origin of terrestrial planets and-the earth-moon...

Origin of Terrestrial Planetsand-the Earth-Moon System

Increasingily eoSristicaH eomf#how the four sdid dat@ could hcoHieiona and aceretiqr, One liate,Earth is the liksly ongin of tha

Robin M. Canup

ff ccording to current theories, the overall architecture ofAour solar system was established more than 4 billionyears ago through an era ofplanet formation lasting from10 million to several hundred millions of years. Before webegan learning about other planetary systems, it was nat-ural to assume that our own was quite representative. Butin the past decade, the discovery of about 100 planetarysystems around other stars has challenged this view; thesesystems display a broad variation in structure and mostdo not closely resemble oril own (see the article by TFistanGuillot on page 63).1

Observational cdpabilities currently are limited to thedetection of giant, Jupiter-sized planets around otherstars, so that we are uncertain ofthe existence and distri-bution of smaller Earth-like planets in such systems. Thusplanetary scientists rely on our own solar system as thecase study for understanding the formation ofterrestrial,solid planets and their satellites-such as Earth and theMoon. But our solar system as a whole may not be partic-ularly characteristic, and recent observations suggest thatthe process of planet formation is ene from which manypotential outcomes may emerge. Theoretical models andcomputer simulations that strive to recreate the planetaryformation process must therefore be able to account forboth the primary characteristics ofour system and the ap-parent diversity of extrasolar systems.

The planetesimal hypothesisUnderstanding of stellar formation processes and obser-vations of other young stars suggest that the early SolarSystem consisted of the newly formed Sun and an orbitingdisk of gas and dust (see figure 1). If one assumes it had aroughly solar composition, such a disk-also referred to asthe solar nebula-would contain a mass in hydrogen gasabout l-00 times that contained in solid particles. Isotopicdating of the oldest known meteorites indicates thatmacroscopic solids began to form within the gas-rich solarnebula about 4.56 billion years ago. Observations of otherstellar systems suggest that the Sun's hydrogen-rich neb-ula would have been lost-possibly due to a strong solar

Robin Canup ([email protected]) is assistaftt dir&,tor ofthe departrnent of space studies in the instrumentation andspace research division at the Southwest Research lnstitute.ihe is based in Boutder, Colorado.

56 April 2004 Physics Today

In this context, how did our solarsystem's large inner objects-MercuryVenus, Earth, the Moon, and Mars-originate? The so-called planetesimal

hypothesis, which in its modern form has been developedover the past 40 years, proposes that solid planets growfrom initially small particles in the protoplanetary diskthrough collisional accumulation, or accretion. As solid ob-jects orbit the Sun, mutual gravitational interactions andinteractions with the gaseous nebula cause their ellipticalorbits to cross. which leads to collisions. The outcome of agiven collision depends primarily on the ratio of the im-pact speed, ui-o, to the gravitational escape velocity ofthecouiding onj"ti., ,""", *Ir"re u"n: JE6r+i)/@llE),G is Newton's gravitational constant, andm.randRr are theobject masses and radii. The impact speed is a function ofboth u"*and the relative velocity u"", between the objects atlarge separation with u2,.o = u2""" + u2*,, so that u-o is al-ways greater than or equdl to u""".

For u*o ) u""", collisions result in rebound, erosion, oreven fragrirentation, while for lower-impact velocities,with u*" - u""", €nerg€tically dissipative collisions lead to .-the forriration of gravitationally bound aggregates. Re-peated collisions with low impact velocities thus allow forthe accretional growth oflarger and larger objects.

Terrestrial planet accretion in our solar system is typ-ically described in three stages: growth of approximatelykilometer-sized "planetesimals" from dust and small par-ticlps; accretion of planetesimals into planetary embryoscontaining around t-LUVo of the Earth's mass Mr; and thecollision of tens to hundreds of planetary embryos to yieldthe frnal four terrestrial planets.

