Planet formation: Compositional mixing and lunar compositional anomalies

ICARUS

27, 553-559

(1976)

Planet

Formation : Compositional Mixing Lunar Compositional Anomalies WILLIAM

and

K. HARTMANN’

Planetary Science Institute, 2030 East Speedway, Received August 4, 1975

Tucson, Arizona 85719

; revised September 3, 1975

Significant fractions of each planet’s late-accreted mass originated not at its own distance from the Sun, but from a neighboring planet’s orbit, according to results that follow from calculations by Wetherill(l975). “Late-accreted” refers to a loosely defined period after planets acquired most of their present mass. In an idealized model, Mercury, Venus, Earth, and Mars received 47,45, 37, and 52% of their late-accreted mass from planetesimals formed closer to other planets. Resulting compositional anomalies in outer parts of early planets could be significant ; atmospheric tests of Lewis’s predicted S deficiency on Venus may be inconclusive. The Moon’s orbit around Earth puts it in a special category : sorting occurs between Moon-impacting and Earth-impacting material according to approach velocity. In the above model, the moon receives 60% of its late-accreted mass from planetesimals formed near Venus’ orbit. Distant planetesimals could be perturbed into the Earth-Moon system and cause major changes in the Moon’s composition with only minor effect on Earth. The entire lunar bulk composition anomaly could be explained by plausible reservoirs of distant low-density material.

INTRODUCTION Investigators trying to account for differences in composition between Moon and Earth have postulated, in some instances, that the Moon’s bulk or surface material formed at a different distance from the Sun than the Earth’s material. In several cases they have assumed that this required formation of the Moon at a distant location and capturing it by Earth in some (unlikely?) process. For example, the high content of refractories found in surface materials could be attributed to a hightemperature nebular origin of the material closer to the Sun (Cameron, 1973) ; Cameron (1973) and Bailey (1969) proposed formation of the Moon near Mercury and its later capture by Earth. Others, seeking to account for the low bulk iron content, have proposed lunar origins outside Earth’s orbit. One purpose of this paper is to point out 1Revision completed while Visiting Professor at Institute for Astronomy and Department of Physics and Astronomy, University of Hawaii. Copyright 0 1976 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain

that appreciable quantities of materia,l formed in distant parts of the solar system arrived at the Moon, probably concentrate in the surface layers, and reached different concentrations than on Earth. Thus, a distant origin may not be required. Large amounts of matter originating near Venus accrete onto Moon and Earth, with the M oon getting a much higher share. As early as 1970, Ganapathy et al. (1970) described t)he sorting of interplanetary d e b ris onto Moon and Earth due to different cross sections, and Singer and B an d ermann (1970) improved the treatment, noting that the ratio of Earth’s massaccretion rate to lunar accretion rate differs for materials in different orbits from 13 at an approach velocity near 30 km/set, to 130 at about 3km/sec, and to 270 near O-l km/ sec. No quantitative data were available to show what compositional effecm this would cause. Speculat,ions that different impact velocities on the Moon would create volatile depletions were rejected by Ganapathy and Anders (1974). Whipple (1973) described a sorting mechanism involving gas 553

