Editor-in-ChiefProfessor Gerald SchubertDepartment of Earth and Space Sciences and Institute of Geophysics and Planetary Physics,University of California Los Angeles, Los Angeles, CA, USAVolume EditorsVolume 1 Seismology and the Structure of the EarthDr. Barbara RomanowiczUniversity of California at Berkeley, CA, USADr. Adam DziewonskiHarvard University, Cambridge, MA, USAVolume 2 Mineral PhysicsDr. G. David PriceUniversity College London, London, UKVolume 3 GeodesyDr. Tom HerringMassachusetts Institute of Technology, Cambridge, MA, USAVolume 4 Earthquake SeismologyDr. Hiroo KanamoriCalifornia Institute of Technology, Pasadena, CA, USAVolume 5 GeomagnetismDr. Masaru KonoTokyo Institute of Technology, Tokyo, JapanVolume 6 Crust and Lithosphere DynamicsProfessor Anthony B. WattsUniversity of Oxford, Oxford, UKVolume 7 Mantle DynamicsDr. David BercoviciYale University, New Haven, CT, USAVolume 8 Core DynamicsDr. Peter OlsonJohns Hopkins University, Baltimore, MD, USAVolume 9 Evolution of the EarthDr. David StevensonCalifornia Institute of Technology, Pasadena, CA, USAVolume 10 Planets and MoonsDr. Tilman SpohnDeutsches Zentrum fur Luft und Raumfahrt, Berlin, GermanyiiPrefaceGeophysics is the physics of the Earth, the science that studies the Earth by measuring the physical con-sequences of its presence and activity. It is a science of extraordinary breadth, requiring 10 volumes of thistreatise for its description. Only a treatise can present a science with the breadth of geophysics if, in addition tocompleteness of the subject matter, it is intended to discuss the material in great depth. Thus, while there aremany books on geophysics dealing with its many subdivisions, a single book cannot give more than anintroductory flavor of each topic. At the other extreme, a single book can cover one aspect of geophysics ingreat detail, as is done in each of the volumes of this treatise, but the treatise has the unique advantage of havingbeen designed as an integrated series, an important feature of an interdisciplinary science such as geophysics.From the outset, the treatise was planned to cover each area of geophysics from the basics to the cutting edge sothat the beginning student could learn the subject and the advanced researcher could have an up-to-date andthorough exposition of the state of the field. The planning of the contents of each volume was carried out withthe active participation of the editors of all the volumes to insure that each subject area of the treatise benefitedfrom the multitude of connections to other areas.Geophysics includes the study of the Earths fluid envelope and its near-space environment. However, inthis treatise, the subject has been narrowed to the solid Earth. The Treatise on Geophysics discusses the atmo-sphere, ocean, and plasmasphere of the Earth only in connection with how these parts of the Earth affect thesolid planet. While the realm of geophysics has here been narrowed to the solid Earth, it is broadened to includeother planets of our solar system and the planets of other stars. Accordingly, the treatise includes a volume onthe planets, although that volume deals mostly with the terrestrial planets of our own solar system. The gas andice giant planets of the outer solar system and similar extra-solar planets are discussed in only one chapter of thetreatise. Even the Treatise on Geophysics must be circumscribed to some extent. One could envision a futuretreatise on Planetary and Space Physics or a treatise on Atmospheric and Oceanic Physics.Geophysics is fundamentally an interdisciplinary endeavor, built on the foundations of physics, mathematics,geology, astronomy, and other disciplines. Its roots therefore go far back in history, but the science has blossomedonly in the last century with the explosive increase in our ability to measure the properties of the Earth and theprocesses going on inside the Earth and on and above its surface. The technological advances of the last century inlaboratory and field instrumentation, computing, and satellite-based remote sensing are largely responsible for theexplosive growth of geophysics. In addition to the enhanced ability to make crucial measurements and collect andanalyze enormous amounts of data, progress in geophysics was facilitated by the acceptance of the paradigm ofplate tectonics and mantle convection in the 1960s. This new view of how the Earth works enabled an under-standing of earthquakes, volcanoes, mountain building, indeed all of geology, at a fundamental level. Theexploration of the planets and moons of our solar system, beginning with the Apollo missions to the Moon, hasinvigorated geophysics and further extended its purview beyond the Earth. Today geophysics is a vital andthriving enterprise involving many thousands of scientists throughout the world. The interdisciplinarity andglobal nature of geophysics identifies it as one of the great unifying endeavors of humanity.The keys to the success of an enterprise such as the Treatise on Geophysics are the editors of the individualvolumes and the authors who have contributed chapters. The editors are leaders in their fields of expertise, asdistinguished a group of geophysicists as could be assembled on the planet. They know well the topics that hadto be covered to achieve the breadth and depth required by the treatise, and they know who were the best ofxvtheir colleagues to write on each subject. The list of chapter authors is an impressive one, consisting ofgeophysicists who have made major contributions to their fields of study. The quality and coverage achievedby this group of editors and authors has insured that the treatise will be the definitive major reference work andtextbook in geophysics.Each volume of the treatise begins with an Overview chapter by the volume editor. The Overviews providethe editors perspectives of their fields, views of the past, present, and future. They also summarize the contentsof their volumes and discuss important topics not addressed elsewhere in the chapters. The Overview chaptersare excellent introductions to their volumes and should not be missed in the rush to read a particular chapter.The title and editors of the 10 volumes of the treatise are:Volume 1: Seismology and Structure of the EarthBarbara RomanowiczUniversity of California, Berkeley, CA, USAAdam DziewonskiHarvard University, Cambridge, MA, USAVolume 2: Mineral PhysicsG. David PriceUniversity College London, UKVolume 3: GeodesyThomas HerringMassachusetts Institute of Technology, Cambridge, MA, USAVolume 4: Earthquake SeismologyHiroo KanamoriCalifornia Institute of Technology, Pasadena, CA, USAVolume 5: GeomagnetismMasaru KonoOkayama University, Misasa, JapanVolume 6: Crustal and Lithosphere DynamicsAnthony B. WattsUniversity of Oxford, Oxford, UKVolume 7: Mantle DynamicsDavid BercoviciYale University, New Haven, CT, USAVolume 8: Core DynamicsPeter OlsonJohns Hopkins University, Baltimore, MD, USAVolume 9: Evolution of the EarthDavid StevensonCalifornia Institute of Technology, Pasadena, CA, USAVolume 10: Planets and MoonsTilman SpohnDeutsches Zentrum fur Luft-und Raumfahrt, GERIn addition, an eleventh volume of the treatise provides a comprehensive index.xvi PrefaceThe Treatise on Geophysics has the advantage of a role model to emulate, the highly successful Treatise onGeochemistry. Indeed, the name Treatise on Geophysics was decided on by the editors in analogy with thegeochemistry compendium. The Concise Oxford English Dictionary defines treatise as a written work dealingformally and systematically with a subject. Treatise aptly describes both the geochemistry and geophysicscollections.The Treatise on Geophysics was initially promoted by Casper van Dijk (Publisher at Elsevier) who persuadedthe Editor-in-Chief to take on the project. Initial meetings between the two defined the scope of the treatise andled to invitations to the editors of the individual volumes to participate. Once the editors were on board, thedetails of the volume contents were decided and the invitations to individual chapter authors were issued.There followed a period of hard work by the editors and authors to bring the treatise to completion. Thanks aredue to a number of members of the Elsevier team, Brian Ronan (Developmental Editor), Tirza Van Daalen(Books Publisher), Zoe Kruze (Senior Development Editor), Gareth Steed (Production Project Manager), andKate Newell (Editorial Assistant).G. SchubertEditor-in-ChiefPreface xvii9.01 Earth Formation and EvolutionD. J. Stevenson, California Institute of Technology, Pasadena, CA, USA 2007 Elsevier B.V. All rights reserved.9.01.1 Introduction 19.01.1.1 How Should We Think of Earth and Earth Evolution? 