Moon formation sasaki

The Origin of the Moon
佐々木貴教

月
・人類が降り立った唯一の地球外天体
・地球からの距離：38万4400km
・半径：1737km（地球の0.27倍）
・質量：7.3 1022kg（地球の0.012倍）
・地球に常に同じ面を向けている
・地球と比べてコア（Fe）が小さい
表裏
•  ik
d T
T (Fe) hT
0

月の起源の研究史
• 黎明期（紀元前∼1960年代）
• 開化期（1970年代∼1980年代）
• 円熟期（1990年代∼2000年代前期）
• 混乱期（2000年代後期）
• 革命期（2010年代）
• 混迷を極める現代

• 古事記 
イザナギノミコトが右目を洗い月読命が誕生（左目が天照大神）
• 旧約聖書 
創造主が4日目に天の太陽と月と星を誕生させた
• エジプト 
創造主ラーの左目が月となった（右目が太陽）
• 中国 
創造神盤古の右目が月となった（左目が太陽）
神話における月の起源

XIII. On the Precession of a Viscous Spheroid, and on the remote History of the Earth.
By G. H. Darwin, M.A., Fellow of Trinity College, Cambridge.
Communicated by J. W. L. Glaisher, M.A., FM.S.
Received July 22,—Read December 19, 1878,
Plate 36.
The following paper contains the investigation of the mass-motion of viscous and
imperfectly elastic spheroids, as modified by a relative motion of their parts, produced
in them by the attraction of external disturbing bodies ; it must be regarded as
the continuation of my previous paper/" where the theory of the bodily tides of such
spheroids was given.
The problem is one of theoretical dynamics, but the subject is so large and complex,
that I thought it best, in the first instance, to guide the direction of the speculation
by considerations of applicability to the case of the earth, as disturbed by the sun
and moon.
In order to avoid an incessant use of the conditional mood, I speak simply of the
earth, sun, and moon ; the first being taken as the type of the rotating body, and the
two latter as types of the disturbing or tide-raising bodies. This course will be justi-
“Fission Theory” による月形成シナリオ

月の起源説
捕獲説
分裂説
双子説
原始地球が高速回転によりふくらみ,
その一部がちぎれて月が誕生
地球軌道付近での微惑星の集積により,
地球とは独立に月が形成
地球とは別の場所で作られた月が,
地球の近くを通ったときに捕らえられた

Constraints of Moon Formation
(1) 地球ー月系の角運動量（Ltotal が保存）
(2) 地球より低密度（コアが小さい）[Hood & Zuber, 2000]
(3) 揮発性元素が強く枯渇 [Jones & Palme, 2000]
(4) 表面が大規模溶融を経験 [Warren, 1985]
(5) 酸素同位体比が地球とほぼ一致 [Wiechert et al., 2001]
ng that similar proportions of material
rom the silicate portions of the proto-
and Theia. Only if the proto-Earth and
⌬17
O values were identical to within
would it be possible that the average
value of the Moon plots within 0.005‰
terrestrial fractionation line.
me computer models assume a larger
r the impactor, i.e., a mass ratio of 7:3
n the proto-Earth and Theia (2, 13).
ese models assume that the Earth had
chieved about two-thirds of its final
fter the Giant Impact, because a larger
Earth would produce greater angular
ntum for the Earth-Moon system than
bserved. Models assuming that the
Earth had reached just 66% of its mass
he Giant Impact (2, 3) and identical
of the Moon and Earth require that late
ng material came from the same res-
as the material that made up Theia and
system or that oxygen isotope alteration
continued on icy planetesimals (18). How-
ever, computer simulations of the colli-
sional growth stage of the inner solar sys-
tem (19) demonstrate that terrestrial planets
were fed from a zone with a heliocentric
distance of 0.5 to 2.5 astronomical units
and beyond. Regardless of how heteroge-
neous the early inner solar system was at
the beginning, it developed toward a homo-
geneous composition by collisional growth.
This is endorsed by the small ⌬17
O differ-
ences of about 0.6‰ observed for the
Earth-Moon system, Mars, and Vesta com-
pared with more than 10‰ differences
among chondrites. Collisional growth will
smooth out pre-existing heterogeneities but
is unlikely to result in identical oxygen
isotopic compositions for all planets be-
cause a correlation between final heliocen-
tric distance and average provenance of a
planet is predicted (19). The differences in
⌬17
O among large planetary embryos and
Comparison between conventional and
ser 16
O, 17
O, and 18
O measurements of
amples. ⌬17
O gives displacement from
Fig. 3. The ⌬17
O values for lunar samples plot
within standard deviation (2␴i) error of Ϯ
0.016‰ (long-dashed lines) on the TFL. If the
impactor had formed from the same raw ma-
terial as Mars or the HED parent body, then all
lunar samples must have obtained, within 2%,
the same portion from the impactor and proto-
Earth as obtained by Earth using the triple
standard error of the mean (3␴mean) as signif-
icant, shown by short-dashed lines. On average,
the H-chondrites plot 0.7‰ above the TFL,
allowing a maximum of 3% chondritic material
mixed into any of the studied lunar samples,
2␴ conﬁdence level. Other chondrite groups
like L, LL, or carbonaceous chondrites show an
even larger deviation from the TFL and, there-
[Wiechert et al., Science, 2001]

月の起源説
捕獲説
分裂説
双子説
原始地球が高速回転によりふくらみ,
その一部がちぎれて月が誕生
地球軌道付近での微惑星の集積により,
地球とは独立に月が形成
地球とは別の場所で作られた月が,
地球の近くを通ったときに捕らえられた
高速回転が難しい & 角運動量が大きすぎる
月の内部構造が説明できない & 月を残せない
捕獲確率が低い & 化学的制約を満たせない

[Schreiber & Anderson, Science, 1970]
月はチーズでできている？

ジャイアントインパクト説
[Hartman & Davis, Icarus, 1975]
[Cameron & Ward, LPI Conference, 1976]

520 BENZ, SLATTERY, AND CAMERON
T: 7.76217 [ -2.0. 2.0. -2.0. 2.01 T: 8.83375 ( -2.0. 2.0. -2,0. 2.0]
,,:iii:i~iiiiii!iii!i,li!~iliiiiiii~!!!iiii:~iii~:i,:
T: 9,q0986 ( -2.0. 2.0. 2.0, 2.01 T: 11.03161 I -~.0. ~,.0, -q,0. ~.0]
/,,l--¢/ t~
FIG. 2. Snapshots of run 1. (u~ = 0 km/sec; rmi,= 0.77Rearth; Eint = 107erg/g). Velocity vectors are
plotted at particle locations. The velocity has been normalized to its maximum value in each frame.
Time and coordinates of the four corners of the plotted field are given in the upper line (in units defined
in Section 3). For particles in the vapor phase a "O" is plotted.
before the time at which the particles
spread out in space. Since this happens af-
ter the time of closest approach, the trajec-
and this completes the description of the
equation of motion.
520 BENZ, SLATTERY, AND CAMERON
T: 7.76217 [ -2.0. 2.0. -2.0. 2.01 T: 8.83375 ( -2.0. 2.0. -2,0. 2.0]
T: 9,q0986 ( -2.0. 2.0. 2.0, 2.01 T: 11.03161 I -~.0. ~,.0, -q,0. ~.0]
/,,l--¢/ t~
FIG. 2. Snapshots of run 1. (u~ = 0 km/sec; rmi,= 0.77Rearth; Eint = 107erg/g). Velocity vectors are
plotted at particle locations. The velocity has been normalized to its maximum value in each frame.
Time and coordinates of the four corners of the plotted field are given in the upper line (in units defined
and this completes the description of the
equation of motion.
T: 9,q0986 ( -2.0. 2.0. 2.0, 2.01 T: 11.03161
/,,l--¢/ t~
FIG. 2. Snapshots of run 1. (u~ = 0 km/sec; rmi,= 0.77Rearth; Eint = 1
plotted at particle locations. The velocity has been normalized to its m
Time and coordinates of the four corners of the plotted field are given in
tories of the various clumps forming after
collision are calculated accurately.
The total "viscous" force therefore be-
comes
F visc= F/bulk -I- F~rag
and this comple
equation of mot
4.2. Energy Con
The variation
given by thermo
du
d--i =
ENZ, SLATTERY, AND CAMERON
2.0. 2.01 T: 8.83375 ( -2.0. 2.0. -2,0. 2.0]
.0, 2.01 T: 11.03161 I -~.0. ~,.0, -q,0. ~.0]
/,,l--¢/ t~
(u~ = 0 km/sec; rmi,= 0.77Rearth; Eint = 107erg/g). Velocity vectors are
The velocity has been normalized to its maximum value in each frame.
our corners of the plotted field are given in the upper line (in units defined
n the vapor phase a "O" is plotted.
T: 1%68976
COLLISIONAL ORIGIN OF THE MOON
-6.0. 6.0. -6.0. 6.0} T: 22.19287 -6.0, 6.0, -6.0. 6.01
521
", S s
3. "j'q~k','"
'. 0 ~,'e~4"
FIG. 2--Continued.
i %
where dQ is the amount of energy absorbed its first derivative, to assure the continuity
T: 1%68976
COLLISIONAL ORIGIN OF THE MOON
-6.0. 6.0. -6.0. 6.0} T: 22.19287 -6.0, 6.0, -6.0. 6.01
521
", S s
3. "j'q~k','"
'. 0 ~,'e~4"
FIG. 2--Continued.
i %
where dQ is the amount of energy absorbed its first derivative, to assure the continuity
Giant Impact by SPH（初）
[Benz et al., Icarus, 1986]

Giant Impact によって形成される周惑星円盤の
~80% が Impactor 起源のマントル物質である

太陽系形成標準理論（林モデル）
©Newton Press[Hayashi et al., 1985]

KOKUBO AND IDA
m on the (a) a–e and (b) a–i planes. The circles represent planetesimals and their radii are
m initially consists of 3000 equal-mass (1023
g) bodies. We used the radii of planetesimals five
s of planetesimals are 1533 (t 5 5000 years), 1294 (t 5 10,000 years), and 1059 (t 5 20,000 years).
[Kokubo & Ida, Icarus, 1996]
OLIGARCHIC GROWTH OF PROTO
runaway sta
typical orbi
ing is abou
mass of pro
rial, and th
is a genera
in a disk wh
are effectiv
If we ass
the final st
planets is e
model that
model, the
given by
S 5
Adopting t
b Q 0.07 A
b Q 2 AU
b Q 8 AU
Earth mass
mass and t
smaller tha
oligarchic g
planetary aFIG. 4. The same as Fig. 1 but for the system initially consists of
4000 equal-mass planetesimals (m 5 3 3 1023
g). The radius increase orbital sepa
factor is 6. In the final frame, the filled circles represent protoplanets region, if t
[Kokubo & Ida, Icarus, 1998]
暴走成長＆寡占成長

ORIGIN OF MOON AND SINGLE IMPACT HYPOTHESIS 129
[Cameron, Icarus, 1997]
Giant Impact by SPH