554

WlLLIAM

K. HARTMANN

How around the Moon, aerodynamically different’ late-accreted materials added t,o inhibit’ing capture of certain materials of planetary surface layers. The conversion is made in a series of distant origin, but this is difficult to evaluat)e quantitatively, and probably applies seeps as follows. Wetherill’s results (his primarily in the early stages when the Table 1) are first multiplied by the area of each planet to give t’he relative number of nebular gas was import,ant in controlling impact’s on each planet for a given st#arting dust mot8ion, and when dust was more imorbit. The initial orbits selected are portantS in terms of t,otal mass (being \\‘etherill’s orbits 6 t’hrough !I, circular %generated by collisions among small bodies that were cieplet’ed as time passed). Thus, heliocent,ric orbits, one lying near each terrestrial planet’. That is, the solar system tlisc*usnions of velocity sorting and compositional effects have been primarily in t’he is pictured as consisting of the planets and four distinct groups of planetesimats. The vein of hypothesizing effect’s that, l~icqht accotmt for some observed lunar compoxinext’ step is to include the bodies that escape from the inner solar system, casit!. tional properties, wit,houtj establishing that calculated from t’he tlat,a giveir 1)~ (listant material Ic*o/tldarrive. It will be sho\vn here that Wetherill’s \l’etherill. B.y summing t,he bodies st,riking ( 1975) ralculation of gruvita,tional dispereach t’arget’ planet, plus t’hose that cscal)~~. the total number of bodies in each starting sal of’ pl;tnet~esimals from different’ orbits orbit is accountetl for. Thus the fraction of ii.1 1 ou’ quantitative proof that current each nlodets of plaiietcsimat evolut’ion ~/~~;~p.r;+j-initial bodies in each orbit’ striking t’arget planet. can be calculated. These IYIrrt~ con~posit~ional mixing of niatJeriaIs suits are shown in Table 1. from rcmott~ sources onto each of the In order to tabulat,e the iota1 urrcouut l)tanc~t~s, wit,11 different fractions striking (relative mass) of rnat’eriat striking t ht. Aloon and Earth. The only assumption in Earth or any other planet wr must havtb al)pl\G~g Wet heritl’s results to t’lie Earth sonle basis for est,imating t,lif, ainount of hloon systf>m is t,liat the Moon or prot ornat8erial in each starting orbit. To t’ake the moon be in orbit’ around t,he Earth ; simplest8 case, let us assume that) this mass (:anapatll,v and Anders (I !)74) give eviis a small fixed percentage of the total mass dence from votat i te abuiidances that’ this of each planet. (It is viewed as t,he last I ‘3,. must have been ttuc by the time the &!oon say. of the material left from the formation ~~~;~~lietl aboltt I /S its present mass. of each planet .) Multiplying each entry in Tabte 1 h?: it fixccl proportion of the mass of t)he imtlal parent, planet, and normalizing all total impact masses t,o the total for t)he Moon gives \\‘ethcrill ( 1975) considers statistical the relative mass hit’ting each planet (Tabtc samples of particles start,ing in nine tlif11). The same data RlT renormalizcd in ferent orbits in the solar system a,nd t’abuTable TIl to give the relative percentages tat-es their tinal impact, destinat!ions. For of material added to each planet. Looking each init,ial orbit’, he t’abulates the rdnfd~w do\vu the vertical columns, one hinds as ~~~.~rrr~brr of impacts per syua,re km on each expected that’ the maximum-mass source terrestrial planet’ and the Noon. Let us striking each planet is the family of planediscuss a lat’c point, in planetary accretion. trsimals bhat began near that planet. For when terrestrial planets had rea,ched most the planets, Mercury, Venus, Earth, and of t(heir present mass but’ a few percent of Mars. t)he percentages of ma,ss originatiup those masses were st’ill present, as planetenearby are, respectively, X4? 4%. 63, and 4X. simals; to these planetesimals the system In the case of the Moon, however, onl) looked dynamically as it does now, so that 37%) of the mass comes from t>he material M’etherill’s calculations are relevant. If one initially near the orbit of the Earth-Moon converts Wetherill’s relative numbers of system. Sixty percent comes from the orbit impacts to total masses striking each of Venus! Physically this can be understood planet, one obtains data on the sources of

555

COMPOSITIONALMIXINGAMONGPLANETS TABLE

I

FRACTION OF INITIAL “X-CROSSING” BODIES STRIKING TARGET PLANETS

Source Orbit X

Perihelion

Aphelion

(AU)

(AU)

~ Mercury

crossing Venus-

0.33

0.41

1.00

crossing Earth-crossing Mars-crossing

0.67 0.98 1.27

0.82 0.99 1.89

0.034 0.017 0.015

Target Planet Venus Eart’h

Moon

Mars

Ejected

Total

Mercury0.48 0.31 0.23

TABLE

--

-

0.016 0.008 0.007

0.30 0.45 0.28

-

0.011 0.031 0.33

1.00

0.16 0.19 0.14

1.00 1.00 1.00

II

RELATIVE MASS STRIKING TARGET PLAKETS FROM EACH SOURCE (NORMALIZED TO MOON) Target Planet Source Orbit