19.01.1.2 History and Themes 29.01.2 Physical and Chemical Constraints 49.01.2.1 Important Ideas 49.01.2.2 Some Useful Estimates 59.01.3 Commentary on Formation Models 89.01.4 Commentary on Early Evolution Models 99.01.5 Outstanding Questions 10References 119.01.1 Introduction9.01.1.1 How Should We Think of Earth andEarth Evolution?Evolutionary science is for the most part based onobservation and indirect inference. It is not experi-mental science, even though experiments cancertainly play a role in our understanding of processes.We can never hope to have the resources to build ourown planet and observe how it evolves; we cannoteven hope (at least in the foreseeable future) toobserve an ensemble of Earth-like planets elsewherein the universe and at diverse stages of their evolution(though there is certainly much discussion aboutdetection of such planets; e.g., Seager (2003)). Thereare two central ideas that govern our thinking aboutEarth and its history. One is provenance: the natureand origin of the material that went into making Earth.This is our cosmic heritage, one that we presumablyshare with neighboring terrestrial planets, and (tosome uncertain extent) we share with the meteoritesand the abundances of elements in the Sun. The otheris process: Earth is an engine and its current structureis a consequence of those ongoing processes, expressedin the form it takes now. The most obvious andimportant of these processes is plate tectonics andthe inextricably entwined process of mantle convec-tion. However, this central evolutionary processcannot be separated from the nature of the atmosphereand ocean, the geochemical evolution of various partsof Earth expressed in the rock record, and life.Figure 1 shows conceptually the ideas of Earthevolution, expressed as a curve in some multidimen-sional space that is here simplified by focusing on twovariables (this and that), the identities of which are notimportant. They could be physical variables such astemperature, or chemical variables (composition of aparticular reservoir) or isotopic tracers. The figureintends to convey the idea that we have an initialcondition, an evolutionary path, and a present state.The initial condition is dictated not only by provenancebut also by the physics of the formation process. Byanalogy, we would say that the apples from an appletree owe much of their nature not only to the genetics ofapples (the process of their formation) but also, to someextent, the soil and climate in which the tree grew. Weare informed of this initial condition by astronomy,which tells us about how planets form in other solarsystems, by geochemistry (a memory within Earth ofthe materials and conditions of Earth formation), and byphysical modeling: simulations and analysis of whatmay have occurred. Notably, we do not get informationon the initial condition from geology since there are norocks or landforms that date back to the earliest historyof Earth. Geology, aided by geochemistry and geobiol-ogy, plays a central role informing us about Earthhistory. Though some geophysicists study evolution,nearly all geophysical techniques are directed towardunderstanding a snapshot of present Earth, or a veryshort period prior to present Earth, and it is onlythrough modeling (e.g., of geological data) that thephysical aspects of evolution are illuminated.In Figure 2, another important idea is conveyed: formany purposes, we should think of time logarithmi-cally. This is in striking contrast to the way manygeoscientists think of time, because they focus (natu-rally enough) on where the record is best. As a result,far more geological investigations are carried out for1the Phanerozoic (10% of Earth history) than the entireperiod before this. More importantly, the processes thatgovern early history are very energetic and fast. As aconsequence, more could have happened in the firstmillions to hundreds of millions of years than through-out all of subsequent geologic time.Table 1 develops this idea further by identifyingsome of the important timescales of relevance to Earthhistory and prehistory (here taken to mean the impor-tant events that took place even before Earth formed).From this emerges the subdivision of geologic timeinto the accretion phase (the aggregation of bodies tomake Earth), lasting a hundred million years at most,an early evolution in which the high-energy conse-quences of the accretion (the stored heat) and possiblylater impacts still play a role, perhaps lasting as long ashalf a billion years, and the rest of geologic time inwhich the energetics of Earth is strongly affected bythe long-lived radioactive heat sources.In this overview chapter, an attempt is made toidentify the main themes of Earth history, viewedgeophysically, and to provide a context for appreciat-ing the more detailed following chapters. At the end,some of the outstanding issues are revisited, remind-ing us that this is very much a living science in whichthere are many things not known or understood.9.01.1.2 History and ThemesHopkins (1839) in his Preliminary observations on therefrigeration of the globe illustrates well the prevailing106Earth accretion1010107108(years)109PhanerozoicFigure 2 The logarithmic representation of geologic time.The energy budget and rapidity of processes at early timesmotivates this perspective. A similar view is often taken ofcosmology.Table 1 Some important timescalesProcess Timescale CommentsFormation of Earth 107108years Infrequent large impacts; backgroundflux of small impactsCooling of Earth after a giant impact 1000 years (deepest part of magmaocean)1001000 years (condensation of asilicate vapor atmosphere)$106years (condensation of steamatmosphere, assuming noadditional energy input)A wide range of timescales, some ofwhich are very fast but nonethelessimportant. Formation of a water oceancan be fastElimination of heat in excess of thethermal state that allows convectiveheat transport in equilibrium withradioactive heat production$108years Earth loses most of the thermal memoryof a possible very hot beginningDecline of impact flux (17) 108years The late heavy bombardment at 3.8Gamay have been a spike rather thanpart of a tail in the impact fluxCurrent timescale to cool mantle by500K5 1091010years Very slow because of the high mantleviscosityThis Initial conditionEvolutionaryPathAstronomyGeochemistryGeochemistryGeologyGeophysicsPresent stateGeobiologyPhysical modelsThatPhysical modelingFigure 1 Conceptual view of Earth evolution, identifyingthe three crucial elements (the initial condition, the evolutionpath, and the present state) and the sciences that contributeto their understanding. The axes are unimportant, since thediagram is merely a 2-D slice of a multidimensional phasespace. They might represent temperature or composition,for example.2 Earth Formation and Evolutionview of that time when Earth started hot and wascooling over time. This hot beginning now seemsnatural to us as a consequence of the gravitationalenergy of Earth formation, and it has been a consis-tently popular view even when the justifications for itsadvocacy were imperfectly developed. Famously, LordKelvin (Figure 3) took the hot initial Earth and appliedconduction theory to the outermost region to estimatethe age of Earth at 100 My or less. Burchfield (1975) inhis book, Lord Kelvin and the Age of the Earth, documentsKelvins various estimates and the conflict with theVictorian geologists of the time who believed thatKelvins estimates could not be sufficient to explainthe features we see. Kelvins confidence was bolsteredby the similar estimate he obtained for the age of theSun. Indeed, astrophysicists refer to the Kelvin time asa characteristic cooling timescale for a body, defined asthe heat content divided by luminosity. We now knowthat Kelvin was wrong about the Sun because he wasunaware of the additional (and dominant) energysource provided by fusion of hydrogen to helium.Ironically, Kelvin could have obtained a correct orderof magnitude estimate for Earths age had he evaluatedEarths Kelvin time. For a plausible estimate of meaninternal temperature of $2000 K (a number that wouldhave seemed perfectly reasonable to Kelvin), a heatcapacity of 700 J kg1, a mass of 6 1024kg and anenergy output of 4 1013W, he could have obtainedtKelvin % 6 1024 700 20004 1013 % 2 1017s% 7 Ga 1It should not have been unreasonable for him tosuppose