Ttre processes that control growth during the frrststage are the least well understood. In general, the inter-action of small, subkilometer-sized particles with the neb-ular gas causes their mutual impact velocities to greatlyexceed their gravitational escape velocities, so that growthduring two-body collisions must instead rely on either non-gravitational surface sticking forces (such as van derWaals or electrostatic forces) between the colliding parti-cles or the collective gravitational influence ofneighboringparticles. Such collective effects could become important ifdynamical mechanisms exist that can concentrate solidsin a region ofthe disk; in that case, an enhanced local spa-tial density ofparticles can allow groups ofparticles to col-lapse under their self-gravity to form larger objects.Whether kilometer-sized planetesimals were formed bysticking and binary collisions or by gravitational instabil-ity-or both-is a subject of active research.2

wind or photoevaporation-afterabout 1-10 million years. At that time,the protoplanetary disk transitionedfrom one whose mass was predomi-nantly gas to one composed solely ofsolid objects orbiting the Sun.

@ 2004 Amerimn Institute of Physics, 5-0031-9228-0404-030-X

Planetesimals to planetary embryosOnce planetesimals become large enough (approximatelykilometer-sized) for their dynamics and collisional growthto be controlled by gravitational interactions, a much bet-ter understanding exists ofhow growth proceeds. That un-derstanding is due in large part to improvements in com-putational modeling techniques.

fiig rate of accretion is primarily controlled by therate of,'collisions among orbiting planetesimals. Consideran ann-ulus in the protoplanetary disk centered at some or-bital radius a with volume V: Ah, where A is the mid-plane area and h is the disk thickness. Ifthe annulus con-tains N small planetesimals with some characteristicrandom velocity u"* relative to that of a circular orbit atradius a, then a larger embedded object of radius R willaccumulate the small particles at an approximate rate

,, xrlnff\p- ,( ,,2 \Coll ision rate _

"ro,, \1.:-- /- e = nO(oR \lf *g l, tf fv t ' l .- u"*,r

where F* : I + (u"n/u,^)2 is the gravitational enhancementto the collisional cross section due to two-body scattering,n : NlA is the number of particles per surface area in thedisk, and h = v,*/O, with O the Keplerian orbital angularvelocity. Equation t has its roots in kinetic theory and isknown as the "particle-in-a-box" collision rate. In the caseof an orbiting "box" of planetesimals, the random particlevelocities arise from the planetesimals' orbital eccentrici-ties and inclinations and are analogous to the random ther-mal velocities of gas molecules confined to some volume. Asthis simple expression shows, the rate of collisions, andtherefore ofaccretional growth, depends on the local Kep-lerian orbital velocity (which increases with decreasing dii-tance from the Sun, so that regions closer to the Sun gen-erally accrete more rapidly), the number density ofplanetesimals, and their sizes and relative velocities.

The mass and velocity distributions of a swarm ofplanetesimals are themselves d5mamically coupled. Gravi-

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the system toward a state of equipartition of kinetic en-erf_f, _witfr smalle_r particles having typically higher u.*and the largest objects having the lowest. This effect isknown as dynamical friction:Aswarrn ofbackground smallparticles acts to damp the velocities ofthe largest objects.From equation 1, ifthe largest objects in a given region ofthe disk also have the lowest velocities; then theii colli-sional cross sections will be signifrcantly enhanced, com-pared to those ofsmaller objects, due to the gravitationalfocusing facto4 F". For large objects, u""" will be large com-pared to u.*, which will be controlled by the smaller plan-etesimals that still contain most of the system's mass. Thelargest objects thus grow the fastest, and a single objecttypically ends up "running awa/ with the great majorityof the total available mass in its annular region in the disk.Through this so-called runaway growth, approximatelylunar-sized objects, containing roughly LVo of M,, grow inthe inner Solar System in as little as 105 years.

Once a large object has consumed most of the mass inits annulus, growth slows, primarily due to the reducedamount of locally available material and planetesimal ve-

- locities that have increased to around u"* ofthe largest em-bryo. Figure 2 shows the predicted aislrilutlon of plan-etesimal masses in a region extending between the currentorbits of Mercury and Mars from a 106-year accretion sim-ulation performed by Stuart Weidenschilling (of the Plan-etary Science Institute) and colleagues.3 After a millionyears, 22 large planetary embryos have formed in theinner Solar System and contain g\Vo ofthe total mass. Theembryos are radially well separated on nearly circular,coplanar orbits, with each containing a mass of at least10269 (for comparison, M, = 6 x 1027 g).