Roche radius, whereas Fig. 3 is a rather extended disk case (run 9).
The extension of a disk is indicated by Jdisk/Mdisk, where Jdisk is the
total angular momentum of the starting disk. For the disks in Figs 2
and 3, Jdisk/Mdisk are0:692 GM!aR and 0:813 GM!aR, respectively.
Figure 3 The same snapshots as in Fig. 2 but for run 9 of a more extended disk
(Jdisk=Mdisk ¼ 0:813 GM!aR). At t ¼ 1,000 the largest moon mass is 0.71ML.
[Ida et al., Nature, 1997]FIG. 2. Snapshots of the circumterrestrial disk projected on the R–z plane at t = 0, 10, 30, 100, 1000TK for runs (a) 29a
centered at the coordinate origin stands for Earth. Circles represent disk particles and their size is proportional to the physic
[Kokubo et al., Icarus, 2000]
Moon Formation by N-body

Moon Formation by N-body
N = 1,000
~3hours@MacPro
数ヶ月∼数年で、ひとつの月ができる

Giant Impact by SPH
[Canup & Asphaug, Nature, 2001]

1. Hf-W Chronometry
Hf → W（半減期 ∼ 9My）182 182
・Hf：親石性 W：親鉄性
・Hf, Wともに難揮発性元素
metal/silicate分離
年代を示す時計！
t =τでコア形成による平衡化
が起きたとすると
ε(t) = f (τ)
※初期比は始源的なコンドライトから決定
ε(t) =
182
W /184
W( )
182
W /184
W( )CHUR
−1








×104
ε(t) が観測可能量なのでコア
形成年代τが求まる

Giant Impact による平衡化プロセス
３. Equilibration by G.I.
Giant Impact !
全球的なマグマオーシャン
(target + impactor)のマントル
と impactor のコアの mixture
現在の地球
マントルと impactor のメタルとの間で平衡化が起こり、
コア形成の際に過剰Ｗがコアに持ち去られる182
impactorのメタル粒
によってマントルが平衡化

l
-
-
n
-
n
r
e
-
r
.
e
n
.
d
n
t
e
f
-
e
,
,
-
t
l
e
a
o
o
t
W
l
-
-
,
for Ste Marguerite is our preferred approximation for the initial
182
Hf/180
Hf ratio of the Solar System. This precisely defined value is
in agreement with previous estimates obtained from internal
chondrite isochrons16
, the comparison of W isotopes in iron
meteorites and chondrites16,30
, and the W isotope compositions of
Figure 1 1w values of carbonaceous chondrites compared with those of the Toluca iron
meteorite and terrestrial samples analysed in this study. The values for Toluca, Allende,
G1-RF and IGDL-GD are the weighted averages of four or more independent analyses.
Also included are data from ref. 16 (indicated by a), ref. 30 (b), and ref. 2 (c). For the
definition of 1w see Table 1. The vertical shaded bar refers to the uncertainty in the W
isotope composition of chondrites. Terrestrial samples include IGDL-GD (greywacke), G1-
RF (granite) and BB and BE-N (basalts).
[Kleine et al., Nature, 2002]
with the f Hf/W
of ,12 for the BSE15
provide the basis for such a
calculation. The D1w value of the BSE is þ2, and a plot of D1w
versus the mean time of core formation is shown in Fig. 2. A two-
stage model age for the BSE of 29 Myr since the formation of the
Figure 1 Hf–W systematics for the early Solar System. Shown is a plot of 1w versus
180
Hf/183
W represented as f Hf/W
(see Table 1 for definitions of 1w and f Hf/W
). a, Data for
metal and silicate fractions from ordinary chondrites Dalgety Downs (L4) and Dhurmsala
(LL6), and from carbonaceous chondrites Allende and Murchison, define a good fossil
isochron, identical within error of the individual isochrons for the two ordinary chondrites.
Least-squares fitting of the data include the Allende and Murchison whole-rock data, but
exclude the Allende CAI. Including or excluding the Murchison and Allende whole-rock
data or the CAI data does not significantly change the slope or the intercept. Our Juvinas
eucrite datum plots on the eucrite isochron6
. The Moon, with a residual 1w ¼ 1.3 ^ 0.4
from 182
Hf decay27
and f Hf/W
¼ 18 defined by the lunar La/W ratio28
, falls within error on
the extension of the tie-line between the bulk chondrite (CHUR) and bulk silicate Earth
(BSE) points. b, Magnified area for bulk chondrite data. Dotted curves show the 2j error
band. Our results are consistent with E-chondrite data19
, the zircon data for the Simmern
Figure 2 Models for timing of core formation in the Earth. Shown is the expected
radiogenic 182
W/183
W value in the Earth relative to chondrites ðD1w ¼ ½1wðBSEÞ 2
1wðCHURÞŠ for a range of mean times of core formation (given by T 0 2 kTlcf; where T 0 is
the age of the Solar System and kTlcf is the mean age of core formation; see ref. 14) in the
Earth for two different models of core segregation: a two-stage model, and a magma
ocean model. For the D1 w value of þ1.9 ^ 0.20 reported in this work, we obtain as
shown a two-stage model age of 29.5 ^ 1.5 Myr and a mean time of core formation of
[Yin et al., Nature, 2002]
Age of the Moon Formation
CAI 形成から約3,000万年後に last giant impact = 月形成

“CAI 形成から約3,000万年後
原始地球に火星サイズの原始惑星が斜め衝突し
飛び散ったマントル物質が周惑星円盤を形成し
それらが約数年かけて集積し
月が誕生した”

は遠いけど，まだだれも知らないことを自分が最初に知ることの喜びやわくわ
れが好きだから，研究を続けているのだと思います。“国語” の教科書に載る

Earth
9
and
a fully
ory as
ularly
ocess
lease,
antial
mme-
of the
of the
ght to
tures,
rial is
re are
then
high
e and
quili-
e may
high
icant:
e fate
ory of
much
o the
after
mally
ming
rlier).
xpect
p that
ature,
ondi-
11
.
been
mpor-
ewas
wever,
phere
ocean
describes the melting responsible for the generation of basaltic magma,
the dominant volcanism on Earth and most voluminously expressed at
the low mantle pressures immediately beneath mid-ocean ridges. Recent
work13,14
suggests that this picture may not apply for the deeper part of
Earth’s mantle, so that freezing may begin at mid-depths.
Even so, there will eventually come a point (perhaps as soon as a few
thousand years) after a giant impact when the bottom part of the mantle
a
b
c
Lunar-forming giant impact
Core
Core
Magma disk
Silicate vapour
atmosphere
Radiative cooling
Blobs of iron settling
to core
Partly
solidified mantle
Rest of disk falls
back on Earth
Newly formed
Moon, mostly or
partly molten
Figure 2 | The effect on Earth of the giant impact that formed the Moon.
a, A giant planetary embryo collides with the nearly complete Earth. b, A
magma disk is in orbit about Earth, while blobs of iron from the planetary
Mixing in the Magma Disk
[Stevenson, Nature, 2008]
[Pahlevan & Stevenson, EPSL, 2007]
原始地球と原始月円盤の間で
数100年間 mixing すればよい

ophysical Journal, 760:83 (18pp), 2012 November 20 Salmon & Canup
Table 3
Hybrid Simulation Parameters
Ld /Md Ld Md Min Mout q amax√
GM⊕aR) (LEM) (M ) (M ) (M ) (R⊕)
0.843 0.304 2.00 2.00 0.00 N/A 2.9
0.843 0.365 2.50 2.50 0.00 N/A 2.9
0.955 0.345 2.00 1.00 1.00 5 4
0.960 0.347 2.00 1.00 1.00 3 4
0.965 0.348 2.00 1.00 1.00 1 4
0.955 0.414 2.40 1.20 1.20 5 4
0.960 0.416 2.40 1.20 1.20 3 4
0.965 0.418 2.40 1.20 1.20 1 4
0.899 0.325 2.00 1.50 0.50 5 4
0.901 0.326 2.00 1.50 0.50 3 4
0.904 0.326 2.00 1.50 0.50 1 4
0.899 0.390 2.40 1.80 0.60 5 4
0.901 0.391 2.40 1.80 0.60 3 4
0.904 0.392 2.40 1.80 0.60 1 4
0.888 0.401 2.50 2.00 0.50 5 4
0.890 0.402 2.50 2.00 0.50 3 4
0.892 0.403 2.50 2.00 0.50 1 4
0.880 0.477 3.00 2.50 0.50 5 4
0.882 0.478 3.00 2.50 0.50 3 4
0.884 0.479 3.00 2.50 0.50 1 4
0.986 0.356 2.00 1.00 1.00 5 6
1.009 0.365 2.00 1.00 1.00 3 6
1.036 0.374 2.00 1.00 1.00 1 6
0.986 0.427 2.40 1.20 1.20 5 6
1.009 0.437 2.40 1.20 1.20 3 6
1.036 0.449 2.40 1.20 1.20 1 6
0.914 0.330 2.00 1.50 0.50 5 6
0.926 0.335 2.00 1.50 0.50 3 6
0.940 0.339 2.00 1.50 0.50 1 6
0.914 0.396 2.40 1.80 0.60 5 6
0.926 0.401 2.40 1.80 0.60 3 6
0.940 0.407 2.40 1.80 0.60 1 6
0.900 0.406 2.50 2.00 0.50 5 6
0.909 0.411 2.50 2.00 0.50 3 6
0.920 0.416 2.50 2.00 0.50 1 6
0.890 0.482 3.00 2.50 0.50 5 6
0.898 0.487 3.00 2.50 0.50 3 6
0.907 0.492 3.00 2.50 0.50 1 6
1.068 0.386 2.00 1.00 1.00 1 7
1.068 0.463 2.00 1.20 1.20 1 7
0.998 0.361 2.00 1.00 1.00 5 8
1.043 0.377 2.00 1.00 1.00 3 8
1.099 0.397 2.00 1.00 1.00 1 8
0.998 0.433 2.40 1.20 1.20 5 8
1.043 0.452 2.40 1.20 1.20 3 8
1.098 0.476 2.40 1.20 1.20 1 8
mulation parameters with a Roche-interior ﬂuid disk and Roche-
Figure 2. Snapshots of the protolunar disk, projected on the R − z plane, at
t = 0, 0.03, 1, 30, 200, and 1000 years, for Run 34 using the hybrid model with
a ﬂuid inner disk. The size of circles is proportional to the physical size of the
corresponding particle. The horizontal thick line is the Roche-interior disk. The
[Salmon & Canup, ApJ, 2012]
粘性モデル
Roche 半径以内は
流体的に振る舞う
・固体への凝縮
・物質の輸送
N 体計算
Roche 半径以遠は
固体的に振る舞う
・衝突合体成長
月の形成時間
~1,000年

