may explain
Martianandcraters
suchlayered
as ice ejecta
blankets found around the craters [3, 4],
in many regions [1]. The widespread impact cratersonlayered ejecta
blanketsfoundaroundthecraters[3,
4],
Introduction:and S2(255 K) were similar in appearance to Fig 1a,so
the nature of the Martian surface
is clearly importantThe Martian surface is increasingly
Mars will therefore not all have occurred in eitherrock,so the nature
Martianis clearly
importantsandoforthepureice, butsurface
some will
have taken
placeinin understanding
impact processes.
seen as a mixture of rock/sand and near-subsurface ice
whereas those in S2(182 K) and S4 were like Fig. 1b.
in understanding
processes.
mixturesimpact
or layeredmaterials. It has been suggested [2]Laboratory experiments are not at the correct size
Laboratory
experiments
are not at
the correcticesize
for example
that the presenceof sub-surface
layerin many
regions
scale to provide full explanationsof large
impact[1].
cra- The widespread impact craters on
ing mayfull
explainfeatures ofofMartiancraters crasuch as
scale to provide
explanations
large impact
teringevents.
However,theycanprovideinsights
intolayeredejecta blankets
foundaround insights
the cratersinto[3, 4],
Mars will therefore not all have occurred in either rock,tering events.
However,they canprovidegeneralbehaviour under impact. Accordingly here weso the natureof theimpact.
MartianAccordingly
surface is clearly
importantgeneral behaviour
under
here
we
sandintoormixed
pure
ice,tar-but some will have taken place inin understanding impact processes.
look at hypervelocity impacts
sand:ice
look at hypervelocity
impacts into mixed sand:ice tarLaboratory experiments are not at the correct
sizeNote these are not layered, the sand and ice are
gets.
mixtures or layered materials. It has been suggested [2]Notescalethese
not fulllayered,the sandand impact
ice arecrato areprovideexplanationsof large
41stgets.
Lunar
andPlanetary
Science
Conference(2010)
1357.pdf
intimately
mixed.
intimatelytering
mixed.
events. However, they can provide insights into
forWe
examplethatspeed
the presence of sub-surface ice layerMethod:used an impact
Experimental
Method:Weimpact.
used animpact speed
general behaviour
under
Accordingly
here Experimental
we-1-1
at hypervelocity
impacts into
mixed
sand:icetar- km s (close to theof ~5speed) obingMartian
mayin-fall
explainfeatures of Martian craters such asof ~5 kmlooks (closeto the Martianin-fallspeed)
obgets.Univ.
Note these
are two
not layered,
the sandand tained
ice are in the Univ. of Kent two stage light gas gun [5]tained in theof Kent
stage lightgas gun[5]
layered ejecta blankets found around the craters [3, 4],
mixed. stainless steel projectiles. We
with 1 HYPERVELOCITY
mmintimatelydia., sphericalwith 1 mm dia., spherical stainless steel projectiles. We
Experimental Method: We usedIMPACT
an impact speed EXPERIMENTS ON LOW TEMPERATURE SAND:ICE TARGETS. T. B.
used 4 different typesof sands in the various targets
theinnatureof targets
the Martian surface is clearly important
used
sands
the various
1 1ofsoof ~5 km1s-1 (close to the Martian 1in-fall speed)
ob-4 different types
Simcox, D.
I. WallandM.
J. Burchell
SchoolofPhysicalSciences, University of Kent, Canterbury, Kent CT2
including(S1) NASA
JSCR.
simulant[6]gas(grainincluding(S1) NASA, JSC
simulant[6] (grain
tainedin the Univ.
ofMars-1
Kent twostage lightgun[5]
inMars-1
understanding
impact processes.
size: 98%with
between
20 and1000stainless!m). The
sands
1 mm
dia.,
spherical
steelotherprojectiles.
We98% between 20 and 1000 !m). The other sands
size:
7NH,
UK
(m.j.burchell@kent.ac.uk).
were: (S2)used
semi-roundedsilicatebuilding
sand(98%
4 different types of sands in the various were:targets (S2) semi-rounded silicate
Laboratory
are not at the correct sizebuilding sandexperiments(98%
including(S1) !m),NASA(S3)
JSC groundMars-1 simulant[6] (grain
between 229
and 836
semi-rounded
between229 and 836 !m),(S3) groundsemi-roundedscale
to provide
full explanations of large impact crasize: 98%
betweenand 100027!m).
The585othersandssilicate building
sand(98%20between
and!m)silicatesand (98% between 27 and 585 !m)(S2) semi-roundedsilicate building(98% building
Fig 1. (a) Crater in S2 at 255 K (coin diameter = 22.5
and (S4) were:diatomaceoussand (individual
grainssand< 20
teringevents.
However,they
provideinsights
into = 22.5
1. (a)can
Craterin S2 at 255
K (coin diameterand (S4)mm).
diatomaceous
grains< 20 cen- Fig
between 229 and 836 !m), (S3) ground semi-rounded(b) Crater
insand
S4 at(individual
203 K, where
theanddeeper!m). The sands
were mixed with water
to form
water surface
Introduction:
The
is increasingly
S2(255K)
werein S4
similarappearance to Fig 1a,silicatebuilding sand (98% between
27Martianand 585!m)The sands were(b) Craterat 203 K,in
where
!m).
mixed
with water
form
water
generalunderimpact.
Accordingly
herethewedeeper centralFigpit1.(arrowed)
issurrounded
bytoanincomplete
spall mm).
saturated andtargets.
By weight, sandthe sand:watergrains
ratios(a) Crater in
S2
at 255 K behaviour(coindiameter= 22.5(S4) diatomaceous(individual< 20
tral pit (arrowed)
is surroundedby S4
an incomplete
spallFig. 1b.
saturated
By weight,
themm).
sand:water
ratiosseen
asa =mixture
rock/sandand targets.
near-subsurface
icewhereasthosein
S2(182
K)
and
were
like
(coin
diameter= at
24.5
were: S1=
2.6:1,
5.3:1,
S3 =of
4.5:1,S4 =mm).
(b) Crater
inlook
S4
203
K,
where
the
deepercen!m).
The S2sands
were mixed
with
water
to 0.52:1.
form water zone
hypervelocity
impacts
mixed
tarzone (coininto
diameter= 24.5 sand:ice
mm).
were:
2.6:1,
S2 = 5.3:1,
S3 at= 4.5:1,= 0.52:1.
pit (arrowed)
is surrounded
an S4
incomplete
spall
The S4insamplesrequiredmuch
greaterof wasaturated
targets.
By weight,
theamounts
sand: widespreadwater
ratios S1 =tral
many
regions[1].targets
The
impactcraters
onby amounts
4requiredS4 samples
much
wa- not layered, the sand and ice arezone (coindiameter= 24.5greater
mm).
were:
S1 = 2.6:1,
S2 = 5.3:1,= 4.5:1,
S4 made= The
0.52:1.
gets.
Notetheseofare
ter in orderto causesaturation.
Two S3
were
4
The andS4willsamplesrequired
muchtemperatures.
greaterall
amountsof waterinoccurredorder to cause
Two targets were madetherefore
nothave
insaturation.
either rock,in eachMars
casefrozento different
The

1. Hypervolocity Impact Experiments on Low Temperature
Sand:Ice Targets [Simcox et al.]

• 砂氷混合物へ1mmステンレス球を5km/sで衝突• 砂：4種類（粒径分布、丸さが異なる）• 砂が浸るだけの水• 温度：255 K or 200 K

Temperature Sand:Ice Targets [Simcox et al.]