Late-sfage terrestrial accretionGiven our four terrestrial planets, the state shown in frg-ure 2 with tens of "miniplanets" must have been a transi-tory one. The gaseous component ofthe solar nebula is ex-pected to have dispersed after 106-10? years, and with itwent an important source of velocity damping for small

tational scattering amongparticles tends to increaseu*, while energy dissipa-tion during collisions anddrag exerted on particlesby the gaseous nebula bothact to decrease u*. For adistribution of objects, anequilibrium between theseprocesses yields u"* on theorder ofthe escape velocityofthe object class that con-tains the majority of thetotal mass.

Interactions amongorbiting particles of differ-ent masses tend to drive

April 2004 Physics Today 57

objects. As the random velocities ofsmall objects increased,their ability to damp the velocities of the larger embryosthrough dynamical friction would decrease. Mutual grav-itational interactions among the embryos would then be-come more potent and lead to the excitation of their orbitaleccentricities, mutual orbit crossings, and finally em-bryo-embryo collisions and mergers. As the embryos col-lided and accreted, the number ofplanets would decreaseand the dynamical stability of the system would increase,until finally a few planets on stable orbits remained. Thefrnal configuration ofplanets would thus be established ina stochastic "process of elimination," and a planet,s dy-namical characteristics-its mass, orbital radius, rotationrate, and rotational axis, for example-would be greatlyin{luenced by its last few large collisions.

Models of the accretion of planetary embryos into ter-ry_st1al planets were pioneered in the 1980s by GeorgeWetherill (Carnegie Institution of Washington's Depart-ment of Terrestrial Magrretism), who utilized a MonteCarlo approach for tracking embryo orbits. Such statisti-cal models use anal5rtic approximations to estimate thelikelihood'of collisions and to describe the effects of mu-tual gravitational perturbations among the planetary em-bryos. Those techniques, however, could not incorporatesome important dynamical effects, including the potentialfor successive and correlated close encounters between agiven pair of embryos.

In the past decade, late-stage accretion models havebeen revolutionized by advances in methods for directly in-tegrating the equations of motion of objects that orbit amore massive central primary. The key breakthrough wasmade in 1991 by Jack Wisdom (MIT) and Matthew Hol-man (now at the Harvard-Smithsonian Center for Astro-physics). The Wisdom-Holman mapping (WHM) methodallows for accurate integrations with relatively long inte-gration time steps.a Whereas classic orbit integrators re-quire 500-600 time steps per orbit, WHM saves time byanalytically tracking the Keplerian motion and integrat-ing only the small perturbations that arise from themasses of the orbiting objects, so that only a few tens oftime steps per orbit are needed to ensure accuracy. TheWHM method is also symplectic: Although it does not ex-


actly conserve energy, the predicted energy oscillatesabout a fixed value so that energy errors do not accumu-late with time. Modern techniquess based on the WHMmethod can track the dynamical evolution of systems ofseveral hundred accreting planetary embryos for morethan 108 years.6'7 Such simulations follow not only the ac-tual orbit of each embryo but also the dynamical encoun-ters between embryos, including collisions or close passes.

Figure 3 shows the frnal planetary systems produced!n eight late-stage accretion simulations recently per-formed using such direct integration techniques by JohnChambers of NASlt's Ames Research Center.? The simu-lated systems display a wide variety of architectures butare generally similar to our solar system's terrestrial plan-ets in terms of the number of frnal planets and theirmasses. Anotable difference is that the planets in the sim-ulated systems have eccentricities and inclinations muchhigher than those of Earth and Venus, whose orbits arevery close to circular and coplanar. This difference is likelya result of simplifications made in most of the models todate, namely ignoring the influence of potential coexistingsmall objects or a remnant of the gas nebula in the latestage. Both would generally act to decrease eccentricitiesand inclinations. While it is conceptually simplest to con-sider a sharp division between the middle and late stagesso that in the late stage such effects can be ignored, Na-ture may not be so accommodating. Recent models that in-clude more initial objects or a small portion of the nebulargas have found systems with orbits closer to those in ourSolar System, although accounting for the nearly circularorbits of Earth and Venus remains an open issue.