lunar material
Junjun Zhang1
*, Nicolas Dauphas1
, Andrew M. Davis1
, Ingo Leya2
and Alexei Fedkin1
A giant impact between the proto-Earth and a Mars-sized
impactor named Theia is the favoured scenario for the
formation of the Moon1–3
. Oxygen isotopic compositions
have been found to be identical between terrestrial and
lunar samples4
, which is inconsistent with numerical models
estimating that more than 40% of the Moon-forming disk
material was derived from Theia2,3
. However, it remains
uncertain whether more refractory elements, such as titanium,
show the same degree of isotope homogeneity as oxygen in the
Earth–Moon system. Here we present 50
Ti/47
Ti ratios in lunar
samples measured by mass spectrometry. After correcting
for secondary effects associated with cosmic-ray exposure
at the lunar surface using samarium and gadolinium isotope
systematics, we find that the 50
Ti/47
Ti ratio of the Moon is
identical to that of the Earth within about four parts per
million, which is only 1/150 of the isotopic range documented in
meteorites. The isotopic homogeneity of this highly refractory
element suggests that lunar material was derived from the
proto-Earth mantle, an origin that could be explained by
efficient impact ejection, by an exchange of material between
the Earth’s magma ocean and the protolunar disk, or by fission
from a rapidly rotating post-impact Earth.
Apart from the effects of radioactive decay, the isotopic
compositions of most terrestrial rocks are related by the laws of
mass-dependent fractionation. Meteorites show departures from
this rule that can be ascribed to unusual chemical processes,
inheritance of nucleosynthetic anomalies, or nuclear transmu-
tations (cosmogenic effects and radioactive decay). In the zoo
of elements that show well-documented isotopic anomalies at
a bulk planetary scale5–8
, highly refractory titanium, with large
nucleosynthetic anomalies on 50
Ti, is the most promising to
assess the degree of homogeneity in the Earth–Moon system9
.
Taking advantage of our new chemical procedure for titanium
separation and developments in multicollector inductively cou-
pled plasma mass spectrometry (MC-ICPMS; see Methods and
¬2 ¬1 0 1 2 3 4 5 6
50Ti
Pre-exposure lunar value
( 50Ti = ¬0.03±0.04)
ε
ε
Ordinary chondrites
Enstatite chondrites
Moon
Earth
Carbonaceous chondrites
Achondrites
CI
CM
CR
CO
CV
CK
EH
EL
H
L
LL
HEDs
Angrites
Aubrites
Ungrouped
Acapulcoite
Figure 1 | Titanium nucleosynthetic heterogeneity,
"50Ti = [(50Ti/47Ti)sample/(50Ti/47Ti)rutile 1]⇥104, for carbonaceous,
[Zhang et al., Nature Geo., 2012]
magma
of the
–142
Nd
dicting
s were
e used
n years
ponent
nly by
lunar
ms of
e data
erived
g that
60 Myr
m–Nd
estrial
n with
ns the
ion of
lunar
erived
in the
e giant
en iso-
REEP-
), rare
nd five
fold to
ed the
ratios.
e con-
fect on
y short
0.01%)
56 and
larger
given
e have
ee with
mples3
.
cates that this anomaly might be due entirely to cosmogenic 182
W.
Kleine et al.3
reported elevated e182
W < 2 for a magnetic separate
from high-Ti mare basalt 79155 but we determined Hf/W 5 7.5 for
an aliquot from the same magnetic separate, most probably indi-
cating the presence of some ilmenite and hence cosmogenic 182
W
in this separate. The calculated cosmogenic 182
W component is ,1.7
–2 –1 0 1 2 3 4 5
–2 –1 0 1 2 3 4 5
e182W
Ref. 3
This study
Ref. 5
Corrected in this study
KREEP-rich
samples
Low-Ti
mare basalts
High-Ti
mare basalts
14310
15445
62235
65015
68115
68815
72155
79155
75075
77516
70035
70017
70035
15475
15555 (WR)
15499
15556
15058
15555
75035
74255
74275
12004
Figure 1 | e182
W of lunar metals analysed in this study compared with data
from refs 3 and 5. Some of the previous data (shown with black dots inside
the symbols) were corrected for cosmogenic 182
W (see the text for details).
[Touboul et al., Nature, 2007]
難揮発性元素の同位体も一致

(6) 難揮発性元素の同位体比が地球とほぼ一致
[Touboul et al., 2007]
すぐに凝結してしまう元素は十分に mixing できない

and vapor, which requires a solution mod
coefficients for trace elements at the
(T=2500 K–3500 K). At present, no s
Fig. 1. Chemical fractionation on an unstratified Earth. A single convective column
characterizes the Earth from the deep magma ocean, where only one phase is present,
through the top of the two-phase atmosphere. Rainout of Mg-rich droplets in ascending
parcels shifts the composition of the upper atmosphere towards an Fe-rich vapor
-2
-1
0
0 0.2
logP(bars)
Fe/Fe+Mg
Fig. 2. Chemical structure of the silicate vapor at
rainout. The parcel represents the composition of t
suspended in a fayalitic vapor) and shifts with altitu
as the droplets separate via rainout. The lower
convection from the underlying magma ocean
composition. This calculation assumes that 40% o
every three-fold decrease in pressure (fL =0.4). Thi
the top of the atmosphere – a two-fold enhancemen
enhancement is comparable to a widely postulated
has observable consequences (see text).
438 K. Pahlevan et al. / Earth and Planetary Science Letters 301 (2011) 433–443
[Pahlevan et al., EPSL, 2011]
“Unstratified” Magma Disk
難揮発性元素についても mixing の可能性を提案

lunar glasses are given in Ta
of all the bulk lunar sam
(±2rSD) which is identical
et al. (2010) for bulk
À0.29 ± 0.08 (±2rSD). The
alts (d30
Si = À0.31 ± 0.07,
(2007) and Fitoussi et al.’s (
of d30
Si = À0.30 ± 0.05& (
narrow observed range of S
the variety of samples obser
lunar lithologies analysed
within error (2rSD): d30
d30
SiHigh-Ti basalt = À0.32 ±
0.05; d30
SiHighland rocks = À
Fig. 2. d29
Si versus d30
Si plot. The error bars represent ±2rSEM for
the samples. The calculated slopes for mass dependent equilibrium
fractionation (0.5178) and mass dependent kinetic fractionation
(0.5092) are also plotted.
30
Fig. 4. Histograms of d30
Si val
and bulk silicate Earth samples
The lunar breccia from Chakra[Armytage et al., GCA, 2012]
Si 同位体比も一致

Si 同位体分配には圧力（＝サイズ）依存性がある
(7) Si 同位体比が地球とほぼ一致 [Armytage et al., 2012]

Hf-W Chronometry の弱点
[Sasaki & Abe, PPV, 2005]
どう考えても Hf-W 系の完全平衡化は実現できない

T. SASAKI AND Y. ABE: IMPERFECT EQUILIBRATION OF HF-W SYSTEM 1041
ge of the last giant impact as a function of the resetting ratio
nt impact, fitting to the observational data (ϵ = 2) from Earth
he number of giant impacts is assumed to be five. The initial
= 10 at t = 10. The formation age of the Earth for perfect
resetting ratio = 1) is about 30 Myr, in agreement with a
udy (Yin et al., 2002).
ate equilibration. This would not be a realistic
Fig. 7. The age of the last giant impact as a function of the resetting ratio
of each giant impact, fitting to the observational data (ϵ = 2) from Earth
samples. The number of giant impacts is 2 to 10 from left to right. The
initial state is ϵ = 10 at t = 10.
[Sasaki & Abe, EPS, 2007]
[Wood & Halliday, Nature, 2005]
Age of the Moon Formation?
Hf-W chronometry では
月形成の年代は決まらない

2.3. Initial Conditions
We follow Canup & Asphaug (2001) and Canup (2004) for the
orbital parameters of the impactor for which the most massive
satellite is expected. The masses of the proto-Earth and the im-
pactor are assumed to be 1.0 and 0:2 MÈ, where MÈ is the Earth
mass. The radii of the proto-Earth and protoplanet are rE ¼ 1:0
and 0:64r , respectively. Note that no signiﬁcant differences in
Fig. 1.—Giant impact simulation with EOS-1, which represents a state in which most of the impactor mass is vaporized. Left, face-on views of the system; right, edge-
on views. The numbers in the upper right corners of the panels show the time in units of hours. The color represents log-scaled density (the units are 0 ¼ 12:6 g cmÀ3
).
WADA, KOKUBO, MAKINO1182 Vol. 638
[Wada et al., ApJ, 2005]
高解像度格子法による G.I. 計算
蒸発した原始月円盤内に衝撃波が立ちまくって
円盤が角運動量を失い数日で全て地球に落下！？

Ćuk Stewart, Science (2012)
-200
-150
-100
-50
0
50
100
150
200
0 20 40 60 80 100
Resonantangle(°)
Time (kyr)
D
2.5
3
3.5
4
4.5
5
5.5
6
6.5
Earthísspinperiod(hr)
C
0
0.1
0.2
0.3
0.4
0.5
0.6
Eccentricity
B
4
5
6
7
8
9
10
Semi-majoraxis(RE) A
Synchronous at perigee
Fig. 3. Tidal evolution of the Moon through the
evection resonance, starting with an Earth spin
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0 20 40 60 80 100 120
Earth+Moonangularmomentum
Time (kyr)
P=2.25 hr QE=48 QM=48
P=2.25 hr QE=96 QM=97
P=2.5 hr
P=2 hr
P=3 hr
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0 20 40 60 80 100
Earth+Moonangularmomentum
Time (kyr)
QE=48 QM=48
QE=96 QM=97
QM=117
QM=73
QM=57
A
B
Fig. 4. Change in total angular momentum of the Earth-Moon system during tidal evolution
Moon for different simulation parameters. (A) Simulations starting with Earth’s spin period of 2.5
with different tidal quality factors for Earth (QE = 96, where not noted otherwise) and the Moon
(B) Simulations starting with 2-, 2.25-, 2.5-, and 3-hour spin periods for Earth (QE = 96 and QM
RESEARCH A
地球-月-太陽の間の永年共鳴で系の角運動量が減少

(2) 地球より低密度（コアが小さい）[Hood Zuber, 2000]
(3) 揮発性元素が強く枯渇 [Jones Palme, 2000]
(7) Si 同位体比が地球とほぼ一致 [Armytage et al., 2012]

Collision Scenarios
w/o angular momentum constraints
formed from a magma ocean (5), implying an
intensely energetic fiery start at a time when
heat-producing short-lived nuclides (26
Al and
60
Fe) were extinct. Third, the oxygen isoto-
silicon isotopic composition of Earth and the
Moon (13) is not readily explained; the rain-
out process is expected to generate a silicon
isotopic difference, so the problem persists.
A
Standard impactor Small impactor Large impactor
B C
Collision scenarios. Examples of the three new models of the Moon-forming Giant Impact, each of which
allows more angular momentum to be lost and thereby achieves oxygen isotopic compositions that cannot be
resolved between Earth and the Moon. (A) “Standard” impactor, 10% of Earth’s final mass, works with “hit
and run” collision (14). (B) “Small” impactor, 2.5% of Earth’s final mass (1). (C) “Large” impactor, 45% of
Earth’s final mass (2).
(A) 質量比 10:1 で “Hit-and-Run” collision [Reufer et al., 2012]
(B) 質量比 40:1 で “Fission-like” collision [Ćuk Stewart, 2012]
(C) 質量比 1:1 で “Twins” collision [Canup, 2012]
[Halliday, 2012]