2. Asteroids Without Ejecta [Housen & Holsapple]

3. Comparing Experimental and Numerical Results

ピット

for Subsurface Failure Following Oblique Impacts
スポールなしintimately mixed.
sand or pure ice, but some will have taken placein
Experimental
Method: We used an impact speed
into Planar Targets [Stickle & Schultz]
mixtures or layered materials. It has been suggestedof ~5 [2]km s (close to the Martian in-fall speed) ob4

Depth (mm)4. Large-scale Experiments to Determine thecoefficient of Restitution for Meter-scale Granite
Spheres [Durda et al.]Depth (mm)Depth (mm)ter in orderto causesaturation.
targets of
wereinmadeeach case and frozen to different temperatures. The
first temperature
was
255 K
which Twois typicalthat0
in each case and frozen to different temperatures. The
used in many laboratory impact experiments with first
ice temperature was 255 K which is typical of thatfirst temperature was 255 K which is typical of that00targets. The
was experiments
approximately-1 with ice
usedicein many laboratory
impact experiments
used secondin many temperaturelaboratory impact
with180 – 200targets.
K whichmore typicalof Martiansurfacetargets. The second
temperature was approximately
Theissecond
temperature
was approximately-4
forexamplethat
thepresenceof
sub-surface
ice
layertemperatures.
180 – 200 K which is more typical of Martian 180
surfacetainedthe Univ.
– 200 K which
typicalinof Martiansurfaceof Kent two-4 is more
-4 stage light gas gun [5]
After
each
shot thecraters were
measured ofusing
ingtemperatures.
may
explainfeaturesMartian craterswith
such1 mmas dia., spherical stainless steel projectiles. We
temperatures.
After eachthe craters
were andmeasuredusing
micrometer gauges
heldshotabove
the surface
moved
After each -8
shot
the craters were measured using-8 craters
gaugesheld
abovegiving
the surface
andpromoved
ejectablanketsfoundaroundthe[3,4],across layered
twomicrometer
diametersof thecraterdepth
usedthe4 surface
different
types of sandsin the various targets-8
micrometer
gauges held aboveand moved
across two diameters of the crater giving depth
pro5.0
7.5
10.0
12.5
files, from which crater diameter and depth were obsofiles,
thefromnatureoftheMartiansurfaceclearly
5.0 of important
7.5crater giving
10.0
12.5 prowhich crater
diameterand depth wereob- twois
acrossdiametersthedepth
including(S1)
NASA JSC Mars-1 simulant [6] (grain
Horizontal
displacement(cm)
tained accurate
to ±½ mm(see1). Thetargets
tained accurate
to ±½
mmTable(see Table1). Thetargetsfrom which craterHorizontal
5.0
7.5
10.0
12.5
files,
diameterdisplacementand depth(cm)were obin were
understanding
impactprocesses.
were weighed
immediately
pre
and
post
shot
to
obtainweighed immediately pre and post shot to obtain
size:
98%
between
20 and 1000 !m).
Thedisplacement
other sands
Horizontal(cm)
tained accurate
to ±½profilemm(see Table
The
targets
acrosscraterS11).
S1(-18°C).
an estimate
the mass
duringcratering(Table1). ImFig.2 2Depth
Depthprofile
acrosscrater(-18°C).
NoteNotethe thean ofestimateof themass duringcratering(Table1). Im- Fig.
Laboratory
experimentsarenotat immediatelythecorrectsize
prepost scales
shottoobtaindifference
verticalandhorizontal
which
exag-exagwere:(S2)
semi-roundedsilicate building sand (98%agescratersof twoarecraters
are shownanda ofawere
depthweighed
difference
ininverticalandandhorizontal
scaleswhichages of two
shown
in Fig.in1Fig.
and1 of
depth
Fig. 2 Depth profile across crater S1 (-18°C). Note theoflargetheduringthemass
craterdepth. cratering
inThe
Fig.
2. The craters
fromexplanations
impacts
on an
S1,
S3 gerates
thecraterdepth.
profilescale
in profile
Fig. 2.
cratersfrom
impacts
on S1,
S3 estimate
toprovidefull
ofgerates
impactcra- (Table 1). Im-