Venus

Mercury

Earth

Moon

Mars

n

Ejected (I

(I

Mercury-crossing

2.5

0

a

Venus-crossing Earth-crossing ,Mars-crossing

1.3 0.78 0.075

18 14 1.1

11 21 1.4

Total (all sources)

4.7

33

33

1.00

3.5

15

.Percentages (distribution of total terrestrial-planet inventory of planetesimals; total = 100°/;,)

5%

37%

37%

1%

4%

16%

0.60 0.37 0.035

0.42 1.4 1.7

6.0 8.7 0.69

a Negligible. TABLE PERCENTAGE

OF MASS

III SOUROE (NORMALIZED FOR

STRIKING TARGET PLANETS FROM EACH PLANET-TABLEIIRECALCULATED)~

EACH

Target Planet Source Orbit ---

Mercury

Venus

Earth

Moon

Mars

Mercury-crossing

53 -

b

*

b

b

Venus-crossing

28

-55

33

60

12

39

17

42

-63

37

40

57

2

3

4

3

-48

4

100%

100%

100%

100%

100%

100%

Ejected

-~

Earth-crossing Mars-crossing

u Underlined numbers mark accretion of material formed nearby. b Negligible.

b

556

WILLIAM

K. HARTMANN

as follows. The material starting in a heliocentric orbit near a planet approaches the planet’ wit,h very slow velocity and consequently the capture cross-section of the planet is large. Because of the Earth’s large mass its capture cross-section from such bodies is much greater in comparison to the Moon’s than the ratio of their geometric cross-sections. Thus t,he Earth gets much more hhan its “fair share”. However among the large number of plnnetesimals scattered outward by Venus a different situaCon exists. They approach t’he Earbh-~ Moon system with much higher velocities and therefore the capture cross-sections are more nearly in proportion to the geometric cross-sections of the Earth and Jloon. Therefore, the Moon gets much tnor’c nearly its “fair share” of t’he al)proaching planetesimals from Venus.’ According to Wet~herill’s calculations this effects is so great that, most, of the Moon’s mass from such late planet’esimals would have originated near V~I~IIS.

Is this result really representative of an> actual period in the history of the solar system ! Because planets’ accretion rates iucrease rapidly with mass. the more rnassive ljlanets might be expected to use up their nearby material first. as in models b? Hakmann and Davis (1!)75). in which case the material from Venus would be slightI) mo~‘c abundant and t’he effect on the Moon great’er than calculated here. But the uncac>rtaintyin such st,atements is indicated I)>,other authors’ models, in which t)he four planets, in order from the Sun, have different accretion times (in millions of Jears) of about 8, 1. 11, ~tnrl 325 (according to Safronov, 1972, 1). I I I), or li!), 55. 156. nntl

2600(!)

(according to Weidenschilling. In these models the Venus-planetesimals would be depleted first, and the effect on the Moon would be minimized, while Mars-planetesimals would be the last to impact the planets during the early accretion period. In reality the initial conditions drawn from Wetherill’s calculations are probably not u~~oElyrealistic for any given period of solar system growth. Only if the scattering had begun and continued with the planets near their present masses would Wetherill’s results be directly applicable. But the sca,ttering must have begun when the various planets’ gravitational cross sections began to exceed t,heir geomet’ric cross sections. at less than present planetary masses. Thus, the initial dynamics would have been somewhat different when t’he Venus planetesimals began reaching t’he Earth-Moon system. [The Eart,h-Moon system’s d\.namics would not have been much different. because if t’he Moon and Earth originated t80get’her, the Moon’s tidal motion would havr moved it well outside thtl Eart,h’s gravit’at’ional cross section in a fe\\ thousand years, and half way to its present position in 5()ru.~~.1 Thus where we havtb used t,lie term “late-accret’ed mass,” it should be understood to refer to ma.ss iucareted sometime between the onset ot gravitational scattering and the time tllch planet reached its present mass. If Venus and Earth grew at8the same time. \\-it11 similar masses. one can imagine an writ wheu large reservoirs of heliocentric circularorbiting planetesimals b tilled with planet~esimals. Those nearest planets’ orbits would have been swept) out fit&. and those between planets’ orbits perturbed later. Thus, t,he latest-accreting material would have shown less distinction between Venus- and Earth-planetesimals. But’ t’he implicaGon remains that the Moon 1975).