Fig. 1a. Five snapshots from the 30° impact angle and 1.30 vesc impact velocity case
(cC06) showing cuts through the impact plane. Color coded is the type and origin of
21 (2012) 296–299 297
“Hit-and-Run” Collision
[Reufer et al., Icarus, 2012]

Moon-formation events for
th less angular momentum.
angular momentum by add-
actors generated successful
er-spinning planets. Because
is carried away with debris
iant impacts, the spin period
ses. Thus, the spin state of
to be near fission before or
ming impact in our scenario
ntry in Table 1). However,
the spin of each body and the impact geometry)
is near the stability limit.
Our candidate Moon-forming events have
more than double the kinetic energy of previous
scenarios, and the impact velocities were suf-
ficient to substantially vaporize silicates (33). As
a result, the silicate atmosphere and vapor-rich
disk are more massive and hotter than found
in previous work (34). At the resolution of the
simulations, the projectile-to-target mass ratio is
uniform from the atmosphere to the Roche radius.
the
th’s
pact
r at
−0.3
pin-
2.3
Gray
oche
w of
ower
own
spin
note
and
arth
disk
erial
th’s
pact
S1).
view
de-
ue),
and
nsity
e of
hich
38 SCIENCE www.sciencemag.org
onNovember25,2012www.sciencemag.orgDownloadedfrom
“Fission-like” Collision
shifted inward. Eventually, the lunar semimajor
axis evolved within 5RE, whereas the Moon main-
Earth-Moon system with its current momentum
and found that capture in the evection resonance
and the Moon is within ~50% of the value op-
timal for their balance (26). This balance of tides
Fig. 2. Summary of the range of outcomes for expected terminal giant
impacts onto the proto-Earth: Mproj ≤ 0.1ME and 1 to 3Vesc (Vesc ~ 10 km s−1
).
The target was a 0.99ME body with a 2.3-hour spin. Projectiles had no spin
and masses of 0.026, 0.05, or 0.10ME. The radius of each filled colored circle
is proportional to the satellite mass; the black circle indicates MS = 1.0MM.
Color indicates the difference in projectile composition between the silicate
disk and silicate Earth. Within a colored circle, a gray dot denotes too much
iron core mass fraction in the disk. The number above each symbol gives the
final mass of the planet; bold numbers indicate cases that satisfy the relaxed
Moon-formation criteria in Table 1. Collisions in the middle region of the
figure, head-on and slightly retrograde impacts from 10 to 30 km s−1
, are the
best fit to the observational constraints for Moon-forming impacts.
RESEARCH ARTICLE
[Ćuk Stewart, Science, 2012]

into a single moon at an orbital distance of about
3.8R⊕, where R⊕ is Earth’s radius (19, 20),
MM
MD
≈ 1:9
LD
MD
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2:9GM⊕R⊕
p

−
1:1 − 1:9
Mesc
MD

ð1Þ
where Mesc is the mass that escapes from the
disk as the Moon accretes. To estimate MM, we
used Eq. 1 and made the favorable assumption
that Mesc = 0.
We tracked the origin (impactor versus tar-
get) of the particles in the final planet and the
disk. To quantify the compositional difference be-
tween the silicate portions of the disk and planet,
we define a deviation percentage
dfT ≡ [FD,tar/FP,tar − 1] × 100 (2)
where FD,tar and FP,tar are the mass fractions of
the silicate portions of the disk and of the planet
derived from the target’s mantle, respectively (21).
Identical disk-planet compositions have dfT = 0,
whereas a disk that contains fractionally more
impactor-derived silicate than the final planet has
dfT 0, and a disk that contains fractionally less
dfT 0.
Prior impact simulations (1–3, 14, 15) that
consider g ≡ Mimp/MT ≈ 0.1 to 0.2 produce disks
with −90% ≤ dfT ≤ −35% for cases with MM
ML, where ML is the Moon’s mass. Results with
larger impactors having g = 0.3, 0.4, and 0.45
are shown in Figs. 1 and 2 and Table 1. As the
relative size of the impactor (g) is increased, there
is generally a closer compositional match be-
tween the final disk and the planet. For g ≥ 0.4,
some disks have both sufficient mass and an-
gular momentum to yield the Moon and nearly
identical silicate compositions to that of the final
Fig. 1. An SPH simulation
of a moderately oblique,
low-velocity (v∞ = 4 km
s–1
) collision between an
impactor and target with
similar masses (Table 1,
run 31). Color scales with
particle temperature in
kelvin, per color bar, with
red indicating tempera-
tures 6440 K. All particles
in the three-dimensional
simulation are overplotted.
Time is shown in hours,
and distances are shown
in units of 103
km. After
the initial impact, the plan-
ets recollided, merged,
and spun rapidly. Their
iron cores migrated to the
center, while the merged
structure developed a bar-
type mode and spiral arms
(24). The arms wrapped
up and finally dispersed
to form a disk containing
~3 lunar masses, whose
silicate composition dif-
fered from that of the
final planet by less than
1%. Because of the near
symmetry of the colli-
sion, impactor and target
material are distributed
approximately proportion-
ately throughout the final
disk, so that the disk’s dfT
value does not vary ap-
preciably with distance
from the planet.
REPORTS
onNovember25,2012www.sciencemag.orgownloadedfrom
“Twins” Collision
larger impactors h
are shown in Figs
relative size of the
is generally a clo
tween the final dis
some disks have
gular momentum
identical silicate co
from the planet.
Fig. 2. Compositional differ-
ence between the disk and final
planet (dfT) (Eq. 2) produced by
simulations with (A) g = 0.3
and (B) g = 0.4 (triangles) and
0.45 (squares) versus the pre-
dicted mass of the moon that
would accrete from each disk
(MM) (Eq. 1) scaled to the final
planet’s mass (MP). There is a
change in y axis scales between
the two plots. Gray, purple, dark
blue, light blue, green, yellow,
orange, and red points corre-
spond to vimp/vesc = 1.0, 1.1,
1.2, 1.3, 1.4, 1.6, 1.8, and 2.0,
respectively. The open square
is run 60* from Table 1, which
includes pre-impact rotation.
Forming an appropriate-mass
Moon mass requires MM/MP 0.012, the region to the right of the vertical solid line. Constraints on dfT needed to satisfy Earth
are shown by horizontal lines for oxygen (solid), titanium (dotted), and chromium (dot-dashed), assuming a Mars-composition im
www.sciencemag.org SCIENCE VOL 338 23 NOVEMBER 2012
dfT ≡ [FD,tar/FP,tar − 1] × 100 (2)
dfT 0.
simulation are overplotted.
Time is shown in hours,
and distances are shown
in units of 103
km. After
the initial impact, the plan-
ets recollided, merged,
and spun rapidly. Their
iron cores migrated to the
center, while the merged
structure developed a bar-
type mode and spiral arms
(24). The arms wrapped
up and finally dispersed
to form a disk containing
~3 lunar masses, whose
silicate composition dif-
fered from that of the
final planet by less than
1%. Because of the near
symmetry of the colli-
sion, impactor and target
from the planet.
Fig. 2. Compositional differ-
ence between the disk and final
planet (dfT) (Eq. 2) produced by
simulations with (A) g = 0.3
and (B) g = 0.4 (triangles) and
0.45 (squares) versus the pre-
dicted mass of the moon that
would accrete from each disk
(MM) (Eq. 1) scaled to the final
planet’s mass (MP). There is a
change in y axis scales between
the two plots. Gray, purple, dark
blue, light blue, green, yellow,
orange, and red points corre-
spond to vimp/vesc = 1.0, 1.1,
1.2, 1.3, 1.4, 1.6, 1.8, and 2.0,
respectively. The open square
is run 60* from Table 1, which
includes pre-impact rotation.
Forming an appropriate-mass
Moon mass requires MM/MP 0.012, the region to the right of the vertical solid line. Constraints on dfT needed to satisfy Earth-Moon compositional similarities
are shown by horizontal lines for oxygen (solid), titanium (dotted), and chromium (dot-dashed), assuming a Mars-composition impactor.
[Canup, Science, 2012]

standard
“Fission-like” “Twins”
[Simulations by Miki Nakajima]

colors. In the canonical scenario, the impactor grazes around the target’s mantle
and is deformed. Due to the low impact velocity, material supposed to end up in or-
bit around the Earth must not be decelerated too strongly in order to retain enough
velocity to stay in orbit. This is only achieved for the parts of the impactor mantle
most distant to the point of impact, and some minor part of the target’s mantle. But
if impact velocity is increased from 1.00 (cA08) to 1.30 vesc (cC01), parts from dee-
per within the target mantle receive the right amount of energy for orbit insertion,
the material. Dark and light blue indicate target and impactor iron; Red and orange
show corresponding silicate material. The far right shows the situation at the time
of impact. At 0.52 h, it can be seen how the impactor ploughs deep through the
targets mantle and pushes considerable amount of target material into orbit. A
spiral arm of material forms and gravitationally collapses into fragments. The outer
portions of the arm mainly consist of impactor silicates and escapes due to having
retained a velocity well above escape velocity. The silicate fragments further inward
are stronger decelerated and enter eccentric orbits around the target. The
impactor’s iron core also looses much of its angular momentum to the outer parts
of the spiral arm and re-impacts the proto-Earth. (For interpretation of the
references to color in this ﬁgure legend, the reader is referred to the web version of
this article.)
221 (2012) 296–299 297
“Hit-and-Run” Collision?
[Reufer et al., Icarus, 2012]
uggests that this issue can be resolved if Theia
ble to that of the proto-Earth. In this case, both
forming disk are a roughly even mixture of the
a. (This scenario relies on the angular momen-
oon system later decreasing via an evection
Sun (C´ uk and Stewart, 2012).)
umber of terrestrial planet formation simula-
te the statistical likelihood that Theia’s mass
he proto-Earth. To do this, we simply look at
mass ratios for Earth analogs struck by Theia
lations. This distribution is shown in Fig. 17,
arameter c, which is the ratio of Theia’s mass
ss of Theia and the proto-Earth at the time of
Earth and Moon evenly enough, Canup (2012)
t have had cJ 0:4. In Fig. 17, we see that such
und in any of our simulations. Out of the 104
ated in our collisions, the largest recorded c
7% of our Earth analogs experienced impacts
mpacts with cJ 0:4 must be exceedingly rare,
parably massed Theia and proto-Earth is a very
result agrees with Jacobson and Morbidelli
nd that major mergers between protoplanets
are rare.
rable masses for Theia and the proto-Earth,
2012) and C´ uk and Stewart (2012) invoke a
if the proto-Earth was spinning very rapidly before impact. Because
of this ﬁnding, we also look at our collision statistics for last major
mergers on Earth analogs that involve impacting bodies with
masses below 0:1 MÈ. These are also shown in Fig. 18. We see that
smaller impactors do collide with the Earth at higher velocities, but
Fig. 18. The cumulative distribution of impact velocities between Earth and Theia
analogs in the ANN simulations. Theia analogs are split into three different mass
bins: m = 0.025–0.05 MÈ (solid line), m = 0.05–0.1 MÈ (dashed line), and
m 0:1 MÈ (dotted line). Impact velocity is calculated in terms of the mutual
escape velocity of the Earth and Theia analogs.
N.A. Kaib, N.B. Cowan / Icarus 252 (2015) 161–174 171
[Kaib Cowan, Icarus, 2012]
N 体計算で Giant Impacts の過程を追ったところ
衝突速度が必要な大きさに達しないことが判明