that this was physically sensible since at thattime the fluidity of Earths interior was still in doubtand the concept of efficient convective transportalready existed. The subsequent discovery of fissionand long-lived radioactive heat sources was not thereason he got the wrong answer. Indeed, we nowthink that Earth could have a significant part of itsheat outflow and dynamics even if those radioactiveheat sources did not exist. Davies discusses this at fargreater length in his chapter.Plate tectonics and mantle convection is a centraltheme as the primary controlling principle of most ofEarth evolution. Mobility of Earth was proposed byWegener (1912) and the connection to deep-seatedmotions was also suggested long ago, for example,Bull (1921). The acceptance of these ideas wasdelayed, especially in the geophysical community,by the perceived absence of compelling evidencetogether with doubts about physical process: Couldrocks flow in the way that was needed? So much hasbeen written on this that any attempt to summarizebriefly here would be superfluous. However, oneaspect deserves comment our current view ofEarth evolution is not merely the physical pictureof how Earth loses heat and thereby drives the plates;it is the profound interconnection of this to all theother aspects of Earth: (1) the nature of the atmo-sphere, (2) the existence and persistence of thehydrosphere, (3) the maintenance of the magneticfield, (4) the evolution of the continents, and (5) theevolution of life. Most importantly, these are coupledsystems, not one where the mantle is dictating allelse. For example, life influences the sediments onEarth, which in turn influence what is cycled backinto the mantle, which in turn influences volcanismand pate motions. These interconnections are illu-strated in Figure 4.There are some other themes that are important andyet sometimes escape critical attention. The first is thecentral role of common processes rather than specialprocesses. In the early, perhaps more speculative, daysFigure 3 Lord Kelvin played a major role in ideas aboutEarth evolution and the age of Earth. Although he got thewrong answer for Earths age, he could have obtainedroughly the right age had he used for Earth the method thathe used for the Sun.Earth Formation and Evolution 3of scientific theory-building, it was acceptable to invokea special process for planet formation, including Earth,one that is rare for stars in general. Beginning in the1950s, the Soviet school of cosmogony developed theview that planet formation is a natural process, buildingon much older Laplacian ideas of a nebula around theSun, but placing that in the context of a universalconcept of a disk around a forming star. Safronov(1972) played a central role in this development.Contemporaneously, the astronomical communitydeveloped a star formation scenario that naturallydeveloped an attendant disk designed to handle theangular momentum budget of the originating interstel-lar cloud of gas and dust. Support for this picture grewfrom the 1980s onward because of astronomical obser-vations. We now have abundant evidence for planetsaround Sun-like stars (of order 200 examples), thoughit is not yet clear how many of these systems possessterrestrial planets. This absence of evidence is notsurprising given the insensitivity of the Doppler tech-nique used to find most planets. Still, the prevailingview now is that there is nothing very special abouthow Earth came to be. Similarly, we are reluctant tosuggest something very special about how Earthevolved, even though there is clearly a major differencebetween the nature of Earth and the nature of Venus,the most Earth-like of our neighbors in size, though notthe most Earth-like in habitability.Another important theme comes from meteori-tics. It is widely accepted, yet not entirely obvious,that meteorites inform us about terrestrial planetsand about the building blocks for Earth. Certainlywe have a remarkable amount of information aboutmeteorites: (1) their composition, (2) the timing oftheir formation, and (3) the conditions that theyencountered (both physical and chemical). Chapter9.02 provides much information on this. We must ask,however, whether the validity of this approach is asself-evident as it is sometimes portrayed or whetherit is more an example of using what we have, as in theclassic story of the drunk looking for his lost car keysunder the lamppost because it is the only place wherehe can see. The relationship of materials in the Earth-forming zone to those that formed asteroids (meteoriteparent bodies) remains poorly understood.Also central to current ideas is the role of largeimpacts rather than dust or merely small bodies in theaccumulation of Earth. Unlike the other themes listedhere, this one is more theoretical, though it is consis-tent with the clearing of dusty disks around stars,taken to infer the formation of planetesimals (thoughnot necessarily requiring the formation of mostly largebodies). This theme originated in work in the 1970s(Hartmann and Davis, 1975; Cameron and Ward,1976) motivated in large part by ideas of lunar forma-tion, but also consistent with the Safronov model ofplanet formation as developed further by Wetherill(1976) in particular. Our current ideas of planet for-mation (e.g., Chambers, 2004) retain the feature, firstnoted by Wetherill, that the material that goes intomaking Earth comes from a wide range of heliocentricdistances, but that there is nonetheless some expectedvariation in final composition simply because of thesmall number of large bodies that participate. Thisimportant idea is illustrated in Figure 5. It is notknown whether this is in fact true; the test lies in abetter understanding of the compositions (includingisotopic make-up) of the other terrestrial planets.9.01.2 Physical and ChemicalConstraints9.01.2.1 Important IdeasWe cannot figure out origin and early evolution exceptto the extent that Earth has a memory. The mostobvious memory of a planet is its total mass: we donot know of any way of significantly modifying thisafter the planet forms. In respect of major elements,the planet is a closed system. The application of cos-mochemistry and meteoritics to planets is heavilydependent on this idea of closed systems, especiallywhen we speak of provenance (the reservoir of mate-rial that was available for forming a planet). It is lessobvious but true that a planet will not change its orbitalradius significantly. Some other physical attributes suchas spin or obliquity or orbital eccentricity can varyAtmospherePlate tectonics andvolcanismMantle convectionmoderatesGeomagnetismCoreconvectionLifeHydrospheredeterminesis responsible forFigure 4 The interconnected aspects of Earth evolution.4 Earth Formation and Evolutionsignificantly (they are not conserved quantities). Aspectsof the history of Earth rotation are in Chapter 9.10.The retention of a memory is not guaranteed,especially for physical attributes, even when conser-vation principles apply. For example, the propertiesof an ice cube are independent of whether the watermolecules were once in the vapor phase or once in aliquid form, at least if the material is in strict thermo-dynamic equilibrium. The water molecules have nomemory. More subtle analysis would however dis-cern whether the isotopic mix of the oxygen on theice cube were similar or the same as some other icecube. One could in this way decide whether the icecube came from Mars or Earth.Thermal memories can be elusive. For example,consider a body that cools according to this equationdTdt kTa12where T is temperature, t is time, and k is a constant.The exponent a is assumed to be greater than unity,and in many realistic cases (e.g., mantle convection) itmay be substantially larger than unity. The solutionTt akt T0 a