557

COMPOSITIONALMIXINGAMONGPLANETS

drew prejudicially from more distant planetesimals than the Earth did, at some stage, and that all planets received significant amounts of late mass formed in other regions. Thus, according t’o Table II, to the extent that Venus planetesimals are distinguishable, and Wetherill’s model is applicable, Earth received about 33% of its late accretion from the Venus population, and the Moon would have received more-between 33% and 60%. Cert,ain isotopic or elemental anomalies in t,he lunar surface layers are likely to be accounted for by this mechanism. However, it is not out of the question that the entire bulk composition difference between Earth and Moon could be explained in this ‘way, because a planetesimal input negligibly altering h’arth could substantially change the Moon’s bulk chemistry. For example, if the Moon and Earth had accreted initially from Earth-like material of uncompressed density 4.0, with a late addition of distant material of 2.2 (lowest of recorded meteor&es), then about 27% of the Moons mass would have to consist of this distant material. According to the above discussion, Earth would receive about 25 times this much material, or about 0.08 Earth-masses. This is a relatively small input into Earth, only slightly changing Earth’s density. If all of this material were supposed to have originated near Venus, (to take an unlikely but quantitative example), it would require a reservoir of about 0.25 Earth-masses near Venus at a time when Venus was about 85’/, complete. This is derived from Table I, whereby it can be seen that, 0.48(0.25)M, = O.l5M, would be swept up by Venus, completing that planet, while another 0.32(0.25)M, = 0.08 M, would be deflected to the Earth-Moon system, reducing the Moon’s densitv. In other words, plausibly small reservoirs of distant, low-density material might supply enough material to explain the Moon’s aberrant composition relative to Earth. The reservoir of Jupiter planetesimals, not included here, might be such a source; additional Wetherill-type calculations are urgently needed for planetesimals near the other planets. Two additional observations are con20

sistent with a late addition of distant lowdensity material to the Moon. First’, the greater thickness of the Moon’s far side crust could be explained. Bandermann (1971) notes that, the accretion rates are greater on t,he far side. A thicker low-density crust would arise there, with the center of mass displaced toward Earth from the center of figure, as is actually observed. Second, Morgan et al. (1974) have attempted to reconstruct the chemist,ry of the large (D - 100km) planetesimals that formed basins, and find that they were different in composition from either Earth or Moon? with some tendency toward a higher volatile content than the Moon (though being chondrite-like and having siderophiles). Late material added to the Earth in such a scenario has presumably been mixed in the Earth’s crust and mantle by churning associated with erosion and plate te&onics. However, other terrestrial planets exhibit’ more craters, indicating much less churning. Hence, the late-added planetesimal materials of nonlocal origin may be still distributed in the outermost layers, though they would be diluted in megaregoliths consisting mostly of ejecta from still earlier-accreted material of the planet. A referee of this paper pointed out an example, relating to the quest,ion of sulfur on Venus and Earth. Condensation models assuming local accretion suggest a scarcity of S on Venus, relative to Earth. Lewis (1972) suggests “sulfur is probably virtually absent (on Venus).” But Table III suggests that nearly half of the late-added Venus crust, could have come from Earth’s vicinity, and a third of Earth’s crust from the Venus vicinity. Tests of Venus’s atmospheric sulphur may be ambiguous in meaning. CONCLUSIONS In conclusion, it is found that (1) large fractions (nearly half) of the last masses added to bhe terrestrial planets in their later stages of growth could have originated in planetesimals formed nearer other planets’ orbits, affecting the composition of their init,ial outer layers. (2) The Moon could have the largest, resulting anomaly in