スポールなしJSC-Mars1（20-1000µm） 丸砂（230-830µm）@ 255 K

general behaviour under impact. Accordinglyand
here(S4)
we diatomaceous sand (individual grains < 20
Fig 1. (a)珪藻土（<20µm）＠
Crater in S2 at 255 K (coin= 22.5204diameterK
＠ The
255sands
K were mixed with water to form water
look at hypervelocity impacts into mixed sand:ice
tarmm). (b) Crater in S4 at 203 K, where the deeper cen!m).
gets. Note these are not layered, the sand andice are targets. By weight, the sand: water ratios
tral pit (arrowed) is surrounded by an incomplete spall
saturated
intimately mixed.
zone (coin diameter = 24.5 mm).
were: S1 = 2.6:1, S2 = 5.3:1, S3 = 4.5:1, S4 = 0.52:1.
Experimental Method: We used an impact
ThespeedS4 samples required much greater amounts of wa-1
4
of ~5 km s (close to the
speed)
ob-Scienceter in orderto causesaturation. Twotargets were made41stMartian
Lunar in-falland Planetary
Conference(2010)
2354.pdf
tained in the Univ. of Kent two stage light gasingun
each[5]case and frozen to different temperatures. The
41st Lunar and Planetary Science Conference (2010)
1357.pdf
with 1 Conference
mm dia., sphericalstainless steel projectiles.
We
first temperature
was 255 K which is typical 2354.pdf
of that
41st Lunar and Planetary Science(2010)
0used 4 different types of sands figure).
in the various
targetsused
manylaboratory
with ice
Given
theinverylowcohesionimpactof the experiments
material,
including (S1) NASA JSC Mars-1[6](grainTheandsecond
targets.
temperaturewasapproximately
thissimulant
shape wasunstablecollapsed
to form the
final
Table 1. Crater sizes in this study.
water content
than
the
other
targets
those
in
98%
between
20material,and1000here,!m). and
The
other
sands
180
– 200
K whichis morecraterwhose
profileis shown
by theblue typicalcurve. of Martian surface-4
figure). Given the very size:
low cohesionof the[14] wereeven
so. Inthe[14]it wasproposed
that
Sand
Temp.
Vel.
Dia.
Depth
Spallwas unstable
were:(S2)moresemi-roundedsilicatebuilding
sand(98%
temperatures.
Silicate
this shapeandcollapsed
to form
final
Discussion:
These
results
supportthecraterformation-1
Content(K)(km s ) (mm) (mm)excavatedcratervolumedepended
only
on silicate
conAfter each shot the craters were measured using
between229
andcurve.
836!m), (S3)groundsemi-rounded
craterZone
whose profileis shown
by theblueand ejection proceses described in [3]. That is, in-8
micrometer
gauges held above the surface and moved
sandwe(98%
betweenand scales
585 of!m)tent bysilicate
mass. building
By contrast,
suggestthat 27at porosity
the
S1
255
5.08
32.5
7.33
No
creasedthe target material results in lower
20-1000µm
72%
Theseused
results
supportthe grain
cratersize
formation
Fig 1. (a)Craterin S2
at 255depth
K (coinacrosstwoFurthermore,diametersofthe
the quarter-spacecratergivingpro-diameter = 22.5
and(S4)sanddiatomaceoussand also(individual
grains
< 20
here,
the
may
be important.
S1
189±10 5.08
26.5
7.28Discussion:
Noejection
velocities.
and ejection procesesPrevious
described
insands[3]. wereThatmixedis,in-with water havemm).
(b)
Craterin S4
203 K,
where
5.0
7.5
10.0
12.5
files,
fromshowwhichcraterdiameterandatdepth
wereob- the deeper cen!m). Thehypervelocity
to form
water
experiments
also
S2
255
5.05
28.0
10.14 No
experiments
clearlythatcraterformationincreased porosity of84%
the target material
results inweight,
lower the sand: water
229-836µm
Horizontal displacement (cm)tralpit (arrowed)
is surrounded
an incomplete spall
accurate
to mainly±½
mmby(seeTable1). The bytargets
targets.
ratioshighlyover
porosustargets
occurscompaction,
lookedsaturated
at impacts
in pureBywater
ice targets
a tainedrange
S2
182±13 4.96
45.0
9.00ejection
Yesvelocities.
Furthermore,
the quarter-spacezone(coin diameter
24.5shotmm).
wereweighedand
immediately
premechanisms
and =post
to obtain
were: S1 =[15].
2.6:1,
S2= 5.3:1,
S3 rather= 4.5:1,
S4 the=con0.52:1.
thanshearing
excavationof temperatures[15]
craterremained
S3
255
5.02
29.5
8.19experiments
No
clearlyshow
thatcrater In
formationin dia.
Fig. 2 Depth profile across crater S1 (-18°C). Note thean ofestimate
ofwiththe mass
duringcratering (Table 1). Im27-585µm
TheS4
samplesrequiredmuch
greateramounts
wa81%
typicallyobserved
in soils
moderate
porosity.
stant
as
the
targettemperature
fell
over
the
range
here,
S3
188±14 5.13
31.0
7.16highlyNo
porosus targets occurs
mainlyby compaction,
4showndifference in vertical and horizontal scales which exagagesmadeof twocraters
in Fig.forms
1 and of a depth
ter in orderto causesaturation. Two The
targets
werequestionofwhetheranare
ejectablanketwhereascrater
depth
fell
by
~17%
as
the
temp.
deS4
255
5.03
48.5
9.97ratherYes
than the shearinginandmechanisms
gerates the crater depth.
profileinofFig.
2. Thecraters
frombeyond
impacts on S1, S3
eachexcavationcase and frozen
to different
temperatures.
The
depends
on themassmaterial
thatis ejected<20µm
34% with
qualitatively
to here.
in soilsfirstmoderatesimilar
porosity.
S4
203±14 4.97
46.5
9.77typicallyYesobservedcreased,
the crater
rim. ofThis
temperature
was 255 K which
is typicalthatin turn depends on the magnitude
0
Conclusions:
We
have
shown
that
in
mixed
water
The question of whether
ejectalaboratory
blanket forms
the ejecta velocities
used anin many
impact ofexperimentswith ice and the size of the crater. Figice:sandtargets,
thecratermorphology
depends
depends
on the massof material
that
ejectedbeyondAnalysis: At 255 K the craters in S1 andS3 wereurewas3 shows
the results of a preliminary model that istargets.
The issecond
temperatureapproximately
craterrim. Thisin turndepends
themagnitudestronglyoncomposition.
This
may
duesurface
todata for ejection velocities and crater
based
onbe
current
very similar in size. This may reflect the thesimilar
size
180
– the
200targetKon
which
is more typicalofMartian-4of the inejectaandof the crater.
Fig- scalinglaws [4].
the sizeofthe
thesize
componentsand grainsor the water
con-For a given size of body, ejecta blandistributions of the sand grains used. The crater
S2 velocities
temperatures.
ure
3
shows
the
resultsofapreliminary
model
that
is
kets
are
extinguishedaboveathresholdcrater size.
tent,
this
remainstobefully
determined.
It
has
previAfter
each
shot
the
cratersweremeasuredusing
however was noticeably deeper. When comparing imbased on current data
forbeenejection
velocities
and strain
crater rate
Below
size,
ously
reported
in low
tests,thisthat
the a significant mass
-8 of material is
micrometer
gauges
held
above
the
surfaceandmovedpacts at different temperatures for S1 and S3 there isscaling laws [4]. For
a givensize
body,ejectaejectedbeyondthecrater rim. Lines are shown fortensilestrengthofdiameters
ice:silicate
mixturesincreaseswith
acrosstwoofof blanthe
cratergivingdepth
prolittle difference as the temperature is lowered,
Craters above theketshowever
are extinguished above a threshold crater size. target porosities of 45% and 70%. 5.0
7.5
10.0
12.5
from
crater indiameterand depth
the % files,
contentof whichthe silicate
the sample
and atwere
over obfor S2 there is a significant increase in crater
diameterejecta. displacement (cm)Below this size, a significant mass of material is line for a given porosity should exhibit minimal
Horizontal
tained accurate
todeformation±½ mm (seeisTable1). Thetargets
50%
content,
plastic
reportedratherby a factor of ×1.6. This is because the deeper
centralejected beyond the crater rim. Lines are shown for The model results are consistent with observations ofwere fracture
weighed [16],immediately
pre
post
shot
to obtain
there
alsoandsome
it shown in the figure. Additional
crater in S2 at 182 K is surrounded by a shallow
thefourevidence
small bodies
targetspallaporosities ofthan
45%brittle
and 70%. Craters
aboveisthe
Fig.to2explore
Depth profile
across craterFigure
S1 (-18°C).
Note thetrajectories for an impact into aan estimategrainof thesize.
massInduring(TableIm- planned
may depend[16] cratering
itexperiments
is suggestedthe2. Material
are1).
being
crater formation zone typically 2 mm deep. By examining
photoline fora given porosity
should on
exhibit minimal
ejecta.
differencein verticaland horizontal
scalesexagagesofofspall
two craters
arein Fig. in1 highlyand experiof porous
a depthmaterials
targetwithwhich
83% porosity.
and toporosity=83%
revealthe condiin shownlaboratory
graphs taken of the target pre-shot it appears
there
wasresultsdiameter
The
model
are consistent
withzones,
observationsof tionimpact
geratesare
theexpectedcrater depth.
profileFig. 2.inversely
The cratersfrom
impactson
S1, ejecta
S3 blankets
tions
under
which
to form
ments
on in
ice,inwithtensilestrength,
four
shown
thescalefigure. Additionala thin ice layer on the surface of this targetthedue
to smallex- bodies
craters
porous bodies.
2. onMaterial
trajectories for an impact into awhich
giventothe
highcrater
sandformacontentaroundinFigure
samples
S1,
experiments
plannedexplorecess water. If the spall zone is excluded thecrater di- are being
with was
83% porosity.
in highlymaterials
and S3to reveal
the condiS2(255
K) andexplains
the lackThis
oftargeta worksignificant
supported by NASA Grant
ameter is 27 mm. Shallow spall zones are tionobservedin porous
tions
undertowhich spallejectazone.
blankets
expected
to form
NNX08AG11G.
We arehave
also shownthat asin [15] the tarboth impacts on targets S4 (extra care was
takenaroundcraters
bodies. plays a role in determining crater depth
get temperature
remove all excess surface water from the S4targets
so on porous

Sand:Ice Targets [Simcox et al.]