A seemingly inherent feature of the late stage is giantimpacts, in which lunar- to Mars-sized objects mutually cot-lide to yield the final few terrestrial planets. Figure 4 showsthe mass ofimpactors as a function of time for collisions thatoccurred in 10 late-stage simulations performed by CraigAgnoa Harold Levison, and me at the Southwest Researc[Institute.G The "Earths" produced in those simulations re-quire an average of 10-50 million years to accrete, with thelargest late-stage impacts occurring predominantly in the107- to 108-year time interval. The collisions display a ran-dom distribution ofimpact orientation, so that a final planet

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is as likely to end up rotating in the prograde sense (that is,in the same sense as its orbit about the Sun, as is the casefor Mercury, Earth, and Mars) as in a retrograde sense (asis the case for Venus).

Origin of the Earth-Moon systemAccording to current thinking, the growing Earth experi-enced one such late-stage impact that ejected into orbit thematerial from which our Moon later formed. The giant im-pact theory for lunar origin (see the box on page 60) is fa-vored for its ability to account for the high angular mo-mentum of the Earth*Moon system and for the iron-poorcomposition of the Moon. Reconciling the type of impact re-quired with the actual Earth-Moon system thus providesan important benchmark for terrestrial-accretion models.' The impact theory proposes that the collision that cre-ated the Moon was also the primary source of the angularmomentum L*_* of the Earth-Moon system. The angularmomentum delivered by an impactor of mass yMris

L^o = l.\L*-*

where b : sin 6 is the impact parameter normalized to thesum of the impactor and target radii, f is the angle betweenthe surface normal and the impact trajectory (so that agrazing impact has b : 1 and f : 90o), Mris the total com-bined mass of the impactor and target, and 7 is the frac-tion of the total mass contained in the impactor. From thisequation, a minimum impactor mass of about 0.08 M* isrequired to yield L*_*in the limit of a b :1 grazing colli-sion for Mr= M* and u,-o ! u.*. Imparting the Earth-Moon angular momentum by an oblique impact with Earththus implies an impactor roughly the size of Mars-thatis, about 0.1 M,.

For impact-ejected material to achieve Earth-boundorbit, some modification to standard ballistic trajectoriesmust occur, otherwise ejecta launched from the planet'ssurface either re-impacts or escapes. TWo nonballistic ef-fects are gravitational torques due to mutual interactionsamong ejected material or to interaction with a nonspher-ical distortion ofthe target planet, and pressure gradientsassociated with vaporization. These effects become impor-tant for large impacts: the first when the impactor is a sig-nificant fraction of the target's mass, and the second whenthe specific impact energy (that is, the impact enerry perunit mass) exceeds the latent heat ofvaporization for rock,about 1011 erg/g , which occurs for u,.o i 5 km/s.

For a lunar-forming impact, the-expected impact ve-locity is around 10 km/s, and both torques and vaporiza-tion could be important. Modeling potential lunar-formingimpacts thus requires a full hydrodynamic approach thatincludes both an explicit treatment of self-gravity and anequation of state appropriate to describe the thermody-namic response of material subjected to very high impactenergies and pressure.

Models of lunar-forming gant impacts have primarilyused smooth particle hydrodynamics. SPH, developed overthe past 25 years,s represents a significant advance in themodeling of deforming and spatially dispersing hydrody-namic systems, including giant impacts. SPH is a La-grangian method, which is advantageous because its nu-

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merical resolution tracks the spatial distribution of theevolving material, and compositional histories can be easilyfollowed. In SPH, a planetary object is represented by agreat number of spherically symmetric overlapping "parti-

cles," each containing a quantity of mass of a given compo-sition, whose three-dimensional spatial distribution is spec-ified by a density-weighting function, the kernel, and by thecharacteristic width of the particle, the smoothing length.

For impacts between planet-scale objects, each parti-cle's kinematic variables (position and velocity) and statevariables (internal enerry and density) evolve due to grav-ity, compressional heating and expansional cooling, andshock dissipation. The forces between particles thus in-clude attraction due to gravity, which acts inversely withthe squared distance between particles, and a repulsivepressure for adjacent particles closer than approximatelythe sum of their smoothing lengths. The equation of staterelates a particle's specifrc internal energy and density topressure as a function ofinput material constants.

The use of SPH in modeling lunar-forming impactswas pioneered by Willy Benz (now at the University ofBern), Alastair Cameron (now at the University of Ari-zona), and colleagues in the 1980s.s The general approachin performing such numerical impact experiments hasbeen to vary the four impact variables-b , Mr,.l, and u*o-of equation 2 in a series of simulations to determine whatsets of impact conditions yield the most favorable results.The challenge is that the possible parameter space is largeand individual impact simulations are computationally in-tensive. Recent works10,11 have successfully identifred im-pacts capable of simultaneously accounting for the massesof Earth and the Moon, the Earth-Moon system angularmomentum, and the lunar iron depletion.