1,a% akt 1,a3retains poor memory of its initial condition if a >1and substantial cooling has taken place, that is, T(t) issubstantially smaller than T(0). This is a commonsituation in planets. The loss of memory can be evenmore striking if there is a long-lived heat source(radioactivity). Examples of this are displayed in thethermal histories discussed in Chapter 9.08. By con-trast, a planet that differentiates (e.g., into core andmantle) may retain some memory of initial thermalstate should the deeper reservoir (e.g., the core) beconsiderably hotter than the near-surface reservoir.This would appear to be the case for Earths core.Planets are not in thermodynamical equilibrium;that is, one part of the planet is often prevented (byfinite diffusivity) from equilibrating with other parts,especially if at least one of the reservoirs is solid. Thisis a central tenet of many aspects of geochemistry.For this reason, chemical reservoirs are a very impor-tant source of memory.9.01.2.2 Some Useful EstimatesIt is useful to have an appreciation of various energybudgets, timescales, and dimensionless numbers.Among terrestrial planets, solar energy is large com-pared with the energy normally available from theinterior of a planet. For example, the incident sun-light on Earth exceeds the current heat flow fromEarths interior by a factor of 5000. This means thatthe thermal state of a planet surface is determined bythe Sun. However, nonsolar energy (e.g., accretion)can be comparable or more important for short per-iods of time during the planet formation phase.The total time of planet accumulation can be longcompared to free fall times because the starting mate-rial is so widely dispersed. This initial dilution is duein turn to the requirements of angular momentumconservation. For example, suppose we allowed themass of Earth to be initially dispersed in a volumethat is of order one-tenth of a cubic astronomicalunit, that is, 0.1 AU3(where 1 AU is the EarthSunseparation). Then if an embryo Earth were plowingthroughthis material witha relative velocity of 1 kms1(a significant fraction of orbital velocity), it wouldgrow at a rate given by4,oR2 dRdt R2v, 4where ,o is the density of solid matter, , $10M/(1 AU)3is 12 orders of magnitude smaller, v $1kms1, R is the radius, and a geometrical cross sectionis assumed. This predicts dR/dt of a few centimeters1.0Distance from Sun (AU)1.5 2.0 0.5Figure 5 The results of four outcomes for the final stagesof accretion of the terrestrial planets. The shaded bar graphrepresents an initial distribution of some tracer (e.g., oxygenisotopes or some compositional variable). The circles andtheir relative sizes give the final outcome in number spacingand relative masses of the resulting planets. The piediagrams within each circle represent the relative amountsof material arising from each part of the initial distribution.This shows how substantial mixing is typical, that is, thematerial that ends up in Earth is not typically the materialthat was originally at 1 AU from the Sun. Reproduced fromChambers JE (2004) Planetary accretion in the inner solarsystem. Earth and Planetary Science Letters 223: 241252,with permission from Elsevier.Earth Formation and Evolution 5per year and a planet formation time of order 100 Ma.Notice that this is independent of whether the accret-ing material is in the form of dust or larger bodies.The formation of a planet takes dispersed matterand aggregates it into a mass M of radius R. As aconsequence, the gravitational energy changes from asmall value to about GM2/R. By the first law ofthermodynamics, this energy release must go some-where. A small part at most is consumed breaking upmaterial but most of this energy is converted intoheat. If all that energy were stored internally then thetemperature rise isT $ GMRCp$ 40 000 RR_ _25where Cp is the specific heat of terrestrial materialsand Ris Earth radius. For the larger bodies, this is solarge that some of the rock and iron is converted intovapor; indeed, GM/RLv$1 at Earth mass, where Lvis the latent heat of vaporization.If a planet is initially undifferentiated and thenseparates into core and mantle, then the resultingenergy released as heat (from the resulting largerbut more negative total gravitational energy) is evi-dently some fraction of this amount. For a core that isone-third of the mass but twice the density of rockand settles an average of one-half the planetaryradius, the resulting temperature increase is reducedfrom eqn [5] by a factor of roughly 10, implying alarge effect (thousands of degrees potentially) forEarth. As with accretional heating, this energy maynot be uniformly distributed internally, but unlikethat in eqn [5] it is not readily radiated to space.Suppose we were to radiate away all of the energyof accretion in time t at a temperature of Tr (ignoringthe effect of the Sun or local nebula environment) asinfrared (IR) black body radiation. Accordingly,4R2oT4r t $ GM2R) Tr $ 350 107yrt_ _1,4RR_ _3,46This equation requires careful interpretation. If it wereindeed true that Earth formed from small particles(e.g., dust) over 10 or 100 My, then it would not gethot the energy of accretion is similar to deliveredsunlight (at current solar luminosity) over that period.However, the delivery of mass is highly nonuniformand much of the mass is delivered in giant impacts.This same equation would say that if you had toradiate away one-tenth of Earths energy of formation(the energy arising from impact with a Mars-sizedimpacting body) at T$2000 K appropriate to a sili-cate vapor atmosphere, then it would take $1000years. This is far longer than the delivery time of theenergy in a giant impact ($a day or less) implying thatvery high temperatures are unavoidable.The early state of the planet depends on thepartitioning of energy input between surficial (avail-able for prompt radiative loss) and deep seated(available for storage and only eliminated if there isefficient heat transfer from the interior). A crude butuseful way to estimate this relies on the introductionof a parameter f, the fraction of input energy that isdelivered to the deep interior. In the simple case oflittle energy transport from interior to surface, eqn[5] might then be replaced byT % fGMt Rt 7where T is the temperature difference between thenear-surface interior and surface at the time when theplanet has mass M(t) and radius R(t). It is commonpractice to think of f $0.1 or even less, but the phy-sical basis for this choice is unclear since the heat losswill be high if eqn [7] predicts a high temperature. Inother words, f is a function, not a number. However,the prevailing view of the initial state of Earth is thatit is set by a giant impact, presumably the impact thatmade our Moon. For this view, eqn [7] is not usefuland one must instead appeal to the outcome of impactsimulations, for example, Canup (2004). These showthat temperature increases of many thousands ofdegrees are likely, though the temperature distribu-tion is very heterogeneous. This is discussed furtherin Chapter 9.03 and also figures prominently in theinitial condition for the discussion of the resultingmagma ocean in Chapter 9.04.An enormous range of heat fluxes F from Earthsinterior is possible, both in the accretion epoch andsubsequently: in fully molten medium, convectivetransport can be enormous if the medium is evenonly slightly superadiabatic. For a superadiabatic tem-perature difference cT, convective length scale L, andcoefficient of thermal expansion c, mixing length the-ory (see Chapter 9.04) predicts F $,CpcT(gccTL)1/2,assuming viscosity is small enough to be unimportant.For layer of thickness L, the time to cool by T isaccordinglytcool $ 10 1000T_ _1,2TcT_ _3,2Lg_ _1,286 Earth Formation and EvolutionSince (L/g)1/2is a short timescale (e.g., hours), we seeimmediately that the cooling time is short, even forvery small temperature fluctuations driving the con-vection (e.g., of order one degree).By contrast, cooling times in a system that is mostlysolid (and therefore very viscous) can be enormouslylonger. The corresponding formula for heat flux inthis case is F $0.1,CpcT(gccTi2/v)1/3, where i isthe thermal diffusivity and v is the kinematicviscosity (see Chapter 9.08). For the usually realisticchoice of i$0.01 cm2s1, this predicts a cooling time,tcool $ 1010yr L1000 km_ _ T1000_ _ 100cT_ _4,3 v1020cm2s 1_ _1,39where the result has been scaled to a choice of visc-osity that is roughly like that expected for silicatematerial near its melting point. The precise value isnot important because the real significance of thisresult lies not in the specific numbers predicted butin the profound difference between cooing of a liquidand cooling of a solid. A planet that melts can loseheat prodigiously, but when Earth is mostly solid, thecooling rate is far slower. One consequence of this isthat the time that elapses between the very hot Earthand the formation of a water ocean can be small.Evidence of an early ocean is discussed in Chapter9.05 and also figures in the discussion by Stein andBen-Avraham on the origin and evolution of conti-nents. It may also be relevant to the initiation of platetectonics (see Chapter 9.06).We also note thatGM2R_ 10Qradiot dt$ 10 RR_ _210where Qradio is the chondritic radiogenic heat