2. Asteroids Without Ejecta [Housen & Holsapple]
Depth (mm)1. Hypervolocity Impact Experiments on Low Temperatureejecta丸砂
細丸砂
珪藻土• 純氷上のクレーターより直径が小さい• クレーター形状の依存性• 温度：低温では若干浅くなる• 粒子サイズ：小さいほど浅い• 砂含有量少：スポールが起こる• 定量化は今後の課題• quartz sand+ perlite、

Porosity = 83%
Poly弾(1.33g)、1.3km/s

Depth (mm)JSC-Mars1

スポール

betweenand836 !m),(S3)in verticalgrounddifference
and semi-roundedhorizontal scales which exagages of two craters are shownin Fig. 1229
and ofa depthtering events. However, theyprofile
can inprovide
intogerates between
the crater depth.
Fig. 2. Theinsights
cratersfrom
impacts
on S1,sand
S3silicatebuilding(98%
27 and 585 !m)transient

final•• 掘削粒子流を自動検出• クレーター形成• compactionが主（下向きの流れ）• shearing・ejectionは少ないof the ejecta velocities and the size of the crater. Fig-

based
on current data for ejection velocities and crater
porosity.
tion in highly porous materials and to reveal the condi- ure
3 targetshows
results83%
ofporosity
a preliminarymodelthat exhibit
isline
for thea withgiven
shouldminimal ejecta.
scaling
on current data for ejection velocities andcrater laws [4]. For a given size of body, ejecta blantions under which ejecta blankets are expected to form based
The laws
model
resultsareconsistentobservations
scaling[4]. For
a given sizeof body,ejectaketsblanare withextinguishedabove a ofthreshold crater size.
around craters on porous bodies.
kets are extinguished above a threshold crater size.
thisfigure.
size, a Additionalsignificant mass of material is
the four small bodies shownBelowin theBelow this size, a significant mass of material isejectedcrater formarim. Lines areFigureshown 2.
for Material trajectories for an impact into abeyond the crater
rim. Lines
are shownfor beyond
This work was supported by NASA Grant ejected
experiments
are beingplannedtoexplorethecrater
target porosities of 45% and 70%. Craters above
targettheporosities of 45% and 70%. Craters above the
NNX08AG11G.
targetwith
83% porosity.
tioninhighlyporousmaterials
andtorevealthecondiline
for
a
given
porosityshouldexhibitminimalejecta.
2. Asteroids Without Ejecta [Housen & Holsapple]
2. Asteroids
Without Ejecta [Housen & Holsapple]

J. Geoph(1980), L
Schultz, Pline for a given porosity should exhibit minimal ejecta.

The model results are consistent with observations of
The model results are consistent with observations of
the four small bodies shown in the figure. Additional
Figure2. Material
for an impact
into aexperiments are being planned to explore crater
theformafour small
bodiesshowntrajectories
in the figure.
Additionaltargetwith 83%
porosity.to explore crater formation in highly porous materials and to reveal thecondiexperiments
are beingplannedtions under which ejecta blankets are expected to formtion in highly porous materials and to reveal the condiaround craters on porous bodies.

tions under which ejecta blankets are expected to formaround craters on porous bodies.

quartz sand+perlite+ water•This work was supported by NASA Grant
空隙率が大きいとtions under which ejecta blankets are expected to form
NNX08AG11G.
This
work was supported by NASA Grant

放出速度が小さいThis

NNX08AG11G.

•

重力増大と伴にLess Ejecta Blanket

Figure 2. Material trajectories for an impact into atarget with 83% porosity.

around craters on porous bodies.
work was
NNX08AG11G.

supported

by

NASA

Grant

Mathilde
41st Lunar and Planetary Science Conference (2010)

空隙率大、重力大

放出量減少 (Housen &Phobos#ejecta少Holsapple, 2003)

Figure 1. Comparison between observed and predicted2598.pdf
damage zone sizes. Impact
by a Pyrex projectile at 5.5v：エジェクタ速度km/s for a 30 degree impact: a) 8 !sec after first conU：衝突速度
Figure 3. Thresholds for ejecta blanket
formation.
Figure 3.References:
Thresholds for ejecta
formation.
[1] blanket
Schultz,
P.H. and Anderson, R.R.
x：衝突点からの距離
tact;
b)
!sec
after first contact, after damage zone
a：弾丸直径(1996)
Geol.
Soc.
Of
Amer.
Spec.91
Paper,
302, Boulder,
References:
References:[1]
VeverkaJ.
etal.
(1999).
ICARUS
140,
3Tempel1!：弾丸密度CO; [2] Schultz, P.H.
andCrawford,
D.A.
(2008)
finished growing. LPS
Though morphologically Hyperion
similar,16. [2] Thomas P.C. et al. (2007) Nature, XXXIX,
448, 50-53.
[3]
"：0.4
Abstract #2451; [3] Stickle, A.M, Schultz, P.H.
Housen K.R. and K.A. Holsapple (2003) ICARUS
163,Crawford
102- CTH
cannot exactly reproduce the observedand D.A.
(2009) simulations
LPS XL, Abstract #2357;
Figure 1. Ejection velocity vs launch position for sand
119.materials.
[4] Housen K.R. and K.A. Holsapple (2010)
Submitted[4] O’Keefe,
J,.D. and Ahrens, T.J. (1993), J. Geo.
and porous
damagezones.
corresponds
FigureThe
3. Thresholds
for ejecta
blanket formation. to D=1, and98, #1300.
17011-17028;[5] Ahrens,
T.J. andA.M.
Ru-red line
to ICARUS. [5] Housen K.R. (2003) LPSC Res.,XXXIV,
Figure 1. Ejection velocity vs launch position for sandFigure3. Thresholds
for ejecta blanket formation.
bin(1993),
J.
Geo.
Res.,
98,
1185-1203;[6]
Polanskey,
and porous materials.
locations whereconditions
for failure have been met,
References:
C.A. and T.J. Ahrens (1990), Icarus, 87, 140-155;[7][1] Veverka J. et al. (1999). ICARUS 140, 316. [2]ThomasP.C. et al.the(2007)total
Nature, 448, 50-53. [3]
while
the
green
line
shows
Kenkmann, T. et al. (2000),
Meteoritics [1]& Planet.
Sci.,J. et al. (1999).
References:
Veverka
ICARUSextent
140, 3- of the damHousen K.R. and K.A. Holsapple (2003) ICARUS 163, 10235, 1275-1290; [8] Senft,
L.E.
andStewart,S.T.
[2] Thomas
P.C.
(2007)Nature,448,
50-53.
[3]Results
aged
zone
(0 119.
<Experimental
D
<al.
1).
Failurecriterionis set tofor5%[4] etHousenK.R. andK.A.
Holsapple(2010) Submitted
3. Comparing Experimental and Numerical Results for3. 16.
ComparingandNumerical(2007), J. Geo. Res., 112,
E11002; [9] Barnouin-Jha,O.
to K.A.
ICARUS.
[5] Housen
K.R. (2003)
LPSC XXXIV,#1300.
Figure 1. Ejection velocity vs launch position
for sandHousenK.R.
andHolsapple(2003)ICARUS
163,
102S., etal. (2005), LPSC
36, Abstract#Failure
1585; [10]Following
Ba41st Lunar andPlanetary Science
Conference(2010) Oblique Impacts into Planar
2598.pdf
strainto failure.
Subsurface
FailureFollowing
Subsurface
Oblique Impacts into Planarand porous materials.
119. [4] Housen K.R. and K.A. Holsapple (2010) Submitted
41st Lunar and Planetary Science Conference (2010)[1] Veverka J. et al. (1999). ICARUS 140, 316. [2] Thomas P.C. et al. (2007) Nature, 448, 50-53. [3]Housen K.R. and K.A. Holsapple (2003) ICARUS 163, 102119. [4] Housen K.R. and K.A. Holsapple (2010) Submitted
to ICARUS. [5] Housen K.R. (2003) LPSC XXXIV, #1300.