Figure 5 shows a time series of a lunar-forming impactsimulationll using high-resolution SPH and a sophisticatedequation ofstate frrst developed at Sandia National Labo-ratories and recently improved by Jay Melosh of the Uni-versity ofArizona's Lunar and Planetary Laboratoryl2 to in-clude a treatment of both molecular and monatomic vaporspecies. The simulation offers the most realistic treatmentof vaporization of any SPH simulations performed to date,and each impact simulation requires several days of com-putational time on a high-speed workstation.

In the impact simulation, the colliding objects are de-scribed by a total of 60 000 SPH particles. The normalizedimpact parameter is b - 0.7 (that is, a 45o impact angle);

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'. .':iilits.n 1...*:...-$"'..i... '...

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the impactor contains 1.2 times the mass of Mars; the im-pact velocity is 9 km/s; and the impact angular momentumL^o = I.25 Z,-r. Before the impact, both objects are dif-ferilntiated into iron cores and silicate mantles-a rea-sonable assumption given the amount of heating thatwould have been induced as the objects accreted to sizesthis large. Both are 30Vo fuon by mass.

After the initial oblique impact (figure 5a, after about20 simulated minutes), a portion of the impactor is shearedoff and continues forward ahead of the impact.site. A dis-torted arm of impactor material extends to a distance ofseveral Earth radii, and the proto-Earth surface and theinner portions ofthis arm rotate ahead ofthe more distantmaterial (frgure 5b at 80 minutes). This confrguration pro-vides a positive torque to the outer portions of material,helping them to gain sufficient angular momentum toachieve bound orbit. In the 3- to 5-hour time frame. theinner portions of the orbiting material (composed prima-rily of the impactor's iron core) gravitationally contractinto a semicoherent object (figure 5c) that collides again

Theories of the Moon's

with the plarlet after about 6 hours(frgure 5d). Thus at this point, mostof the impactor's iron has been re-moved from orbit. The outer clumpof impactor material (figure 5e)-composed entirely of mantle mate-rial-passes close to Earth and issheared apart by planetary tidalforces that leave a circumplanetary

.; disk after about a day (figure 5f at:..i 27 hours).

At the end ofthis impact, the re-sulting planet and disk are a closeanalog to that needed to produce the

Earth-Moon system. The planet contains about an Earthmass and its rotational day is about 4.6 hours, and the or-biting disk contains about 1.6 lunar masses. Of the orbit-ing material, approximately a lunar mass has suffrcientangulal momentum to orbit beyond a distance known asthe Roche limit, located about 3 Earth radii from the cen-ter of the Earth for lunar-density material. Inside theRoche limit, planetary tidal forces inhibit accretion; it iswithin this distance, for example, that planetary ring sys-tems are found around the outer planets. Accretion willoccur for material orbiting beyond the Roche limit, so theorbiting disk produced by this impact would be expectedto yield a lunar-sized moon at an initial orbital distance ofabout 3-5 Earth radii. The short 4.6-hour day of postim-pact Earth causes the distance at which the orbital periodis equal to the terrestrial day-the so-called s5rnchronousradius-to fall within the Roche limit. at about 2.2 Earthradii. Because the Moon forms beyond this distance, tidalinteraction with Earth will lead to the expansion of theMoon's orbit while Earth's rotation slows.

The impact must also account for the Moon's iron de-pletion. Whereas the colliding objects in figure 5 both con-tained 30Vo fton by mass, the orbiting material is derivedoverwhelmingly from the outer mantle portions of the im-pactor. The protolunar disk contains only a few percent ironby mass, with the iron originating from the impactor's core.The lunar-forming impact dramatically raises Earth's tem-perature, with about 307o of the planett mass heated to tem-

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esis requires the Earth-Moon angular momentum to be sev-eral times higher than its actual value. Coformation supposesthat the Moon grew in Earth orbit from the sweeping up ofsmaller material from the solar nebula. Although coformationmodels were successful in producing satellites, they didn'treadily explain both the lunar iron deficiency and theEarth-Moon angular momentum, since growth via manysmall impacts typically delivers l itt le net angular momentumand produces slow planetary rotation.