(Agnor et al. 1999) is necessary after the giant impact stage.
3.3. Statistics of Spin
In 50 runs of the realistic and perfect accretion models,
we have 128 and 124 planets that experience at least one
accretionary collision, respectively. The average values of each
an isotropic d
the obliquity
distribution w
and Kokubo
K–S probabil
accretion mod
spin anisotrop
Figure 3. Left: average spin angular velocity of all planets formed in the 50 runs of the realistic (circle)
mass M with mass bin of 0.1 M⊕. The error bars indicate 1σ and the dotted line shows ωcr. Right: no
curve) and perfect (dashed curve) accretion models with an isotropic distribution (dotted curve).
(A color version of this ﬁgure is available in the online journal.)
[Kokubo Genda, ApJ, 2010]
k (table S1). The results imply a more narrow
nge for potential Moon-formation events for
pact scenarios with less angular momentum.
creasing the total angular momentum by add-
g spin to the impactors generated successful
ks from the slower-spinning planets. Because
gular momentum is carried away with debris
m these erosive giant impacts, the spin period
the planet decreases. Thus, the spin state of
rth is not required to be near fission before or
er the Moon-forming impact in our scenario
r example, last entry in Table 1). However,
the total angular momentum of the event (from
the spin of each body and the impact geometry)
is near the stability limit.
Our candidate Moon-forming events have
more than double the kinetic energy of previous
scenarios, and the impact velocities were suf-
ficient to substantially vaporize silicates (33). As
a result, the silicate atmosphere and vapor-rich
disk are more massive and hotter than found
in previous work (34). At the resolution of the
simulations, the projectile-to-target mass ratio is
uniform from the atmosphere to the Roche radius.
g. 1. Formation of the
nar disk from Earth’s
ntle. Example impact
a 0.05ME impactor at
km s−1
and b = −0.3
to a 1.05ME Earth spin-
g with a period of 2.3
urs (‡ in Table 1). Gray
cles denote the Roche
dius. (A to F) View of
H particles in the lower
misphere looking down
counterclockwise spin
s, where colors denote
e silicate mantles and
n cores of the Earth
d the impactor. The disk
dominated by material
ginating from Earth’s
ntle near the impact
(fig. S1 and movie S1).
Lower hemisphere view
h particle colors de-
ting the planet (blue),
mosphere (yellow), and
k (green). (H) Density
the equatorial plane of
disk and planet, which
stably stratified.
2012 VOL 338 SCIENCE www.sciencemag.org
“Fission-like” Collision?
衝突破壊の効果も考慮すると
原始地球を高速回転できない[Ćuk Stewart, Science, 2012]

into a single moon at an orbital distance of about
3.8R⊕, where R⊕ is Earth’s radius (19, 20),
MM
MD
≈ 1:9
LD
MD
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2:9GM⊕R⊕
p

−
1:1 − 1:9
Mesc
MD

ð1Þ
where Mesc is the mass that escapes from the
disk as the Moon accretes. To estimate MM, we
used Eq. 1 and made the favorable assumption
that Mesc = 0.
We tracked the origin (impactor versus tar-
dfT ≡ [FD,tar/FP,tar − 1] × 100 (2)
dfT 0.
ulation
blique,
4 km
een an
et with
ble 1,
es with
ure in
r, with
mpera-
articles
sional
plotted.
hours,
shown
. After
e plan-
erged,
Their
to the
merged
a bar-
al arms
apped
persed
aining
whose
n dif-
of the
s than
e near
colli-
target
ibuted
ortion-
e final
k’s dfT
ry ap-
stance
onal differ-
isk and final
produced by
A) g = 0.3
iangles) and
REPORTS
“Twins” Collision?
[Canup, Science, 2012]
20Ne/22Ne
10 11 12 13
40Ar/36Ar
2,000
4,000
6,000
8,000
10,000
21Ne/22Ne
0.07
20Ne/22Ne
10
11
12
13
a
Iceland; this study
MORB (2ΠD43)
Iceland; ref. 18
Air
Air
Iceland
mantle
source
Iceland
mantle
source
Solar
wind
b
0.040.03 0.05 0.06
Figure 1 | Differences in neon and argon isotopic composition between
MORB and the Iceland plume. a, Neon three-isotope plot showing the new
analyses of the DICE 10 sample (filled circles) from Iceland in comparison to
previously published data for this sample (open circles; ref. 18) and the gas-rich
‘popping rock’ (2PD43) from the north Mid-Atlantic Ridge (open triangles; ref.
17). Error bars are 1s, and forclarity, twoprevious analyses18
with largeerrorbars
have not been shown. Step-crushing of a mantle-derived basalt produces a linear
trend that reflects variable amounts ofpost-eruptive air contamination in vesicles
containingmantleNe.Theslopeofthelineisafunctionoftheratioofnucleogenic
21
Ne to primordial 22
Ne, with steeper slopes indicating a higher proportion of
primordial 22
Ne and, thus, a less degassed mantle source. The slope of the Iceland
line based on the new analyses is consistent with that obtained previously18
.
Importantly, 20
Ne/22
Ne ratios of 12.8860.06 are distinctly higher than the
MORB source 20
Ne/22
Ne of #12.5 as constrained from continental well gases20
.
b, Ne–Ar compositions of individual step crushes of the DICE 10 sample. 40
Ar is
generated by radioactive decay of 40
K, and low 40
Ar/36
Ar ratios are indicative of a
less degassed mantle. The data reflect mixing between a mantle component and
post-eruptive atmospheric contamination. A least-squares hyperbolic fit through
the data yields a 40
Ar/36
Ar ratio of 10,74563,080, corresponding to a mantle
solar 20
Ne/22
Ne ratio of 13.8. This Ar isotopic ratio is used as the mantle source
value for Iceland in Figs 2 and 3. Symbols as in a; error bars are 1s.
Kinetic fractionation
10
13
Iceland; this study
MORB (2ΠD43)
a
Air
20Ne/22Ne
3He/22Ne
12
11
3He/36Ar
40Ar/36Ar
5,000
10,000
15,000
20,000
25,000
30,000b
Air
Iceland mantle
source
MORB
(2ΠD43)
mantle
source
0.0 0.2 0.4 0.6 0.8
22Ne/36Ar
40Ar/36Ar
5,000
10,000
15,000
20,000
25,000
30,000
Air
Sea water
c
0.0 0.1 0.2 0.3 0.4
Degassing
0 1 2 3 4 5 6
Figure 2 | Differences in elemental abundances and isotope ratios between
MORB and the Iceland plume. Errorbarsare1s.a,3
He/22
Neversus20
Ne/22
Ne;
b, 3
He/36
Ar versus 40
Ar/36
Ar; and c, 22
Ne/36
Ar versus 40
Ar/36
Ar. The mantle
source composition for 2PD43 (filled grey square in all panels) is based on the
40
Ar/36
Ar and 20
Ne/22
Ne ratios as defined in ref. 30, and the mantle source
composition for Iceland (filled black square in all panels) is based on Fig. 1. The
grey and black arrows at the top ofthe figure indicate how elemental ratios evolve
asaresultofkineticfractionationandsolubilitycontrolleddegassing,respectively.
Good linear relationships are observed between isotope ratios and elemental
ratios, which reflect mixing between mantle-derived noble gases and post-
RESEARCH LETTER
20Ne/22Ne
10 11 12 13
40Ar/36Ar
2,000
4,000
6,000
8,000
10,000
21Ne/22Ne
0.0720Ne/22Ne
10
11
12
13
a
Iceland; this study
MORB (2ΠD43)
Iceland; ref. 18
Air
Air
Iceland
mantle
source
Iceland
mantle
source
Solar
wind
b
0.040.03 0.05 0.06
Figure 1 | Differences in neon and argon isotopic composition between
MORB and the Iceland plume. a, Neon three-isotope plot showing the new
analyses of the DICE 10 sample (filled circles) from Iceland in comparison to
previously published data for this sample (open circles; ref. 18) and the gas-rich
‘popping rock’ (2PD43) from the north Mid-Atlantic Ridge (open triangles; ref.
17). Error bars are 1s, and forclarity, twoprevious analyses18
with largeerrorbars
have not been shown. Step-crushing of a mantle-derived basalt produces a linear
trend that reflects variable amounts ofpost-eruptive air contamination in vesicles
containingmantleNe.Theslopeofthelineisafunctionoftheratioofnucleogenic
21
Ne to primordial 22
Ne, with steeper slopes indicating a higher proportion of
primordial 22
Ne and, thus, a less degassed mantle source. The slope of the Iceland
line based on the new analyses is consistent with that obtained previously18
.
Importantly, 20
Ne/22
Ne ratios of 12.8860.06 are distinctly higher than the
MORB source 20
Ne/22
Ne of #12.5 as constrained from continental well gases20
.
Kinetic fractionation
10
13
Iceland; this study
MORB (2ΠD43)
a
Air
20Ne/22Ne
3He/22Ne
12
11
3He/36Ar
40Ar/36Ar
5,000
10,000
15,000
20,000
25,000
30,000b
Air
Iceland mantle
source
MORB
(2ΠD43)
mantle
source
0.0 0.2 0.4 0.6 0.8
22Ne/36Ar
40Ar/36Ar
5,000
10,000
15,000
20,000
25,000
30,000
Air
Sea water
c
0.0 0.1 0.2 0.3 0.4
Degassing
0 1 2 3 4 5 6
Figure 2 | Differences in elemental abundances and isotope ratios between
MORB and the Iceland plume. Errorbarsare1s.a,3
He/22
Neversus20
Ne/22
Ne
RESEARCH LETTER
contamination processes are ruled out as the reason for the lower
129
Xe/130
Xe ratios at Iceland.
The data in Fig. 3a demonstrate that the Iceland and MORB source
mantles evolved with different I/Xe ratios, requiring the two mantle
sources to have separated by 4.45Gyr ago with limited subsequent mix-
ing between the two. As atmosphere is located near the origin in this plot
(Fig. 3a), and mixing in this space is linear, adding subducted atmo-
spheric Xe to the MORB source clearly cannot produce the Iceland
source, based on its higher proportion of Pu- to U-derived fission Xe, is a
conclusion that is independent of the absolute concentrations of noble
gasesandtherelativepartitioncoefficientsofthenoblegaseswithrespect
to their radiogenic parents.
The combined I–Pu–Xe system has been used to constrain the
closure time for volatile loss of a mantle reservoir through the
129
*Xe/136
*XePu ratio1,2,6,25
, where 129
*Xe is the decay product of 129
I
decay and 136
*XePu is 136
Xe produced from 244
Pu fission. 129
I has a
244 129 136
6.6
6.8
7.0
7.2
7.4
129Xe/130Xe
40Ar/36Ar
2,000 4,000 6,000 8,000 10,000
Iceland mantle
129Xe/130Xe
Air
b
3He/130Xe
0 200 400 600 800 1,000
Air
129Xe/130Xe
6.6
6.8
7.0
7.2
7.4
7.6
7.8
MORB
(2ΠD43)
source
Iceland
mantle
source
a
Figure 3 | Differences in Xe isotopic composition between MORB and the
Iceland plume. a, Correlation between 129
Xe and 3
He in the ‘popping rock’
MORB (2PD43)17
and Iceland (DICE 10). Error bars are 1s. Data points are
individual step crushes that reflect different degrees of post-eruptive atmospheric
contamination in the vesicles. Air lies near the origin and the mantle
compositions at the other end of the linear arrays. The straight lines are robust
regressions through the data. Because mixing in this space is linear, the lines also
represent the trajectories along which the mantle sources will evolve when mixed
with subducted air. The new observations from Iceland demonstrate that the
Iceland plume 129
Xe/130
Xe ratio cannot be generated solely through adding
recycled atmospheric Xe to the MORB source, and vice versa. Thus, two mantle
reservoirs with distinct I/Xe ratios are required. The mantle 129
Xe/130
Xe ratio of
6.986 0.07 for Iceland was derived from a hyperbolic least-squares fit through
the Ar-Xe data (b) corresponding to a mantle 40
Ar/36
Ar ratio of 10,745. Note that
given the curvature in Ar–Xe space, the 129
Xe/130
Xe in the Iceland mantle source
is not particularly sensitive to the exact choice of the mantle 40
Ar/36
Ar ratio.
LETTER RESEARCH
[Mukhopadhyay, Nature, 2012]
地球深部の希ガス同位体不均一
地球深部まで melting していない