41st Lunar and Planetary Science Conference (2010)

2598.pdf

References: [1] Schultz, P.H. and Anderson, R.R.
(1996) Geol. Soc. Of Amer. Spec. Paper, 302, Boulder,
CO; [2] Schultz, P.H. and Crawford, D.A. (2008) LPS
XXXIX, Abstract #2451; [3] Stickle, A.M, Schultz, P.H.
and D.A. Crawford (2009) LPS XL, Abstract #2357;[4] O’Keefe, J,.D. and Ahrens, T.J. (1993), J. Geo.
Res., 98, 17011-17028; [5] Ahrens, T.J. and A.M. Rubin (1993), J. Geo. Res., 98, 1185-1203; [6] Polanskey,
C.A. and T.J. Ahrens (1990), Icarus, 87, 140-155; [7]Kenkmann, T. et al. (2000), Meteoritics & Planet. Sci.,
35, 1275-1290; [8] Senft, L.E. and Stewart, S.T.
(2007), J. Geo. Res., 112, E11002; [9] Barnouin-Jha, O.
S., et al. (2005), LPSC 36, Abstract # 1585; [10] Barnouin-Jha, O. S., et al. (2007), Bridging the gap II,
Abstract # 8059; [11] van der Bogert, C.H., et al.
(1998), LPSC XXIX, Abstract; [12] van der Bogert, C.
H., et al. (2003), Meteoritics & Planet. Sci., 38, 15211531; [13] Langenhorst, F., et al., (2002), Met. andPlanet. Sci., 37, 1541-1553; [14] Schultz, P.H. (1996),
J. Geophys. Res., 101, 21117-21136; [15] Marsh(1980), LASL Shock Hugoniot Data, p. 394; [16]Schultz, P.H. (1996), J. Geo. Res., 97, 11623-1166

rnouin-Jha, O. S., et al. (2007), Bridging the gap II,

Targets [Stickle & Schultz]
Targets& XXXIV,
Schultz]
Abstract for# 8059;vander Bogert,
C.H.,
et K.R.
al. [Stickle
ICARUS.
[5] Housen(2003) LPSC
#1300.
Figure 1. Ejection velocity vs launch position
sand [11] to

8µs(1998), LPSC XXIX, Abstract; [12] van der Bogert, C.

References:
Schultz, P.H. and Anderson, R.R.
and porous[1]materials.
91µs(1996)
H., et al. (2003), Meteoritics & Planet. Sci., 38, 1521Geol. Soc. Of Amer. Spec. Paper, 302, Boulder,

Figure 1. Comparison between observed and predicted
CO; [2] Schultz, P.H. and Crawford, D.A. (2008)1531;
LPS [13] Langenhorst, F., et al., (2002), Met. anddamage zone sizes. Impact by a Pyrex projectile at 5.5
Planet.
Sci.,
37,
1541-1553;[14]
Schultz,
P.H.
(1996),XXXIX, Abstract #2451; [3] Stickle, A.M, Schultz, P.H.
km/s for a 30 degree impact: a) 8 !sec after first conJ.
Geophys.
Res.,
101,
21117-21136;
[15]
Marsh
tact; b) 91 !sec after first contact, after damage zone
and D.A. Crawford (2009) LPS XL, Abstract #2357;(1980),LASL
Shock
Hugoniot
Data,
p.
394;
[16]
finished growing. Though morphologically similar,[4] O’Keefe, J,.D. and Ahrens, T.J. (1993), J. Geo.
CTH simulations cannot exactly reproduce the observed
P.H. (1996), J. Geo. Res., 97, 11623-1166
Res., 98, 17011-17028; [5] Ahrens, T.J. and A.M.Schultz,
Rudamage zones. The red line corresponds to D=1, andbin (1993), J. Geo. Res., 98, 1185-1203; [6] Polanskey,
破壊到達域locations where conditions for failure have been met,
while the green line shows the total extent of the damC.A. and T.J. Ahrens (1990), Icarus,
87, 140-155; [7]$剪断aged zone (0 < D < 1). Failure criterion is set to 5%
Kenkmann, T. et al. (2000), Meteoritics & Planet. Sci.,
ダメージゾーン
strain to failure.
破壊35, 1275-1290; [8] Senft, L.E.
and Stewart, S.T.
Bladed failure%(2007), J. Geo. Res., 112, E11002; [9] Barnouin-Jha, O.
S., et al. (2005), LPSC 36, Abstract # 1585; [10] Ba弾丸による破壊の違い
引張破壊#
rnouin-Jha, O. S., et al. (2007), Bridging the gap II,
Abstract # 8059; [11] van der Bogert, C.H., et al.
Figure 1. Comparison between observed and predicted
Al球：弾丸方向に刃状亀裂、CTHと類似（剪断破壊Figure 1.(1998),
Comparison
betweenobserved[12]andpredicted
LPSC
vanBogert, C.
damageXXIX,
zone sizes.Abstract;
Impact by a Pyrex
projectile
at der5.5
アクリルに衝突角30°でpyrex球をkm/s
for a 30Meteoritics
degreea) 8&!sec
after first condamage zone
Impactby aimpact:
Pyrex
projectile
at5.538, 1521H., etsizes.
al. (2003),
Planet.
Sci.,のため）
Figure 2. Linear failure planes along impact trajectorytact; b) 91 !sec after first contact, after damage zone
5.5km/sで衝突
km/s for a1531;
30 degree
impact:8 !seccon- Met. andfinishedgrowing. a)
Thoughmorphologicallysimilar,[13]
Langenhorst,
F.,
etafteral., first(2002),
for impact of aluminum projectile into PMMA block.
CTH simulations cannot exactly reproduce the observed
Bladed failure is much more apparent following imtact; b) 91
!sec
after
first
contact,after
damagezone
Planet. Sci.,
37,zones.
1541-1553;[14] Schultz,
damageThe red line corresponds
to D=1, and P.H. (1996),
pacts with Aluminum, while failure appears to be dislocations
where
conditions
for
failure
have
been
met,
Pyrex球：亀裂は分散
Hydro code: CTH
finished J.
growing.
Thoughmorphologicallysimilar,Geophys.
Res.,
101,
21117-21136;
[15]
Marsh
while the green line shows the total extent of the damtributed following impact with Pyrex projectile. CTH
aged zone(0 < D < 1).
Failure criterion
is setto p.
5% 394;
CTH simulations
exactly
reproducetheobserved(1980), cannot
LASL
Shock
HugoniotData,[16]models indicate blades are the result of shear failure.
strain to failure.
完全には一致しない
damage zones.
line corresponds
andSchultz,The
P.H.red(1996),
J. Geo. Res.,to97,D=1,11623-1166
locations where conditions for failure have been met,
while the green line shows the total extent of the dam-•••