pro-duction, excluding short-lived sources (26Al, 60Fe).This emphasizes the importance of gravity as settingthe stage for subsequent evolution on Earth.Work done breaking up materials is small becausethe strength of materials is small compared to GM2/R4, the typical energy per unit volume associatedwith gravity. On the other hand, GM2/R4K$(R/R)2where K is the bulk modulus. This meansthat for Earth mass planets, gravitational self-com-pression leads to a higher density (smaller radius)than a body comprising the same constituents butzero internal pressure. This effect is enough to affectsignificantly the mineral assemblage within largerterrestrial planets, thereby affecting melting beha-vior, differentiation, core properties, and possiblemantle layering. It also means that Earths interiorcan be heated by adiabatic compression alone.The biggest effect of adiabatic compression is in apossible massive atmosphere, since gas is highly com-pressible. As a consequence, the radiative temperatureof a planet can be much less than the surface tempera-ture of the planet even when the atmospheric mass is asmall fraction of the total mass. This assumes that it isopaque (e.g., as in the greenhouse effect , but theargument provided here is not limited to that effect).For example, an adiabatic atmosphere that radiates at apressure Pe at temperature Te and has a basal pressurePs)Pe will have a surface temperature Ts given byTs $ Te 1012 RR_ _21 barPe_ _ MatmM_ __ _11where T _ Pis the adiabatic relationship and Matmis the atmospheric mass. The factor of 1012demon-strates the remarkable blanketing effect that ispossible even for an atmospheric mass that is lessthan the planet mass by a factor of a million.Planetary embryos form early enough that they areimbedded in the solar nebula. Gravitational attractionincreases the nebula gas density near the embryo sur-face. For an isothermal atmosphere of negligible mass,,r R,r !1 exp GMRc2_ _ 12where c is the speed of sound for the nebula (primar-ily hydrogen). Since the nebula is very low density,this is only of interest for surface conditions (e.g.,ingassing of nebula at the surface of a magmaocean) if GM/Rc2is larger than $5 or 10. For aMars mass and T$300 K, GM/Rc2$12. For suchan embryo, the nebula might be , $109g cm3and the surface density could then be , $104gcm3, potentially optically thick, and with a surfacepressure ($1 bar with a large uncertainty) that allowsmodest ingassing. Thus, embryos larger than Mars,including the growing Earth, could have had amassive atmosphere of near-solar composition.However, the planetary evidence suggests that thiseffect is small. For example, the neon-to-argonratio for Earth is much lesser than the solar nebularatio even though the ingassing ability (predictedby Henrys law) is similar. This is discussed furtherin Chapter 9.05. Presumably, the nebula waseliminated early in the period of growth of largeembryos.Earth Formation and Evolution 79.01.3 Commentary on FormationModelsAstronomical observations of newly forming starsindicate the presence of disks of gas and dust. Thematerial in the disk is typically a few percent of asolar mass, more than sufficient to explain theobserved planetary mass of our system or other sys-tems discovered thus far. If the disk has solarcomposition, then the amount of condensable mate-rial (as rock or iron) internal to a few astronomicalunits is sufficient to explain the masses of the terres-trial planets. However, the disks extend to tens ofastronomical units or more, and this is enforced bythe angular momentum budget of the originatinginterstellar cloud. This angular momentum is respon-sible for the possibility of planet formation but alsoguarantees that the terrestrial zone is a small part of amuch bigger picture. This means that we probablycannot understand formation of terrestrial planetswithout some understanding of the formation of thegas giants, especially Jupiter. The disks have a radialvariation in temperature, wholly or partly because ofthe energy release of the central body (the formingstar). As a consequence, the region within a fewastronomical units of the star is hundreds of degreeskelvin or more, sufficient to avoid the condensationof water ice. The absence of large amounts of water inthe terrestrial zone in our solar system is interpretedas evidence for terrestrial planet formation internal tothe snow line (the place outward of which water icecan condense). Typically, this temperature is of order160 K (low compared to 270 K because of the verylow vapor pressures characteristic of such a nebula).Chapter 9.05 discusses the source of water on Earth,which is presumably external to the terrestrial pla-netary zone.The central ideas in current models of terrestrialplanet accretion are three: (1) planetesimal forma-tion, (2) runaway and oligarchic growth, and (3) latestage accumulation. Planetesimal formation refers tothe accumulation of bodies of order kilometers insize. Runaway and oligarchic growth are two dyna-mical stages of a process that we can (for our purpose)lump into the rapid-accumulation planetary embryosof up to order Mars in mass but in closely spaced loweccentricity and inclination orbits. The last and slow-est stage proceeds for hundreds of Moon- and Mars-sized objects to the terrestrial planets that we see.According to astronomical observations, this laststage is probably occurring after the solar nebulahas been removed (by accretion onto the Sun orexpulsion to the interstellar medium). Chapter 9.02connects this physical picture to the cosmochemicalevidence.Planetesimal formation remains mysterious eventhough there is no doubt that it occurred, since itsconsequences are expressed among the meteoritesarising from differentiated asteroids that must haveformed in the first million years after the formation ofthe solar nebula. They may have formed by thepoorly understood process of sticking of dust parti-cles during very slow velocity collisions in the dustygas. They may alternatively have formed by a grav-itationally mediated process as the dust settledtoward the mid-plane of the disk. Gravitationalinstabilities are an attractive mechanism, especiallygiven the uncertainties of the physics of sticking, butthe relevant fluid dynamics is still debated(Weidenschilling, 2006). This remains one of themajor puzzles of planet formation.The next stage, from planetesimals to Moon andMars mass embryos, is perhaps better understoodtheoretically but less well founded in direct observa-tion. This stage, lasting 105106years, is rapidbecause of gravitational focusing. Bodies encountereach other at velocities considerably less than theescape velocity from the larger body, and, as a con-sequence, the cross section for collision is far largerthan the geometric cross section, perhaps by as muchas a factor of a thousand. The planetesimal swarm iscold (i.e., the random velocities of the bodies arevery small compared to Keplerian orbital velocities.)This process of embryo growth is terminated byisolation: when the orbits are nearly circular, thebodies reach a stage where there are no crossingorbits (i.e., no overlap of their gravitational spheresof influence). From the point of view of understand-ing the bodies that we see, this stage is of greatinterest in three ways. (1) These embryos formquickly and therefore may be hot, both because ofpossible short-lived radioactive elements and alsobecause of accretional heating (cf. the scaling dis-cussed in Section 9.01.2). They could therefore formcores and primordial crusts. In this sense, the primor-dial crusts and current cores of the terrestrial planetshave the potential to predate the formation of theplanets. (2) The largest of these embryos could con-ceivably be a surviving planet, most plausibly Mars.In this picture, Mars is special as an isolated outlier inthe formation process. (3) Embryos form while thesolar nebula is still present and could therefore have a8 Earth Formation and Evolutioncomponent of solar composition gas. Equation [12]suggests that this, however, is small.The late-stage aggregation is conceptually like thatenvisaged long ago in the work of Safronov (1972),whereby the scattering of bodies causes growth ofeccentricity and inclination allowing the orbits tocross. It has received a lot of attention in recenttimes because of the development of N-body codesthat can handle the outcome of a population of bodiesscattering from one another gravitationally and occa-sionally colliding (Chambers, 2004). The mainshortcoming of these calculations is the