s can be found in the Methods). We calculate the
the feeding zones of the impactor and the planet are
ame distribution, using a two-group Kolmogorov–
babilities shown in the plots and in Table 1). In 3 out
ding zones contributing to the Moon and those con-
anet are consistent with being drawn from the same
of the proto-Earth was mixed into the Moon (as suggested by detailed
collision simulations showing a 10%–40% contribution from the proto-
Earth14
). For the typical 20% mix of proto-Earth material with the
impactor material forming the Moon (as found in simulations), 35%
of cases are consistent with their feeding zones being drawn from the
same parent distribution, and the success rate increases further for a
50
100
50
100
50
100
N
50
100
0.5 1 1.5 2 2.5 3 3.5 4
0
50
100
a (AU)
a
NP = 123, NI = 97
P = 0.0039
10%, P = 0.023
20%, P = 0.13
30%, P = 0.32
40%, P = 0.67
cjs15 number 1
0
20
40
60
0
20
40
0
20
40
N 0
20
40
1 2 3 4
0
20
40
a (AU)
cjs1 number 4
10%, P = 6.7 × 10−27
NP = 128, NI = 78, P = 1.1 × 10−29
20%, P = 5.1 × 10−18
30%, P = 2.7 × 10−10
40%, P = 0.052
b
ibution of planetesimals composing the planet and the
where the origins of the planetesimals composing the
mpactor (blue) areconsistent with being sampled from the
tion for the expected typical 20% contribution of planetary
rming impacts (Kolmogorov–Smirnov test probability
here the planet and impactor compositions are inconsistent
(P , 0.05), but become consistent once a large (40%) contribution of material
from the planet is considered. The lower plots in each panel show the results
when different contributions from the planet are assumed (four cases are
shown 10%; 20%; 30% and 40%). The cumulative distribution for these cases as
well as all other planet–impactor pairs in Table 1 can be found in the Methods.
9 A P R I L 2 0 1 5 | V O L 5 2 0 | N A T U R E | 2 1 3
G2015 Macmillan Publishers Limited. All rights reserved
ProtoEarth ≒ Theia?
[Mastrobuono-Battisti et al., Nature, 2015]
netesimals rather than 1000. The final four cases (EEJS 9-
also had 2000 planetesimals but had eJ ¼ 0:07 and eS ¼ 0:08.
ES (‘‘Jupiter and Saturn in RESonance”). Jupiter and Saturn
re placed in their mutual 3:2 mean motion resonance, follow-
directly from simulations of their evolution in the gaseous
ar Nebula (Morbidelli et al., 2007): aJ ¼ 5:43 AU; aS ¼
0 AU; eJ ¼ 0:005, and eS ¼ 0:01, with a mutual inclination
0.2°.
ESECC (‘‘Jupiter and Saturn in RESonance on ECCentric
its”). As for JSRES but with eJ ¼ eS ¼ 0:03.
e EJS and EEJS simulations assume that Jupiter and Saturn
ot undergo any migration. The EEJS simulations are more
onsistent than the EJS simulations, because scattering of
ant planetesimals and embryos tends to decrease the eccen-
es and semimajor axes of Jupiter and Saturn (e.g., Chambers,
Thus, to end up on their current orbits, Jupiter and Saturn
have had to form on more eccentric and slightly more dis-
orbits. The CJS, JSRES and JSRESECC simulations all follow
the Nice model and assume that Jupiter and Saturn’s orbits
ed significantly after their formation, with Saturn migrating
rd and Jupiter inward (Tsiganis et al., 2005). If migration of
ant planets is really associated with the late heavy bom-
ment (Gomes et al., 2005; Strom et al., 2005), then at least
of the migration of Jupiter and Saturn must have occurred
well after the completion of the terrestrial planet formation
ss.
Raymond et al. (2004, 2006), using data for primitive meteorites
from Abe et al. (2000). The ‘‘water mass fraction”, WMF, i.e. the
water content by mass, varies with radial distance r as
WMF ¼
10À5
; r 2AU
10À3
; 2AU r 2:5AU
5%; r 2:5AU
8

:
ð4Þ
This water distribution is imprinted on planetesimals and em-
bryos at the start of each simulation. During accretion the water
Fig. 2. Sample initial conditions for a disk with R $ rÀ3=2
containing 97 planetary
embryos and 1000 planetesimals. Embryos are shown in gray with their sizes
proportional to their mass(1/3)
(but not to scale on the x axis).[Raymond et al., Icarus, 2009]
planets is hnM i ’ 2:0 Æ 0:6, which means that the typical result-
ing system consists of two Earth-sized planets and a smaller
planet. In this model, we obtain hnai ’ 1:8 Æ 0:7. In other words,
one or two planets tend to form outside the initial distribution of
protoplanets. In most runs, these planets are smaller scattered
planets. Thus we obtain a high efficiency of h fai ¼ 0:79 Æ 0:15.
The accretion timescale is hTacci ¼ 1:05 Æ 0:58ð Þ ; 108
yr. These
results are consistent with Agnor et al. (1999), whose initial con-
ditions are the same as the standard model except for Æ1 ¼ 8.
The left and right panels of Figure 3 show the final planets on
the a-M and M–e, i planes for 20 runs. The largest planets tend to
Fig. 2.—Snapshots of the system on the a-e (left) and a-i (right) planes at t ¼ 0, 1
are proportional to the physical sizes of the planets.
KOKUBO, KOMI1134
[Kokubo et al., ApJ, 2006]
そもそも原始地球と衝突天体は同じ材料で形成
初期条件が極めて恣意的（標準シナリオではない）
結果は初期条件を反映した自然な帰結にすぎない

330,
om-
the
metal
s, we
d by
well
thin
orp-
the
or is
the
ossly
sent
very
his is
unar
pac-
µ182W
–10 0 10 20 30 40 50
68815,396
68115,114
Average 68115,114
68815,394
Figure 1 | Values of m182
W of lunar metals separated from KREEP-rich
impact melts analysed by negative thermal ionization mass spectrometry in
this study. The data for 68115,114, 68815,394, and 68815,396 are shown as
circles, diamond, and square respectively; error bars for our analysis show
internal precision of one single measurement, for which the 2 standard
deviations (s.d.) external reproducibility is ,4.5 ppm, as demonstrated by
replicated standard measurements over the two year period. The white-dotted
circle corresponds to the average of the three replicated analyses of 68115,114
nces
W
6 4.6
6 2.6
6 1.7
6 3.8
6 2.5
6 2.9
6 5.1
LETTER RESEARCH
[Touboul et al., Nature, 2015]
of 10.27 6 0.04 is significantly higher than the previously obtained
mean value of 0.09 6 0.10 for lunar metal samples (ref. 10), but for
non-irradiated samples (68115, 68815) there is good agreement
between our data and previous data (Fig. 2). For more strongly irra-
diated samples, however, the e182
W of the metals tends to be slightly
lower10
, resulting in an overall decrease of the mean e182
W inferred
from the lunar metals. Therefore, the higher pre-exposure e182
W of
10.27 6 0.04 determined here reflects not only the better precision of
our measurements, but also that the previous study10
did not fully
quantify neutron capture effects in the metals.
The well-resolved 182
W excess of the Moon compared to the pre-
sent-day BSE (Fig. 2) places important constraints on the occurrence,
mass and timing of the late veneer as well as on the origin of the Moon.
Below we first evaluate the magnitude of any e182
W difference between
the BSE and the Moon induced by the late veneer, and then we assess
whether there is a resolvable 182
W anomaly in the Moon resulting from
the mixing of impactor and proto-Earth material during the giant
impact. The mass and composition of the late veneer is constrained
through absolute and relative HSE abundances and ratios of S, Se and
Te in Earth’s primitive mantle2,19,20
. On this basis, the late veneer
probably had a carbonaceous-chondrite-like composition with a
minor fraction of iron-meteorite-like material16
, corresponding to
,0.35% of Earth’s mass. This composition can explain several geo-
chemical signatures of the Earth’s mantle, including its chondritic Os/
Ir, Pt/Ir and Rh/Ir but suprachondritic Ru/Ir and Pd/Ir, as well as its
187
Os/188
Os value2
and Se–Te systematics19
. Mass balance considera-
–4–3–2–10
0
1
2
ε180Hf
ε182W
68115
12034
14310
14321
62235
14163
KREEP-rich samples
ε182Wpre-exposure
68815
Figure 1 | Plot of e182
W versus e180
Hf determined for KREEP-rich samples.
e182
W has been internally normalized to 186
W/184
W 5 0.92767: elsewhere this
is referred to as e182
W (6/4) (see Methods and Table 1). Solid line is a best-fit
–0.2 0 0.2 0.4 0.6
14321, 1827
(n = 2)
14321, 1856
(n = 6)
68115, 295
(n = 4)
68115, 112
(n = 3)
68115, 112
(n = 4), ref. 10
BCR-2 (n = 22)
AGV-2 (n = 12)
BHVO-2 (n = 3)
68815, 400
(n = 2)
68815, 400
(n = 4), ref. 10
KREEP-rich samples
Terrestrial rock standards
ε182W
Figure 2 | e182
W data of KREEP-rich samplesandterrestrialrock standards.
Top panel, data from this study (filled symbols) and for metal samples from ref.
10 (open symbols). Data points of 68115 and 68815 (this study) were corrected
for a minor contribution from meteoritic contamination at the lunar surface
(Table 1). Error bars indicate external uncertainties derived from the 2 s.d.
obtained for terrestrial rock standards analysed in this study (if N , 4) or 95%
confidence interval of multiple solution replicates of a sample (if N $ 4)
(Extended Data Table 1). Bottom panel, data from terrestrial rock standards.
Top panel, weighted mean (n 5 5) e182
W 5 10.27 6 0.03 (95% confidence
182
[Kruijer et al., Nature, 2015]
わずかな W 同位体の差
G.I. 直後は完全に identical・その後の天体衝突で変化