Figure2. Linear failure planes along impact trajectory•for impact of aluminum projectile into PMMA block.
• failure is much more apparent following imBladedpacts with Aluminum, while failure appears to be distributed• following impact with Pyrex projectile. CTH
models indicate blades are the result of shear failure.

References: [1] Sc(1996) Geol. Soc. Of A
CO; [2] Schultz, P.H.
XXXIX, Abstract #2451
and D.A. Crawford (2[4] O’Keefe, J,.D. an
Res., 98, 17011-17028
bin (1993), J. Geo. Re
C.A. and T.J. Ahrens (Kenkmann, T. et al. (235, 1275-1290; [8](2007), J. Geo. Res., 11
S., et al. (2005), LPSC
rnouin-Jha, O. S., et a
Abstract # 8059; [11(1998), LPSC XXIX, A
H., et al. (2003), Mete
1531; [13] Langenho
Planet. Sci., 37, 1541J. Geophys. Res., 10(1980), LASL ShockSchultz, P.H. (1996), J.

durda@boulder.swri.edu, 2University of California Santa Cruz, Santa Cruz CA 95064, 3University of Maryland,

Headache balls moved higher up to minimize sphere~150 frames of video data. In each frame the horizonCollege
MD 20742, 4Since
Lousiana Crane Company, LLC.
tion for rocky bodies or for larger
iceParkbodies.
wobble after impacts.
tal and vertical position (pixel index) of the center oflarge rocky bodies tend to have larger and more nuFigure 1. A 1-meter-diameter granite sphere suseach sphere is measured, as a function of time (frame
lowing significant open rock face for unobstructed
The fast
N-body code pkdgrav
merous structural flaws (that fail atIntroduction:
lower stresslevelsFor the actual experiment runs, the two cranes werependedforthelarge-scale‘pendulum’
experiments.
number). Each sphere executes simple pendulum morock-on-rock contact during the experiments (Fig. 1).
[1] is used to study many problems in planetary sciparked back-to-back so that the two spheres could be
and strain rates) than small bodies,
betweenence,collisions
ranging from thecollisional and dynamical
Left:evo-Placement of support strapping and lifting fromtion, with different amplitude before and after collilution of thanplanetaryimpacts
ring systems
planetesimal
suspended in-line between the cranes and so that attachat[2], to1896.pdf
sion. The relative speeds of the spheres both before
nce (2010) larger bodies may be more dissipative
forklift.
Right:
Spheresuspended
in
place
for
experiaccretion [3,4], to the outcomes of disruptive asteroid
pointsontherearbumpersofthecranes
could
be
used
the same speeds between smallercollisions
bodies.
theis the assumption[5,6].Without
Within the codeof withaand after impact can be determined from the fit ampliment
1-meter scale bar and experiment run numto
mountratcheting‘comealongs’usedtodisplacethecoefficientofrestitution(oftenchosen
to
have
a
value
necessary experimental data, however,
we have notudes and angular frequencies of the two pendula, andberinelasmarker shown.
of 0.5) characterizing the outcomes of ~10 m/s
spheres. Three different configurations of the careliable basis for setting the coefficient
restitution
the coefficient of restitution derived from the ratio of
tic collisions of
between~10-m size bodies. Previous
ble/strap
suspension
forthesphereswereused,adjustO DETERMINE THE COEFFICIENT OFworkRESTITUTION
by other researchers [7-10]FOR
has already estabBefore the actual experiment runs began, basic
speeds.
over the full range of compositions,sizes,and impact
3 the coefficient2
lished thatof restitution
varies with size
ing the positions of the so-called ‘headache ball’ (a 90S. D. D. Durda1, N. Movshovitz2, D. C. Richardson,
E.
Asphaug,A.
R.
characterization/calibration
data were obtained. The~1–10speeds presently being modeled. and impact speed for ~1 cm/s impacts between
100 lbs steel sphere) used to stabilize crane loads
Research Institute, 1050 Walnut Street Suite cm
300
Boulderdiameterwater ice CO
spheres,80302,
but little or no work
spheres were weighed using on-board crane sensors at
hasdoneextensive
to characterize sethe coefficient of restitu3 been an
against winds in order to find a configuration that
Experiments: We have conducted
California
Santace
Conference(2010)Cruz, Santa Cruz CA 95064, tionUniversity
for rocky bodiesof
or Maryland,for1896.pdf
larger ice bodies.
Since
3000
and 2700 lbs, to within the 100 lb precision alminimized wobble of the granite spheres after impacts 1.00
ries of large-scale experiments tolarge
measuretherocky bodies
tendcoeffito have larger and more nue Company, LLC.
Figure1. A 1-meter-diameter
granite wassphere displaced
suslowed
the sensors.
One sphere
apdue to ‘double pendulum’ effects.
merous structural(that fail at lower stresslevels by pended
cient of restitution for impacts between
1-mflaws
diameterfor the large-scale ‘pendulum’ experiments.
and strain rates) than small bodies, collisions
betweenproximately
meter offrom
equilibrium
position andLeft:1Placement
supportits
strappingand lifting from
IMENTS TO DETERMINETHE COEFFICIENTRESTITUTIONFORWe began the experiment series with sphere disgranite 1sphereswith2 collisionOFspeeds
up to 2 ~2largermore m/s.
dissipative than impacts at
3 bodies may beforklift.
Right:
Spheresuspended
in
place
for
experiTE SPHERES. D. D. Durda , N. Movshovitz , D. C. Richardson, E. Asphaug, A. smallerR.
allowedfreewithswing
for several cycles to gather data
the same
speedsbetweenbodies. Without
the toment
placement at a minimum (displacements of only ~10
1-meter scale bar and experiment run numThese
data,
the
first
gathered
at
these
size
scalestoour1Southwest
Research
Institute,
1050
WalnutStreetSuite
300
BoulderCO
80302,
necessarydata, however, weon
have
no energy
lowing significant open rockfaceexperimental
for unobstructedde pkdgrav
anylossesber marker
shown. inherent in the suspension syscm) in order to assess both the safety of the strap/sling 0.85
3knowledge,allow
us duringtoestablish
scalinglaws
reliable basis
setting
the forcoefficient of restitution
University of California
Santa
Cruz,will
Santa
Cruz CA
95064,
University
offorMaryland,rock-on-rockcontact
theexperiments(Fig.
1).sizes, andplanetary
sciBefore the actual experiment runs began, basic
tem.
supports and to insure that the spheres would not be
over therange of compositions,
impactousiana Crane Company,
LLC. collisions between bodies
low-speedoffullrepresentative
characterization/calibration
data
were
obtained.
The
speedspresently
being
modeled.
ynamical evooverly damaged or even destroyed during the first few
spheres were weighed using on-board crane sensors atcompositions that can then be reasonably
extrapolatedExperiments:
We have conducted an extensive seruns. For these early runs the spheres were simply
3000 and 2700 lbs, to within the 100 lb precision alplanetesimalries of large-scale experiments to measure the coeffito the ~10-m
size
scalesopenand rock~10m/s
impactspeedslowedbythe
sensors.
One
spherewasdisplacedaplowing
significant
facefor
unobstructed
stptiveN-bodycode
pkdgrav
displaced by hand, by pulling on rope loops that had 0.70
cient of restitution for impacts between 1-m diameter
asteroid
proximately 1 meter from its equilibrium position androck-on-rockcontact
during pkdgrav
thegranite
experiments(Fig.collision1).
problems in planetarysci- widely
spheressimulations.
withspeeds up to ~2 m/s.
being
modeledthroughbeen fed through the strap supports. For the first set ofallowed to free swing for several cycles to gather data
sumptionof a evoThese data, the first gathered at these size scales to ourisionaland dynamicalonanyenergylossesinherentinthesuspension
sysThe scaling laws we determine willallow
reliableesruns, we displaced only one sphere and let it impact
knowledge, will allow us to establish scaling laws forostemshave[2],a valueto planetesimaltem.
low-speed collisions
between bodies of representative
timates
to
be
made
for
the
coefficientofrestitution
the other, undisplaced, sphere. In this manner weomesm/sof disruptive
10
inelas- asteroid
compositions that can then be reasonably extrapolated