failure totake full account of what actually happens when twobodies have a very close encounter (a quite commonoccurrence) or collide. Tidal disruption is possible in aclose encounter (i.e., the outcome is not necessarily thetwo intact bodies that existed before encounter) andcollisions do not always lead to a clean merging of thetwo bodies. Close encounters can also create addi-tional bodies through tidal disruption.It is easy to see by order of magnitude (a slightlymore sophisticated version of eqn [4]) that thislate-stage process can take as long as 100 Ma.However, it is stochastic and it involves large bodies.As a consequence, it is not possible (and may perhapsnever be possible) to say exactly what sequence ofmajor events took place in the formation of a parti-cular planet.9.01.4 Commentary on EarlyEvolution ModelsThe high-energy events of late-stage accumulationare expected to play a central role in setting the stagefor Earth structure and evolution. The buildingblocks are a set of planetary embryos that almostcertainly form iron-rich cores because of the com-bined effects of gravitational energy release in arelatively short time and the possible effects of 26Alheating. This early but important differentiationevent is characterized by relatively modest tempera-tures ($2000 K or less) and pressures (20 GPa or less,perhaps a lot less) appropriate to bodies in this sizerange. It is likely and perhaps significant for someconstituents (e.g., noble gases) that this phase occursin the presence of the solar nebula. In highly idea-lized numerical models (Chambers, 2004), it isusually assumed that nearly all of Earths mass accu-mulates in the subsequent merging of these massiveembryos. In reality, it is not known how much mate-rial arrives in small bodies (planetesimals), whoseorigin could be either the bodies that were notswept up during runaway, or debris created duringfrequent close encounters in the final orbit-crossingphase. Giant impacts will certainly create extensivemelting and at least a transient magma ocean, espe-cially if one assumes that the interiors of the embryosprior to impact are at or even above the solidus ofmantle minerals. This is a reasonable assumptionbecause of the limited time available for eliminationof earlier heating, together with the higher radio-active heating of that epoch. It is also possible thatthere is a persistent magma ocean, even in the longintervals of time ($107years) between the giantimpacts, sheltered by a steam atmosphere greenhousethat is sustained by delivery of a rain of small bodiesthat heat its base. This kind of magma ocean is lesscertain than the transient high-energy ocean that ispresent immediately after a giant impact. Thesemagma ocean scenarios are analyzed in detail inChapter 9.04 and also figure prominently in the dis-cussion of core formation in Chapter 9.03.Of course, short-lived high-energy events couldhave a bigger role than sustained lower-energyevents in determining the composition of currentcore and mantle because they can create extensivemelting in which coremantle separation is espe-cially efficient. There are two central questions thatarise in this picture:1. To what extent is Earths core formation accom-plished by merging the cores of embryos ratherthan by separation of iron alloy from the mantlewithin the Earth?2. To what extent is the separation of core frommantle and possible internal differentiation of man-tle accomplished in a magma ocean environment?These issues figure prominently in Chapter 9.03.In simulations designed to understand the originof Earths Moon, smoothed particle hydrodynamics(SPH) is most commonly used to describe the out-come of an impact involving a Mars-sized projectileand a mostly formed Earth (Canup, 2004). Thisrepresents perhaps the last (and perhaps most impor-tant) giant impact. Core and mantle are tracked andone can follow the extent to which these constituentparts of projectile and target mix. The outcome isessentially stochastic; that is, it varies considerably asa function of details, such as impact parameter andmass ratio of projectile to target, parameters that wecan never hope to establish deterministically.However, in typical simulations, only around 10%of the projectile (and thus at most a few percent of anEarth Formation and Evolution 9Earth mass) is placed in orbit and available for mak-ing the Moon. Very little of Earth is placed into orbit.Nearly all of the rest of the projectile either mergesimmediately with Earth or crashes back into Earthwithin several hours of the initial impact. The ironcore of the projectile may be stretched into filamentsor broken into blobs. These simulations are low reso-lution, so even the finest scale features of SPH arehundreds of kilometers in size. It seems likely thatmuch of the iron is emulsified to small scales andequilibrates with the mantle, but this is not certain.The transitional phase between a mostly moltenmantle and an almost entirely solid mantle is stillpoorly understood. In respect of thermal history, itcould be argued that the details of this phase areunimportant (cf. Chapter 9.08). In respect of thegeochemical evolution, it is probably very importantfor setting up the conditions for formation or preser-vation of the earliest crust (see Chapter 9.02).The initially hot core will be allowed to cool bythe overlying mantle and will therefore convect,allowing for the possibility of magnetic field genera-tion. Nimmo deals with core evolution in Chapter9.09, particularly the puzzle of whether there isenough energy in core cooling and inner growth toexplain the energy budget demanded by the persis-tence of a dynamo throughout nearly all of geologictime. The answer to this puzzle remains uncertain.What about the origin of plate tectonics? On theone hand, this could be viewed as a geologic question,provided there was agreement about the distinctivesignatures of plate tectonics in the rock record. Onthe other hand, this could be viewed as a fluid dyna-mical question (albeit one that is unavoidablycoupled to the crustal evolution and rheologicalpuzzle of a fragmenting lithosphere). Sleep discussesboth aspects of this unresolved question in Chapter9.06.Finally we come to life. The origin of life on Earthremains one of the central scientific problems of ourtime, even though many in the scientific communityhave adopted the view that this origin was easy, bywhich they mean that the physical conditions,amounts of material, energy budget, and abundanceof liquid water and surfaces allows for conditions thatare suitable. Less controversial but perhaps as impor-tant, it is abundantly clear that biological evolutionhas affected the physical aspects of Earth evolutionprofoundly, just as the physical conditions havemediated that biological evolution. In many waysthis geobiological question is the most exciting fron-tier of Earth science, along with the more immediateissues of climate change (Earth evolution on a muchsmaller timescale).9.01.5 Outstanding QuestionsWhat are the main issues that arise in our under-standing of Earth origin and evolution? We end byproviding below a list of 10 questions, linked to thesubsequent chapters in this volume. In some cases,these emerge naturally from the perspectives of thevarious authors while in other cases they show theinterconnections that might be less evident from asingle chapter.1. What is the legacy of Earth formation in the planetas we see it? What range of accretion scenarios isconsistent with Earth? What is the role of chance?What is the role of distance from the Sun? How doesgeochronology compare with physical estimates offormation times? (see Chapter 9.02)2. How is core formation in Earth expressed in thecomposition of Earth now and the thermal structure andevolution? Can we figure out the core formationconditions from the abundances of siderophiles inthe mantle? Or will we find that the pattern is a mixof low-temperature, low-pressure and high-tempera-ture, high-pressure events? (see Chapter 9.03)3. What was the duration of the early magma ocean phaseof Earth and what memory (if any) is there of this phase in theearly mantle differentiation or crust formation? Is there anopportunity for meltsolid separation in the earlymantle and can this be reconciled with current modelsof mantle structure and composition? What of the roleof an early dense atmosphere? How long did it take fora magma layer within Earth (e.g, in the transitionzone) to completely freeze? (see Chapter 9.04)4. Where did Earths water come from? How much do