558

WILLIAM

K. HARTMANN

composibion. During some stage of its late growt’h, more than 33% of its accreting mass, and up to BOO/ in the most favorable circumstances, could have originated neal Venus. (3) Therefore, even if the Moon . . orlgmated in orbit around Earth, the composition of meteoritic material added to its outer layers differed from meteoritic mat’erial added ot Eart,h’s primitive crust). The resulting composition anomalies might be most evident in the lunar uplands, which bear evidence of the lat,e accretionary bombardment by planet’esimals. (4) Small reservoirs of planetesimals near other planets could substantially modiarth by a major impact (Hartmatln and IY?!j), or by certain ot,her suggested Davis. tnearls, was its initial clrornistry already skewed from terrestrial toward observed Iuna,r chomist,ry? (:onld low-density. low-\.olat,ilr planctesirnals llavo appeared it1 other parts of tile solar system f-luring it late st,age of inliolno~f,rleolls ancretioti of planets? Could lo\\,-irori silicatcbs (such as may exist in Jupiter satellit,es) Ilavc formed Ilear Jupiter, been scat,trrrd into thv inner solar system, been stripped of ices while orbiting tlrc Sun as comets, and been added t,o the Moon and other planets as low-density silicates (preceding and including the basinforlning planet,esimwls of Morgan et al. ?). (.“odd Iligll-energy impacts have produced recondc~nsed refractory-rich, volatile-poor plalietesimals Noah (*f*rtain ot,hct pla.net8. lat,ctr scw.t~t,c~rcrJ t)oward tllc-

Earth/Moon system? Answers are uncertain and the uncertainty makes chemical rnodellin,rr difficult. Certainly some chemical changes occurred in the Moon but it is unclear if they were at the level of trace element anomalies or major bulk chemistry changes. Nonetheless, three types of calculation arc’ clearly needed as a next step. First, Wothcrill’s calculat,ions should be expanded by including planetasimals in different orbits near eacll planet; thfb calculations cluoted Ilerc, included only OIIP orbit, near each plan&. Scoond. planetesirnals iu orbits Ilear Jupiter (and otller out)er planets) must be treated in paralk~l fashion, since such tables are not available ill current lit)erature (although .Jupiter. Urarrlls, and other sources have been considered by various authors). Third, all calculations neetl to be redone for evolving plan&s, Lvith Mrrcurv. Venus. etc., at l/4, l/2. 3/4, etc.. times ttAr present masses, to show how planetary masses and compositions evolved together. ‘I’0 my knowlodgc, such calculations are not now undc11 way. They might clarify the cons~~lu~~~~cosof a simultaneous rnixing of refractory-ricall atlltl \.olatile-rich materials from inner and orlt,rv parts of t)he solar system. I acknowledge llelpful discussions with Michael Drako. ( ieorge Wetherill. and Laurel Wilkenirlg.

ACKNOWLET)GMENTS 1 thank Drs. L. W. Bandermann, (1. K. Chapman, D. H. Davis, and M. .J. Price for hrblpful discussions, and t\\-o referees for helful cornmenfs utilized in the final draft.

REFERENCES BAILEY, J M. (1969). The Moon may be a former planat. Sature 223, 251. t3ANDERMANN. 1,. W. (1971). (hi a paper hy D. B. Beard. “Cumulative interplanetary dust concentration on the lunar surface.” Moder?r Geology 3, 53. (‘,~ME~oN. A. ($. W. (1973). Properties of the solal nebula and t,tre origin of the Moon. Aloon 7. 377. (~ANAPATHY, Ii., AND ANDERS, E. (1974). Bulk cornpositions of the Moon and Earth, estimated from meteorites, Ceochim. Cosmochim~. Acta, suppl. 5, 1181. HARTMANN, W. K., AND DAVIS, .D. It. (1975). Satellite-sized planetesimals and Irlnar origin. Icapua 24, 504 515. LEWIS. JOHN S. (1972). Metal/silicate fractionwtiorl ill thn solar syst,em. Earth Plan. Sci. I&t. 15. 286.

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MORC:AN,
AMONG

PLANETS

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SINGER, 8. F., AND BANDERMANN, L. W. (1970). Where was the Moon formed? Science 170,438. WEIDENSCHILLING, S. J. (1976). Accretion of the terrestrial planets. II. Icarus 27, 161l170. WETHERILL, G. W. (1975). Late heavy bombardment of the Moon and terrestrial planets. Proc. Sixth Lunar Sci. Conf., in press. WHIPPLE, F. L. (1973). On the growth of the Earth-Moon system. Bull. Am. Astron. Sot. 5, 292 (abstract).