slowly increased the displacement of the single spherecode is the assumptionof aapplicableat these sizes and impact
speedsandandwill
to the ~10-m
size scales~10 m/s impact speedses.
Previous
Figure 3. Coefficient of restitution as a function of
ften chosen to have allow
a value a reasonable parameterization
being widely
throughfor
pkdgrav simulations.
until displacements of over a meter were achieved,of modeled
its value
impact speed for 1-meter diameter granite spheres.
The scaling laws we determine will allow reliable esalreadyutcomes ofestab~10 m/s inelasyielding
impactspeeds
of
order
~1
m/s.
For
highervariable
impactconditions.
timates to be made for the coefficient of restitution-m sizebodies.
aries
withsize Previous
impactspeedsweneededgreater
displacements.
We
applicable at these sizes and impact speeds and will
Figure 3 shows the resulting derived coefficient of[7-10] has already estabOperations for the large-scale
were of its value forallowexperimentsa reasonable parameterization~1–10found it physically too difficult to pull and hold therestitution as a function of impact speed for the 24
ftweenrestitution
varies with size
variable impact conditions.
conducted
at
SwRI’sSan
Antonio
headquarters
camsphereforthesehigherimpactspeedsanddevisedae or
no between
work ~1–10m/s
impactsexperiment runs analyzed to date. Low-speed impacts
Operations for the large-scale experiments werepus
the week of 26-–30 May, 2009.
contracted
eres,
butrestitulittle or noworkmechanical mechanism to accomplish the task. Ratchconducted We
at SwRI’s
San Antonio headquarters cament ofgenerate a derived coefficient of restitution with larger
pusspheres
the week offor
26-–30May,
2009. We contracted
ze the coefficient of two
restitueting
cable
pullers(‘comealongs’)wereattachedto
40-toncranestosuspendthethe
exuncertainties than the impacts at higher speed (this isbodies.
Since
two 40-ton cranes to suspend the spheres for the exr larger ice bodies. Sincethebumpersofthecranesandheavy-duty(175
lb
ratperiments.
Lifting
strapswereattachedtosuspenddue to our limited image resolution making the fit penperiments.
Lifting
strapswereattachedtosuspend
41st
Lunar
and
Planetary
Science
Conference(2010)
1896.pdf
andnu-more nu-FigureFigure
have morelarger andFigure2.
Granitespheresinequilibrium
position.
1.A A1-meter-diameter
1-meter-diameter
granitespheresus1.
granitespheresuseach sphere from its respective crane. The straps
were 2.
FigureGranite spheres in equilibrium position.
ing) cable ties were looped to the rope loop holding thedula sinusoids look more like step functions with 2–3
fromforitsthe
respective
crane.
The
strapswere to each
atr fail
at lowerstresseachlevelssphere
Left: Headache balls low near the spheres. Right:
stresslevels
slung
under
each
sphereperpendicularothersopendedlarge-scale‘pendulum’
experiments.
for thelarge-scale‘pendulum’
experiments.
sphere. The cable ties were then cut on cue to release
Left:ballsmoved
low
near
spheres.
Right:
bodies, collisions between
steps than sine functions). There is no clear speedthat the spheres
wereothersecurely
cradled whilestill al-Headache
Headache balls
higherup to theminimizesphere~150
frames of video data. In each frame the horizonslungpended
under
each
sphereto
Left:
Placementof perpendicularsupport strapping
andeachliftingfrom sosions
betweendissipative than impacts at
Left:
Placement
supportstrappingandlifting
wobble after impacts.
tal and vertical position(pixelindex) of This
the centerofthesphere.
arrangement
had the advantages ofdependent trend in coefficient of restitution apparent inforklift.
Right:
Spheresuspendedin placefor experithe spheres
wereofsecurely
cradledwhile
still
al-fromeach sphere is measured, as a function of time (framehanat thattheforklift.
mallerimpacts
bodies. Without
For the actual experiment runs, the two cranes werebeing able to pull and maintain greater displacement
Spherein placefor experiment Right:
with 1-meterscale suspended
bar and experiment
run numthis preliminary analysis of a subset of our data, alnumber). Each sphere executes simple pendulum mota,Without
however, thewe have noparked back-to-back so that the two spheres could bebermarkershown.
tion,withdifferent
amplitude
beforeandaftercolliforce
than
could
be
done
by
hand
(thus
achieving
ment with 1-meter scale bar and experiment run numthough it appears that !n " 0.85 for v < 2 m/s impacts
suspended in-line between the cranes and so that attach
he coefficient of restitution
sion. The relative speeds of the spheres both before
we
have
no
higherrelative
impactspeeds)andofestablishingpointsontherearbumpersofthecranes
could
be
used
Beforethe actual experiment runs began, basic
between 1-meter diameter granite spheres.
ber marker
shown.
positions, sizes, and impact
and after impact can be determined from the fit amplito mount ratcheting ‘come alongs’ used to displace theof restitution
muchtudes and angular frequencies
ofmorethe twostabilized
pendula, and initial conditions before spherecharacterization/calibration data were obtained. The
eled.
spheres. Three different configurations of the cathe coefficient of restitution derived from the ratio of
spheres were
on-board craneatthe weighed
actual using
experiment
runssensors
began,
basic
release.
ble/strap suspension for the spheres were used, adjusts,
and impact
conducted
an extensive se- Before
speeds.
3000 and 2700 lbs, to within the 100 lb precision aling the positions of the so-called ‘headache ball’ (a 90References: [1] Richardson D.C. et al. (2000), Icarus,
ents to measure the coefficharacterization/calibration
data were obtained. The
Analysis of Data and Results: We obtained a to100 lbs steel sphere) used to stabilize crane loads
lowed by the sensors. One sphere was displaced apacts between 1-m diameter
143, 45–59. [2] Porco C.C. et al. (2008) Astron. J. 136,
against winds in order to find a configuration thatsphereswereweighedusing
on-board
crane
sensorsat
tal of 108 science data runs. All runs were imaged
proximately
1
meter
from
its
equilibrium
position
andextensiveion
speeds upseto ~2 m/s.
minimized wobble of the granite spheres after impacts
2172–2200. [3] Richardson et al. (2009) Plan. & Space Sci.
to freelbs,
swing
several thecyclesto gatherdatawith HD resolution video to record the raw science
3000 allowed
and 2700
toforwithin
100
lb precision
aldue to ‘double pendulum’ effects.
d at thethesecoeffisize scales to ourure
57, 183–192. [4] Leinhardt Z.M. et al. (2009) Mon. Not.
anytheenergylosses inherent
in the suspension
sysdata: the ratio of initial sphere displacement and speed
We began the experiment series with sphere diso establish scaling laws for
lowedonby
sensors.
One sphere
was displaced
ap1-m
diametertem.
placementataminimum(displacements
of
only
~10
R.
Astron. Soc. 396, 718–728. [5] Durda D.D. et al.
en bodies of representative
beforeimpacttodisplacement
and
speed
after
impact.
proximately
1
meter
from
its
equilibrium
positionandcm) in order to assess both the safety of the strap/sling
pbe reasonably
to ~2 m/s.
(2004) Icarus 170, 243-257. [6] Michel P., et al.
extrapolated
To ensure that prominent measurement points would
supports and to insure that the spheres would not beallowed
to
free
swing
for
severalcyclestogatherdata~10 m/soverly damaged or even destroyed during the first few(2002) Icarus 160, 10–23. [7] Bridges F.G. et al.
endscales
toimpact
our speeds
always be resolved on each sphere we placed several
runs. For these early runs the spheres were simply
on any energy losses inherent in the suspension sysugh pkdgrav simulations.
(1984) Nature 309, 333–335. [8] Hatzes A.P. et al.
aling
laws forwhite, ~1-inch squares of self-adhesive Velcro patches
displaced by hand, by pulling on rope loops that had
mine will allow reliable estem.
been fed through the strap supports. For the first set of(1988) Mon. Not. R. Astron. Soc. 231, 1091–1115. [9]representativeon each sphere (Fig. 1, right).