ln 1975-76, trvo independent groups proposed an alterna-tive model. William Hartmann and Donald Davis (both atthePlanetary Science Institute) suggested that the impact of alunar-sized object with the early Earth had ejected into Earth-bound orbit material from which the Moon then formed. lfsuch material were derived primarily from the outer mantlesof the colliding objects, then an iron-depleted moon might re-sult. Alastair Cameron (now at the University of Arizona) andWilliam Ward (now at the Southwest Research Institute) fur-ther recognized that if the collision had been a grazing one bya much larger, planet-sized impactor---{ne roughly the size ofMars, containing - 10% of Earth's mass-the angular mo-mentum delivered by the impact could account for Earth'srapid initial rotation. The concepts described in those re-searchers' works contain the basic elements of the now fa-vored giant impact theory of lunar origin.l8

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6 lthough the Moon is by far the most familiar satellite, it isffia rather unusual planetary object. Whereas solid objectsin the inner Solar System typically contain about 30olo iron bymass, the Moon's low density implies that it is severely iron-depleted, with an iron core that l ikely is only 1-3% of ismass. The Moon is further distinguished by its large size rela-tive to its parent planet: lt contains about 1% of Earth's mass.Mercury Venus, and Mars, in contrast, lack large moons. Theangular momentum of the Earth-Moon system is also unusu-ally high. lf it were contained solely in Earth's rotation, itwould yield an approximately 4-hour day-much shorterthan those of the other inner planets. And, due to tidal inter-actions with Earth, the Moont orbital radius has expandedmore significantly over its history than any other planetarysatellite, so the Moon in its early stages was about 15 timescloser to farth than it is currently.' Prior to the Apollo era, three lunar origin hypotheses pre-dominated: capture, fission, and coformation.rT However,each of those models failed to account for one or more of themajor characteristics of the Earth-Moon system. Capturing anindependently formed Moon into an Earth-bound orbit doesnot offer a natural explanation for the lunar iron depletion,and that scenario appears dynamically unlikely. In fission, arapidly spinning Earth becomes rotationally unstable, causinglunar material to be flung out from the equator. That hypoth-


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peratures in excess of 7000 I( Thus postimpact Earth wouldhave been engulfed in a silicate vapor atmosphere, with themajority of the planet likely in a molten state.

Since large collisions appear typical in the late stagesof terrestrial planet formation, how often do such impactsproduce satellites? Results of impact simulations suggestthat low-velocity, oblique collisions (those with 6 > 0.5) be-tween planetary embryos generate some amount of orbit-ing material around the larger of the colliding objects. Forrandom impact orientation, the most likely value for 6 is0.7 (which is what has been found to be optimal for theMoon-forming impact), and.75Vo of all collisions will haveb > 0.5. Thus the inner Solar System may have initiallycontained many impact-generated satellites, with the ma-jority lost as they were destroyed or dislodged by subse-quent impacts or as their orbits contracted due to tidal in-teractions with a slow- or retrograde-rotating planet.

lsotopic timing constraintsThe general agreement between the type of impact appar-ently required to yield Earth's Moon and those predictedbv accretion simulations orovides an imnortant corrobo-by accretion si provides an important corrobo-

tf solid-planet formation. Otherion. Otherration of current models of solid-planetimportant pieces of independent evidence are the forma-

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tion times implied by the isotopic compo-sitions of Earth and the Moon.

A key development in the pastdecade has been the use of thehafnium-tungsten chronometer for dat-ing planetary core formation and giantimpacts.l3 Radioactive 182Hf decays to182IM with a halflife ru"of I million years.A critical distinction between hafniumand tungsten is that hafnium isIithophilic ("silicateJiking," tending to beconcentrated in oxygen-containing com-pounds such as silicates), whereas tung-sten is siderophilic ("iron-liking," ortending to enter metallic phases). Duringcore formation in a planetary object,whatever tungsten is present in theplanet's mantle-radiogenic 182W as wellas nonradiogenic W-isotopes such as 183Wand 184w-will be largely removed fromthe mantle and incorporated into theiron core, while hafnium will remain inthe mantle. Thus the mantle of a differ-entiated planetary object will have aHflW ratio larger than that ofbulk Solar-

System composition. The bulk Solar-System compositioncan be inferred from the composition of primitive mete-orites, called chondrites.