wehave and how much of it has cycled between mantle andhydrosphere over geologic time? Did water play anessential role in the onset of plate tectonics? (seeChapter 9.05)5. Why does Earth have plate tectonics? Mantleconvection is easily understood; plate tectonics stillresists understanding because of our imperfect knowl-edge of how the lithosphere fails. The perspective ofgeologic time helps us solve this puzzle. (see Chapter9.06)6. Why continents? When continents? Are continents asideshow in the overall dynamics of Earth evolution(as passengers on plates) or do they play a central rolein how the system evolves? (see Chapter 9.07)10 Earth Formation and Evolution7. How did Earths mantle temperature evolve throughtime? Can we reconcile simple convective models with theradiogenic heat supply, the geologic evidence, and our under-standing of plate tectonics? The mismatch betweenknown heat generation from long-lived radioactivityand the actual heat flow out of Earth persists and isincompletely resolved in simple cooling models, sug-gesting the evolution is more complex. (see Chapter9.08)8. Can we reconcile Earth thermal evolution with thepersistence of the geomagnetic field throughout geologic time?When did the inner core form? The mantle governsthe rate at which the core cools and models accep-table on the mantle side suggest a possible problemfor core heat flows, including the possibility that theinner core was absent for a major part of early Earthhistory. But if so, can we supply enough energy to runEarths magnetic field? (see Chapter 9.09)9. What do variations in Earth rotation tell us about thenature of Earth and its evolution? Have we madesufficient use of rotation history, including truepolar wander, in our attempts to reconstruct howEarth evolved? (see Chapter 9.10)10. How are the geophysical and biological evolutions ofEarth interrelated? What does the history of life tell usabout plate tectonics and the history of water onEarth? To what extent is the co-evolution of lifeand Earths physical attributes so strongly coupledthat we connect major events in biological evolutionto major events in geological history? (Chapter 9.11)ReferencesBull AJ (1921) A hypothesis of mountain building. GeologicalMagazine 58: 364367.Burchfield JD (1975) Lord Kelvin and the Age of the Earth,260pp. New York: Science History Publications.Cameron AGW and Ward WR (1976) The origin of the moon(Abstract). In: Hartmann WK, Phillips RJ, and Taylor GJ (eds.)Lunar Science VII, pp. 120122. Houston: Lunar ScienceInstitute.Canup RM (2004) Simulations of a late lunar-forming impact.Icarus 168: 433456.Chambers JE (2004) Planetary accretion in the inner solarsystem. Earth and Planetary Science Letters 223: 241252.Hartmann WK and Davis DR (1975) Satellite-sizedplanetesimals and lunar origin. Icarus 24: 504515.Hopkins W (1839) Preliminary observations on therefrigeneration of the globe. Philosophical Transactions ofthe Royal Society of London 129: 381385.Safronov VS (1972) Evolution of the Protoplanetary Cloud andFormation of the Earth and the Planets, 206pp. Jerusalem:Israel Program for Scientific Translations.Seager S (2003) The search for Earth-like extrasolar planets.Earth and Planetary Science Letters (Frontiers) 208: 113124.Wegener A (1912) Die Entstehung der Kontinente. GeologischeRundschau 3: 276292.Weidenschilling SJ (2006) Models of particle layers in themidplane of the solar nebula. Icarus 181: 572586.Wetherill GW (1976) The role of large bodies in the formation ofthe Earth. Proceedings of the Lunar Science ConferenceVII: 32453257.Earth Formation and Evolution 119.02 The Composition and Major Reservoirs of the EarthAround the Time of the Moon-Forming Giant ImpactA. N. Halliday, University of Oxford, Oxford, OX, UKB. J. Wood, Macquarie University, Sydney, NSW, Australia 2007 Elsevier B.V. All rights reserved.9.02.1 Introduction 139.02.2 Key Features of the Earth and Moon 149.02.3 The Birth of the Solar System 149.02.4 Meteorites 169.02.5 Meteorites and the Composition of the Earth and Its Primary Reservoirs 189.02.6 The Circumstellar Disk and the Composition of the Earth 219.02.7 Dynamics of Planet Formation 239.02.8 The Age of the Earth 249.02.9 Short-Lived Nuclides and Early Processes 279.02.10 Rates of Earth Accretion and Differentiation 299.02.11 The Age of the Moon 319.02.12 First Principles of Chemical Constraints on Core Formation 319.02.13 Explanations for the Excess Siderophile Problem 339.02.14 The Deep Magma Ocean Model of Core Formation 339.02.15 Core Segregation during Growth of the Earth 359.02.16 Oxidation State of the Earth during and after Accretion 379.02.17 Isotopic Evidence for Volatile Losses from the Earth during Accretion 389.02.18 Hidden Reservoirs, Impact Erosion, and the Composition of the Earth 419.02.19 Concluding Overview 43References 459.02.1 IntroductionA treatise on geophysics needs some summary expla-nation of the current thinking on how the Earthachieved its current composition and formed its pri-mary reservoirs. This subject has taken enormousstrides in the past decade, thanks to significantimprovements in mass spectrometry in particular.However, additional discoveries are being fuelledby exciting developments in other areas and areleading to joint research at the interfaces betweendisciplines traditionally viewed as scientifically dis-tinct. The most significant of these are as follows: Accretion dynamics theoretical calculations ofthe behavior of the gas and dust in the solarnebula, the construction of planetesimals, plane-tary embryos and planets, and the fluid dynamicsof primordial mixing and differentiation. Cosmochemistry the isotopic and chemical his-tory of the solar system deduced from meteoritesand lunar samples. Mineral physics and experimental petrology thesimulation experimentally and theoretically of thephases present in the Earths interior, as well astheir physical properties and behavior. Observations of planets, stars, disks, and exosolarplanetary systems.In this chapter we summarize briefly these lines ofevidence and present the current thinking on theformation and primordial differentiation of theEarthMoon system. We focus on constraints fromcosmochemistry and experimental petrology inparticular because other chapters provide comple-mentary information. In particular, the introductorychapter by Stevenson (Chapter 9.01) covers aspectsof the accretion dynamics as do the chapters byRubie, Melosh, and Nimmo (Chapters 9.03 and9.09). There are no observations of terrestrial planetsaround other stars at the present time although this isexpected to change in the coming years and repre-sents a major thrust in experimental astrophysics.There are however observations of disks and larger13exosolar planets, as well as information from otherparts of our own solar system. These will be referredto where appropriate. Indeed the links between thisarea of Earth sciences and astrophysics have probablynever been stronger given the current search forexosolar Earth-like planets.9.02.2 Key Features of the Earthand MoonAny theory for how the Earth formed and acquiredits present composition and distribution of compo-nent reservoirs after the Moon-forming Giant Impacthas to explain several things:1. rocky terrestrial planets grew from the same diskas the gas giants Jupiter and Saturn althoughplausibly at different stages in its development;2. terrestrial planets and differentiated asteroidalobjects are depleted in moderately volatile ele-ments relative to refractory elements;3. the Moon is larger relative to the size of its hostplanet than any other moon in the solar system;4. the Moon carries most of the angular momentumof the EarthMoon system;5. the oxygen isotopic composition of the Earthand Moon are identical despite their differentchemical compositions;6. Earth has a larger core proportionally speakingthan does the Moon, Mars, or Asteroid Vesta;7. Earth has a more oxidized mantle than theMoon, Mars, or Asteroid Vesta;8. highly siderophile (metal-loving) elements inEarths mantle are inconsistent with low-pres-sure core formation;9. Earth has significant water;10. Earth, unlike the Moon, Mars, or Asteroid Vesta,lacks a geological record for the period prior to4.0 Ga; and11. time-integrated parent/daughter ratios deter-mined from isotopic data provide evidence ofchanges in composition during the accretion his-tory of the protoplanetary material that built theEarth and Moon.Most of the above are still a matter of some uncer-tainty and study. The first is particularly problematic.To tackle these