the deformed
o the Moon.
ocean can be
element parti-
nciples of the
rimental data
ne and ultra-
magma ocean
value of Mg#
ed by a broad
920–80%) or
e of chemical
n the process
ct and partial
modify the composition (e.g., ref. 24). The present
model could also explain the presence of a small
Fe-rich core,25)
if the inﬂuence of reduction at high
proto-Earth proto-Earth
impactor
impactor
magma ocean
vapor jet
(a) (b)
Fig. 4. Schematic drawing of processes of ejection of materials
upon a giant impact. (a) A case where the proto-Earth does not
have a magma ocean. (b) A case where the proto-Earth has a
magma ocean.
fate of ejected materials depends on the ratio h/R and materials
with only for modest value of h/R and velocity will become the
source of the Moon.
m/s)
The temperature
he relation [1] in
mperature at the
e summarized in
olume, q: a non-
(q 9 1 for solids,
[Karato, Proc. Jpn.Acad., 2014]
Giant Impact on Magma Ocean
Magma Ocean 状態の原始地球への Giant Impact
アイデアの提案だけで数値計算等は行われていない

acquire larger late-accreted masses than those in the Grand Tack simu-
lations (see Fig. 1), because the planetesimal population is more dis-
persed in the classical scenario and therefore decays more slowly.
necessary,whereM› representsanEarthmass. Thismas
contributions from the era known as the Late Heavy Bo
Current mass estimates for this very late (approximately
condensation) accretion are21
1023
M›, which we adde
accretedmassesofoursynthetic Earth-like planets, butit
for about 2% of the chondritic mass and therefore doe
important part in our analysis of the correlation.
The chondritic mass can only be identical to the late-a
or to the Late Veneer mass if the Moon-forming event s
the HSEs from Earth’s mantle or was the last episode o
Earth’s core, respectively (as is traditionally assumed). H
conditions are not necessarily true. Consider that som
colliding with Earth after the Moon-forming event mig
differentiated, so that their HSEs were contained in their
of these cores had merged with Earth’s core22
, then the
mass would clearly be larger than the chondritic mass,
would be no HSE record of this fraction of the proje
Earth’s mantle. Additionally, in this case, given thatiron (
HSEs) would have beensimultaneously added to Earth’s m
core, the chondritic mass would be larger than the Late
which is geochemically defined as the mass accreted to E
core has stopped growing.
In fact, as explained in detail in the Methods and in E
Figs3and4,itisunlikelythatmorethan50%ofaprojectile
reaches Earth’s core, otherwise geochemical models cann
the tungsten isotope composition of Earth’s mantle23
. Mor
late-accreted mass, delivered in only a few objects so as
relative HSE abundances of Earth and Moon12
, would hav
able isotopic signature on Earth relative to the Moon24,2
when considering these more complex possibilities, geoc
ence constrains the late-accreted mass probably not to ex
(see Methods).
For these reasons, we first make the usual assumption
accreted mass and the HSE-derived chondritic mass are
Running geometric mean of
all Earth-like planets
Running geometric mean of only Earth-like
planets from Grand Tack simulations
Earth-like planets from
classical simulations
Earth-like planets from
Grand Tack simulations
10 1005020 3015 15070
10–4
0.001
0.01
0.1
1
Relativelateaccretedmass
Time of last giant impact (Myr)
Figure 1 | The late-accreted mass relative to each synthetic Earth-like
planet’s final mass as a function of the time of the last giant impact.
Triangles represent Earth-like planets from the first category: classical
simulations with Jupiter and Saturn near their contemporary orbits7,8
. Circles
[Jacobson et al., Nature, 2014]
地球マントルの HSE 量
を説明するためには、
最後の G.I. は CAI 形成
後 ~100My であるべき
地球マントルの HSE 過剰
→ 地球形成後の late veneer
※ Grand Tack Model を仮定した場合の年代である

~1% come back to strike the Moon within 400
million years (My) (Fig. 1) (8). Because the Moon
only has ~25 ancient (Pre-Nectarian) lunar basins
(16), probably made by the impact of diameter
D 20 km projectiles 4.1 Ga (13, 17), an impact
probability of ~1% implies the GI ejecta popula-
tion could—at best—only contain a few thou-
sand D 20 km bodies (the order of 25/0.01).
Mass balance therefore requires the majority of
GI ejecta to be in a steep size frequency distribu-
tion dominated by D 20 km bodies (8). This
leads us to predict that ~1010
-km-sized projec-
tiles were thrown out of the Earth-Moon system
(fig. S8) (8).
Although GI simulations lack the resolution to
confirm the nature of this steep size frequency
distribution, insights gleaned from numerical
impact experiments on D = 100 km bodies show
that such steep slopes are common outcomes
when the targets are largely left intact (6). An
analog in nature for this may be the formation of
the ~500-km Rheasilvia basin on the D = 530 km
asteroid Vesta; the largest body in Vesta’s family of
fragments is D ~ 8 km, a factor of 70 smaller than
Vesta itself, whereas the exponents of its cumu-
lative power law size distribution are extremely
steep, with –3.7 and –8 observed for D 3 km
and 5 km bodies, respectively (fig. S6) (7, 8, 18).
The shape of this size distribution implies that
much of the mass of GI ejecta was initially in
the form of 0.1 D 20 km fragments rather
than of dust and small debris (8).
A consequence of a steep GI ejecta size fre-
quency distribution is that the fragments should
undergo vigorous collisional evolution with
themselves. Tests using collision evolution codes
(13, 19) indicate that D 1 km bodies rapidly
demolished themselves, enough so to reduce the
population by several orders of magnitude in
mass within 0.1 to 1 My of the GI (fig. S8) (8). This
would lead to a huge dust spike, with small
particles either thrown out of the solar system
via radiation pressure or lost to the Sun via
Poynting-Robertson drag (14, 20). The surviving
Fig. 2. Compilations of impact ages
found within chondritic meteorites.
(A) A representation of 40
Ar-39
Ar
shock degassing ages for 34 ordinary
and enstatite chondrites whose mean
ages are between ~4.32 billion and
4.567 billion years (9–11). All samples
were heavily shocked, shock-melted,
or otherwise had some evidence for
having been part of a large collision. To
create this age-probability distribution,
we separated the sample ages by
parent body (EL, EH, E-melt/Aubrites,
L, LL, and H chondrites) and computed
the sum probability of ages within
each class by adding Gaussian profiles,
with centers and widths corresponding
to the most probable age and 1s errors
of each dated sample (8). The profiles
were then normalized before they
were summed in order to prevent any
single class from dominating the
distribution (fig. S9A). We caution that
systematic errors in measured Ar decay
rates could make these ages slightly
older (8). (B) The age-probability
distribution of U-Pb ages for 24 L, LL,
and H chondrites (table S1) created by
using the same method (fig. S9B). U-Pb
ages 60 My after CAIs are interpreted
to be from impact heating alone, whereas those 60 My after CAIs are an unknown mixture of formation,
metamorphic, and impact ages (26). Both distributions show a feature ~80 to 120 My after CAIs (~4.45
to 4.49 Ga).
Fig. 3. A sample comparison
between our model and ran-
domly derived 40
Ar-39
Ar shock
degassing ages for asteroidal
meteorites. (A) The combined
40
Ar-39
Ar age distribution, in blue,
was created by assuming that
leftover planetesimals and giant
RESEARCH | REPORTS
[Bottke et al., Science, 2015]
,PLANETARYSCIENCEINSTITUTE
By Eric Hand
I
t was the biggest cataclysm the solar
system has ever seen. About 100 million
years after the planets began to take
shape, a Mars-sized body crashed into
the proto-Earth, creating a halo of hot
debris that coalesced into the moon.
There was collateral damage, it turns
out. Scientists now suspect that fragments
of the giant impact were flung all the way to
the fledgling asteroid belt. When this plan-
way to probe that.”
Scientists have long tried to pin down the
age of the moon by analyzing lunar samples
returned from the Apollo missions. But be-
cause of disagreements about the isotope
systems used for dating, the calculated ages
vary from about 30 million years after the
start of the solar system
to 100 million or even
200 million years younger.
A more precise age would
help scientists work out
that 10 billion kilometer-sized bodies would
have been flung out into the solar system—
where many of them could strike asteroids.
Asteroids constantly collide with each
other, but at relatively slow speeds. Some
high-speed projectiles from the giant im-
pact, in contrast, would have struck at
speeds upward of 10 kilometers a second,
melting and transforming asteroid miner-
als into darker, glassy materials. The shock
heating would also have altered a standard
radioactive “clock” used for dating, in which
a radioactive isotope of potassium decays
into argon that remains trapped in the crys-
tal structure of the rock. “If you heat it up
enough, argon moves through the crystal
structures, and you can reset [the clock],”
says study co-author Tim Swindle, director
of the Lunar and Planetary Laboratory at
the University of Arizona in Tucson.
Searching through the literature for me-
teorites that had already been dated, the
team found 34 samples that fit their profile:
those with shock-heating alteration and
ancient argon ages. A significant fraction
of these 34 samples have ages that cluster
around 105 million years after the solar sys-
tem began; that, the team believes, is the
age of the moon-forming impact.
Other scientists are excited about the
method but worried about the small sam-
ple size. The authors used their own judg-
ment to identify meteorites with the right
type of shock heating, and their 34 meteor-
ite samples could hail from as few as five
or six parent asteroid bodies. “Is that really
representative of everything the asteroid
belt saw?” asks Sarah Stewart, a planetary
scientist at the University of California,
Davis. “It’s not a robust
conclusion, but it’s a
robust method.”
Swindle says the new
moon age estimate—a
Moon-forming impact left
scars in distant asteroids
Planetary collision dated through analysis of meteorites
PLANETARY SCIENCE
The giant impact that
formed the moon may
have flung copious debris
into the solar system.
onApril16,2015www.sciencemag.orgDownloadedfrom
(c) Science
Giant Impact Ejecta が高速で小惑星に衝突・年代を
リセットした証拠が隕石に刻まれているはず
※ サンプルが少なすぎる＆モデルがシンプルすぎる