4. Large-scale Experiments to Determine the coefficient of
Restitution for Meter-scale Granite Spheres [Durda et al.]• 大きな物体は小さなものより早くdissipateするか？
（!数値計算）• 1m花崗岩球の振り子衝突（<2m/s）• 反発係数を測定• 反発係数の衝突速度依存性は見られない• Vi ~ 0.2 m/sの誤差大"画像分解能! "〜0.85（@ Vi ＜ 2 m/s）

e coefficient of restitution

impact speeds and will
yndextrapolated
eterizationof its value formpact speedsv
simulations.
ge-scale experiments were
w reliable
es- camAntonio
headquartersMay,
We contractedof 2009.
restitutionnd the spheres for the exeeds
and will
were attached to suspend
itscrane.
valueThefor
tive
straps werependicular to each other sorely cradled while still al-

riments werequarters camWe contracted
es for the exd to suspend
he straps were
each other sowhile still al-

4. Large-scale Experiments to Determine the coefficient of
Restitution for Meter-scale Granite Spheres [Durda et al.]おわり

Figure 2. Granite spheres in equilibrium position.
Left: Headache balls low near the spheres. Right:

Figure 2. Granite spheres in equilibrium position.
Left: Headache balls low near the spheres. Right:

runs, we displaced only one sphere and let it impact
the other, undisplaced, sphere. In this manner weslowly increased the displacement of the single sphere
until displacements of over a meter were achieved,
yielding impact speeds of order ~1 m/s. For higher
impact speeds we needed greater displacements. We
found it physically too difficult to pull and hold thesphere for these higher impact speeds and devised amechanical mechanism to accomplish the task. Ratcheting cable pullers (‘come alongs’) were attached tothe bumpers of the cranes and heavy-duty (175 lb rating) cable ties were looped to the rope loop holding thesphere. The cable ties were then cut on cue to release
the sphere. This arrangement had the advantages ofbeing able to pull and maintain greater displacement
force than could be done by hand (thus achieving
higher relative impact speeds) and of establishingmuch more stabilized initial conditions before sphererelease.
Analysis of Data and Results: We obtained a total of 108 science data runs. All runs were imaged
with HD resolution video to record the raw science
data: the ratio of initial sphere displacement and speed
before impact to displacement and speed after impact.
To ensure that prominent measurement points would
always be resolved on each sphere we placed several
white, ~1-inch squares of self-adhesive Velcro patches
on each sphere (Fig. 1, right).
Video data from 24 runs in the optimal strap/cable
length configuration have been reduced and analyzed
to derive the coefficient of restitution as a function of
impact speed. A typical experiment run consists ofVideo data from 24 runs in the optimal strap/cable
Figure 3. Coefficientlengthof restitution
as a function ofhave been reduced and analyzed
configuration
impact speed for 1-meter diameter granite spheres.

to derive the coefficient of restitution as a function of

Figure 3 shows the resulting derived coefficient of
impact speed. A typical experiment run consists ofrestitution as a function of impact speed for the 24
experiment runs analyzed to date. Low-speed impacts
generate a derived coefficient of restitution with larger
uncertainties than the impacts at higher speed (this isdue to our limited image resolution making the fit pendula sinusoids look more like step functions with 2–3
steps than sine functions). There is no clear speeddependent trend in coefficient of restitution apparent inthis preliminary analysis of a subset of our data, although it appears that !n " 0.85 for v < 2 m/s impacts
between 1-meter diameter granite spheres.
References: [1] Richardson D.C. et al. (2000), Icarus,
143, 45–59. [2] Porco C.C. et al. (2008) Astron. J. 136,
2172–2200. [3] Richardson et al. (2009) Plan. & Space Sci.
57, 183–192. [4] Leinhardt Z.M. et al. (2009) Mon. Not.
R. Astron. Soc. 396, 718–728. [5] Durda D.D. et al.
(2004) Icarus 170, 243-257. [6] Michel P., et al.
(2002) Icarus 160, 10–23. [7] Bridges F.G. et al.
(1984) Nature 309, 333–335. [8] Hatzes A.P. et al.
(1988) Mon. Not. R. Astron. Soc. 231, 1091–1115. [9]Supulver K.D. et al. (1995) Icarus 113, 188–199. [10]Dilley J.P. and Crawford D. (1996) J. Geophys. Res.
101, 9267–9270.

Supulver K.D. et al. (1995) Icarus 113, 188–199. [10]Dilley J.P. and Crawford D. (1996) J. Geophys. Res.
101, 9267–9270.