The HflW ratio and W-isotope compositions of a dif-ferentiated object such as Earth provide timing con-straints on the formation of its core and potentially on thetiming of its last large collision. The tungsten compositionof chondrites includes both nonradiogenic isotopes and182W produced by the decay of primordial 182Hf, and thechondritic W-isotope composition provides a referencevalue believed indicative of early Solar System abun-dances. If a planet's core formed on a timescale shorterthan about 5rur,its mantle, compared to chondrites, wouldcontain excess 182!V (relative to the abundance ofother Wisotopes) produced by decay of 182Hf after core formation.If the core formed later when 182Hf was essentially extinct,all isotopes ofW would have been equally depleted by in-corporation into the iron core, leaving the mantle with achondritic W-isotopic composition.

Earth's mantle contains an excess of 182W compared tothe most recent assessments of chondritic W-isotope conipo-sition,la'ls which implies that Earth's accretion and core for-mation were largely completed in 10-30 million years (seePuYSICS ToDAy, January 2003, page 16). The Moon has a

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similar lff-W-derived formation timri of about 25-30 millionyears.14 These specific timings can be affected by model as-sumptions, such as the degree to which accreting materialisotopically equilibrates with Earth's mantle.l6 However, ingeneral, the Hf-W timings and the late-stage dynamicalmodels both yield estimates in the L0- to 50-million-year timeinterval for planetary accretion, giant impacts, and the finalepisodes of tenestrial-planet core formation. Broadly simi-lar formation times of 107 to 1S years also result from otherisotopic systems such as uranium-lead, iodine-xenon, andplutonium-xenon.lo If the terrestrial planets had grown totheir final sizes through runaway growth, their formationtimes would have been much shorber, on the order of 106years or less. The agreement between the dynamically andgeochemically derived timings thus provides significant sup-port to the existence ofa protracted phase oflate accretiondominated by large impacts.

Whereas early models proposed that Earth-like plan-ets form through the orderly accretion of nearby small ma-terial in the protoplanetary disk, current work insteadsuggests that soliil planets are sculpted by a violent, sto-chastic final phase of giant impacts. The implication isthat our terrestrial planets-and Moon-may only repre-sent one possible outcome in a wide array of potentialsolar-system architectures. With future space missions(such as NASAs Terrestrial Planet Findcr) devoted to de-tecting Earth-like planets around other stars, we maysomeday be able to directly test such concepts.

The author gratefuUy acknowledges support from NSF andNASA.

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57 (1998); M. Mayor, Annu. Reu. Astron. Astrophys (in press).2. S. J. Weidenschilling, J. N. Ctzzi, in Protostars and, Plnnets

III, E. H. Levy, J. I. Lunine, eds., U. of Ariz. Press, T\rcson(1993), p. 1031; W. R. Ward, inOrigin of the Earth and Moon,R. M. Canup, K. Righter, eds., U. of Ariz. Press, Thcson(2000), p. 75; A. N. Youdin, E. I. Chiang, Astrophys. J. 601,1109 (2004).

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(1998); J. E. Chambers, Monthly Not. Royal Astron. Soc. 304,793 (1999).

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(1992).9. See, for example, the review by A. G. W. Cameron, in Origin

of thc Earth and Moon, R. M. Canup, K. Righter, eds., U. ofAriz. Press, T\rcson (2000), p. 133.

10. R. M. Canup, E. Asphaug, Nature 412,708 (2001); R. M.Canup, Annu. Reu. Astron. Astrophys. (in press).

11. R. M. Canup, Icarus 168,433 (2004).12. H. J. Melosh, Lunar Planetary Sci. Conf. 31, 1903 (2000).13. A. N. Halliday, D. C. Lee, S. B. Jacobsen, in Origin of the

Earth and Moon,R. M. Canup, K. Rightea eds., U. of Ariz.Press, Thcson (2000), p. 45.

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16. A. N. Halliday, Nature 427,508 (2004).17. W. K. Hartrnann, R. J. Phillips, G. J. Taylor, eds., Origin of

the Moon, Lunar and Planetary Institute, Houston, TX(1986).

18. R. M. Canup, K. Righter, eds., Origin of the Earth and Moon,U. ofAriz. Press, Tbcson (2000).


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