結局
どうしたらいいの？

• 各 Giant Impact モデルの妥当性がわからない 
→ 多様な Giant Impact のより詳細な計算を行う
• 地球と月の化学組成が一致しすぎている？ 
→ 新たな月の石を取得・サンプルバイアスを除く
• 全ての化学データを満たす解が存在しない 
→ いっそ Giant Impact 説から離れて考えてみる
• 月形成年代をどうやって決める？ 
→ 月の酸素同位体比を持つ欠片＠隕石を探す

h the disk in so short a time
e have no evidence yet that
erior is substantially differ-
th’s near surface in oxygen
on directly from Earth.
mplanetary disk that is de-
from Earth, it seems nec-
ve an impact that violates
r-momentum constraint.
cientists have suggested
ities. One is to hit an Earth
dy close to fission with a
projectile. That could be
s impact-triggered fission.
sibility is for the collision
etween two ”sub-Earths,”
each about half an Earth
2 presents hydrodynamic
f three kinds of giant im-
the first—the standard
t of a smaller body collid-
rth—satisfies the angular-
constraint.9
But the other
arios show how the mate-
make the Moon can come
Earth; for them to be can-
must find a way of getting
angular momentum. One
doing so, proposed by
and Sarah Stewart two
is an evection resonance,
he precession rate of the
it matches Earth’s mean
ut the Sun (see box 3). Al-
resonance is well known,
on to account for a loss of
a
b
c
Standard
Fast-spinning
Earth
Sub-Earth
TIME
Figure 2. Hydrodynamic snapshots of giant impacts that might have been. In
each of three cases, a projectile, whose mantle and core are shown in orange and
white, respectively, obliquely hits Earth, whose mantle and core are shown in green
and gray. Earth’s North Pole points out of the page. The aftermath of each collision,
projected onto the equatorial plane, is pictured from left to right, with several hours
elapsing between each snapshot. (a) In the standard scenario,9
the angular momentum
of the impact equals that of the current Earth–Moon system, but the material that
ends up in orbit is mainly projectile orange, a result at odds with the nearly identical
isotopic ratios of oxygen, silicon, tungsten, and titanium observed in the real Earth
and Moon. In the two other cases, (b) a small projectile smashes into a rapidly rotating
planet,10
and (c) two bodies collide, each with half of Earth’s mass.13
In all three cases,
very little metallic iron ends up in orbit, a result borne out by observation. But only in
[Nakajima Stevenson, 2014]
d
e
i-
e
a
a-
proto-Earth proto-Earth
impactor
impactor
magma ocean
vapor jet
(a) (b)
Fig. 4. Schematic drawing of processes of ejection of materials
R
h
A
B
C
Fig. 3. A schematic diagram showing possible paths of materials
ejected at a certain height. Only a fraction of materials goes to
the orbit (shaded region) from which the Moon was formed. The
fate of ejected materials depends on the ratio h/R and materials
with only for modest value of h/R and velocity will become the
source of the Moon.
2
re
n
he
n
n-
s,
terrestrial magma ocean origin of the Moon 101
[Karato, 2014]
2.3. Initial Conditions
We follow Canup Asphaug (2001) and Canup (2004) for the
orbital parameters of the impactor for which the most massive
satellite is expected. The masses of the proto-Earth and the im-
pactor are assumed to be 1.0 and 0:2 MÈ, where MÈ is the Earth
mass. The radii of the proto-Earth and protoplanet are rE ¼ 1:0
and 0:64rE, respectively. Note that no significant differences in
the results for smaller impactors (e.g., 0:1 MÈ) were found in our
simulations. The initial orbits of the impactor are assumed to
be parabolic, and the angular momentum is 0.86Lgraz, where Lgraz
is the angular momentum for a grazing collision (Canup
Asphaug 2001). Initially, the impactor is located at 4:0rE from
the proto-Earth.
3. RESULTS
3.1. Disk Evolution and the Predicted Lunar Mass
Figure 1 shows a typical time evolution of the giant impact
with EOS-1 (model A). This model corresponds to the ‘‘late’’
impact model in Canup Asphaug (2001). After the first impact
(t ’ 1 hr), the disrupted impactor is reaccumulated to form a
clump at t ’ 3 hr, which finally collides with the proto-Earth at
t ’ 6 hr. During the second impact, the impactor is destroyed,
and a dense part of the remnant spirals onto the proto-Earth
(t ’ 10 hr), and a circumterrestrial debris disk is formed around
t ’ 18 hr. Note that many strong spiral shocks are generated in
this process as seen in the density map (Fig. 2) and azimuthal
density profile (Fig. 3).
Fig. 1.—Giant impact simulation with EOS-1, which represents a state in which most of the impactor mass is vaporized. Left, face-on views of the system; right, edge-
on views. The numbers in the upper right corners of the panels show the time in units of hours. The color represents log-scaled density (the units are 0 ¼ 12:6 g cmÀ3
).
Fig. 2.—Snapshot of the density field of model A at t ¼ 12:3 hr. Strong
spiral shocks in the debris are resolved.
WADA, KOKUBO, MAKINO1182 Vol. 638
[Wada et al., 2005]
[Pahlevan Stevenson, 2007]
ratio of 9:1 and a total mass of 1.05 ME (Canup, 2004). Both the impactor and the
target are assumed to be differentiated bodies with a 30 wt% iron core and a
70 wt% silicate mantle. In these low-velocity collisions, the impactor loses kinetic
energy during its grazing collision with the target, before it is dispersed into a disk
around the target. The resulting proto-lunar disk is therefore mainly composed of
impactor material. We will call this the ‘‘canonical scenario’’.
When the assumption that no mass is lost is dropped however, the collisional
angular momentum is no longer tightly constrained, as lost mass also carries away
angular momentum. The total collisional angular momentum can therefore be con-
siderably higher than the final angular momentum in the Earth–Moon system. With
this additional degree of freedom, new regions in the collision parameter space be-
come feasible.
Apart from the disk mass, another interesting quantity is the origin of the mate-
rial which ends up in the proto-lunar disk, especially for the silicate part.
We call the fraction of target silicate to total silicate material in the disk
fT ¼ ðMsilc
targ=Msilc
tot Þdisk ð1Þ
where Msilc
targ and Msilc
tot denote the mass of the silicate fraction of the disk derived from
the target, and the total disk mass, respectively. If we define a similar target-derived
silicate fraction for the post-impact Earth, we can deduce a deviation factor
dfT ¼ Msilc
targ
.
Msilc
tot

disk
.
Msilc
targ
.
Msilc
tot

post-impact Earth
À 1 ð2Þ
which directly reflects the compositional similarity between the silicate part of the
proto-lunar disk and the silicate part of the post-impact Earth.
Isotopic measurements show (Wiechert et al., 2001; Zhang et al., 2012) a strong
isotopic similarity between the silicate fractions of today’s Moon and Earth. Assum-
ing isotopic heterogeneity of the pre-impact bodies, this suggests that either the
material of the bodies mixed during the collision or re-equilibrated their isotopic
signatures after the collision. Either scenario is represented by a dfT $ 0 between to-
day’s Earth and the Moon. The value of dfT right after the impact thus serves as a
starting point, from which a re-equilibration mechanism leads to todays value of
dfT $ 0.
In a typical simulation of the canonical scenario, only about 30% of the disk
material and 90% of the material of the post-impact Earth is derived from the target
(the proto-Earth) respectively (Canup, 2004), yielding a dfT of À67%.
4. Results
The new class of collisions presented here falls into the broad regime of slow
hit-and-run collisions (Asphaug et al., 2006) with impact velocities between 1.20
and 1.40 vesc. Hit-and-run occurs up to half the time for collisions with impact
velocities in this range. Because of the higher impact velocities in this type of col-
lisions, substantial mass and angular momentum can be lost in the process. There-
fore, the initial angular momentum is less constrained and can be considerably
higher than the post-impact 1.0–1.1 LE–M angular momentum of the Earth–Moon-
system. The higher impact velocities used in these simulations are also encouraged
by more recent models of terrestrial planet formation (O’Brien et al., 2006). In hit-
and-run collisions, a significant part of the impactor escapes, so that the disk frac-
tion is enriched in target-derived materials compared to the canonical case. Fig. 1a
shows four consecutive snapshots of such a hit-and-run collision. While the overall
characteristics of the collision resemble the canonical scenario, here a considerable
part of the impactor is ejected.
colors. In the canonical scenario, the impactor grazes around the target’s mantle
and is deformed. Due to the low impact velocity, material supposed to end up in or-
bit around the Earth must not be decelerated too strongly in order to retain enough
velocity to stay in orbit. This is only achieved for the parts of the impactor mantle
most distant to the point of impact, and some minor part of the target’s mantle. But
if impact velocity is increased from 1.00 (cA08) to 1.30 vesc (cC01), parts from dee-
per within the target mantle receive the right amount of energy for orbit insertion,
while the outer regions of the target mantle, retain too much velocity and leave the
system, thereby removing mass and angular momentum. Both processes work to-
wards increasing the target material fraction in the proto-lunar disk. While in run
cB04 only $10% of the initial angular momentum is removed, $45% are removed
in run cC06.
We have found that collisions with an impact angle of 30–40° and impact veloc-
ities of 1.2–1.3 vesc are successful in putting significant amounts of target-derived
material into orbit, when using differentiated impactors with a chondritic iron/sil-
icates ratio (30 wt% Fe, 70 wt% silicates) and masses between 0.15 and 0.20 ME.
Some runs in this regime show an iron excess of 5 wt% in the proto-lunar disk
and are rejected, as in previous work (Canup, 2004). While none of the runs done
so far provide a ‘‘perfect match’’ in terms of the constraints from the actual
Earth–Moon-system, several simulations come close to that. The best runs coming
the material. Dark and light blue indicate target and impactor iron; Red and orange
show corresponding silicate material. The far right shows the situation at the time
of impact. At 0.52 h, it can be seen how the impactor ploughs deep through the
targets mantle and pushes considerable amount of target material into orbit. A
spiral arm of material forms and gravitationally collapses into fragments. The outer
portions of the arm mainly consist of impactor silicates and escapes due to having
retained a velocity well above escape velocity. The silicate fragments further inward
are stronger decelerated and enter eccentric orbits around the target. The
impactor’s iron core also looses much of its angular momentum to the outer parts
of the spiral arm and re-impacts the proto-Earth. (For interpretation of the
references to color in this figure legend, the reader is referred to the web version of
this article.)
[Reufer et al., 2012]
T. SASAKI AND Y. ABE: IMPERFECT EQUILIBRATION OF HF-W SYSTEM 10
[Sasaki Abe, 2007]

o
i T
k ab
W WPH
i!!
(c) Tetsuya Kawase
New Perspectives by WPH

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