subjects this chapter first provides abrief and elementary summary of how the Sun andsolar system formed and what we know about terres-trial planet bulk compositions. We then give asynopsis of the range of dynamic and isotopicconstraints on the formation of the Earth and Moon,following this with a summary of the huge field ofexperimental and theoretical petrology that providesinsights into how the Earth must have changed dur-ing its accretion history.9.02.3 The Birth of the Solar SystemThe Hubble Space Telescope has provided us withfascinating images of numerous young solar mass starsforming in giant molecular clouds such as the Eagleand Orion Nebulae. It is thought likely that our Sunoriginated in a similar kind of environment. Newevidence confirms a long-held suspicion that the Sundid not form spontaneously but that cloud collapsewas triggered by a shock wave originating from anearby star. Such shock waves might be produced,for example, from supernovae the explosive finaleto the short life of giant stars. This idea, developed bythe late Al Cameron at Harvard (e.g., Cameron andTruran, 1977) among others, appeared to be consistentwith the discovery of the daughter products of a rangeof short-lived nuclides in meteorites (Table 1). Thehalf-lives of these nuclides (100 ky100 My) are suchthat they must have been synthesized in stars shortlybefore the start of our solar system (Figure 1). Themost important paper outlining the likely explanationfor the synthesis of the various nuclides in stars is stillthe work of Burbidge, Burbidge et al. (1957). A varietyof more recent papers explore the growing body ofevidence from short-lived nuclides regarding the laterinputs to the solar nebula (Arnould et al., 1997; BussoTable 1 Short-lived nuclides that have beendemonstrated to have existed in the early solar system as aresult of anomalies in the abundance of their daughterisotopesNuclide Half-life (My) Daughter36Cl 0.3 36Ar, 36S41Ca 0.1 41K26Al 0.73 26Mg10Be 1.5 10B60Fe 1.5 60Ni53Mn 3.7 53Cr107Pd 6.5 107Ag182Hf 8.9 182W205Pb 15 205Tl129I 16 129Xe92Nb 36 92Zr244Pu 80 136Xe146Sm 103 142Nd14 The Compositon and Major Reservoirs of the Earthet al., 2003; Meyer and Clayton, 2000; Meyer andZinner, 2006; Truran and Cameron, 1978;Wasserburg et al., 1994, 1996, 1998). The early Sunmay have been associated with relatively energeticirradiation (Feigelson et al., 2002a, 2002b). It has beenproposed (Shu et al., 1997) that the conveyor belt ofmaterial being swept in toward the Sun may have ledto some light short-lived nuclides being generatedlocally and heterogeneously (Lee et al., 1998). Thesemight then have been scattered across the disk in earlyformed condensates (Shu et al., 1997). Although localproduction in the early Sun is feasible for a range ofnuclides (Gounelle et al., 2001; Leya et al., 2003), formost the abundances would be too low to be a matchfor those found in the meteorites. Furthemore, some ofthese nuclides could only have been made in a largestar that predated the solar system. They were thenintroduced to the gas and dust that ultimately becameour Sun and planets. It is possible that this explosionactually triggered collapse of the cloud material onto acore that became the solar nebula and nascent Sun.Problems have arisen with this theory. First, asupernova is so powerful that rather than causingcollapse it may in fact shred a molecular cloud unlesslocated at sufficient distance that much of the energyand material are already dispersed (Stone andNorman, 1992; Foster and Boss, 1996, 1997; Vanhalaand Cameron, 1998). The time taken to reach thelocation of the potential new star then becomes suffi-ciently long (hundreds of thousands of years) that itwould be difficult, though not impossible, to detectthe former presence of a nuclide such as 41Ca with ahalf-life of just 100 ky, because most of it would havedecayed.The second problem is that the relative abun-dances of many of the short-lived nuclides are notwell explained in terms of the production ratiosexpected in a supernova (Wasserburg et al., 1998).Therefore, attention has turned to other stellarsources, the most likely of which is an asymptoticgiant branch (AGB) star. AGB stars are relativelycommon (99%) ofEarths noble gases were lost subsequently (Porcelliand Pepin, 2000) (Figure 9). The dynamics and time-scales for accretion are dependent on the presence orabsence of nebular gas as discussed below.As already pointed out the moderately volatileelements are also depleted in the Earth (Figures 4,6, and 7) (Gast, 1960; Wasserburg et al., 1964; Cassen,1996). The traditional explanation for this is that theinner terrestrial planets accreted where it was hot-ter, within the so-called ice line (Cassen, 1996;Humayun and Cassen, 2000). It was long assumedfor several reasons that the solar nebula in the ter-restrial planet-forming region started as a very hot,well-mixed gas from which all of the solid and liquidEarth materials condensed. The geochemistry litera-ture contains many references to this hot nebula, aswell as to major T-Tauri heating events that mayhave further depleted the inner solar system in mod-erately volatile elements (e.g., Lugmair and Galer,1992). Some nebula models predict earlytemperatures that were sufficiently high to preventcondensation of moderately volatile elements(Humayun and Cassen, 2000) which somehow werelost subsequently.Understanding how the volatile depletion of theinner solar system occurred can be greatly aided bycomparisons with modern circumstellar disks. Thesewere first detected using ground-based interferome-try. Circumstellar protoplanetary disks (termedproplyds) now are plainly visible around youngstars in the Orion Nebula thanks to the HubbleSpace Telescope (McCaughrean and ODell, 1996).With such refined observations combined with theo-retical considerations, it is possible to trace the likelyearly stages of development of our own solar system(Ciesla and Charnley, 2006).A solar T-Tauri stage during development of thecircumstellar disk could have had a profound effecton volatile depletions. T-Tauri stars are pre-mainsequence stars. They are a few times 105to a fewtimes 106years in age and have many of the char-acteristics of our Sun but are much brighter. Manyhave disks. It has long been argued that the T-Taurieffect causes an early phase of heating of the innerportions of the disk. The T-Tauri stage may last afew million years and is often linked to the Earthsdepletion in moderately volatile elements. Because itheats the disk surface however, it is unsure whether itwould have a great effect on the composition of thegas and dust in the accretionary midplane of the diskwhere planetesimal accretion is dominant. Heating ofinner solar system material in the midplane of thedisk will, however, occur from compressional effects.The thermal response can be calculated for materialin the disk being swept into an increasingly denseregion during migration toward the Sun during theearly stages of disk development. Boss (1990)included compressional heating and grain opacity inhis modeling and showed that temperatures in excessof 1500 K could be expected in the terrestrial planet-forming region. The main heating takes place at themidplane, because that is where most of the mass isconcentrated. The surface of the disk is much cooler.0350124 MXe ()Earth atmospheric Xe3002502001501005050100150200250300Solar wind XeUXeMass M (amu)126 128 129130 131132 134 136Figure 9 Xenon is isotopically fractionated in the Earthsatmosphere relative to the estimated composition of thematerial from which it formed. Porcelli D and Pepin RO(2000) Rare gas constraints on early earth history. In: CanupRM and Righter K (eds.) Origin of the Earth and Moon. pp.435458. Tucson: The University of Arizona Press.22 The Compositon and Major Reservoirs of the EarthThis process would certainly be very early but how itwould have evolved with time and tie into the time-scales for disk heating deduced from cosmochemistryis unclear.Chondrules and CAIs provide us with the mostimportant information about the processes of heatingand melting in the disk that occurred within the firstfew million years of the solar system. The exactnature of these events has been hard to establish butchondrules are most likely produced by flash meltingof the dusty disk (Kita et al., 2006). What role theyplayed in the formation of planetesimals has beenunclear but some models predict that they mighthave accumulated preferentially in certain stagnantregions of the disk, facilitating planet formation(Cuzzi et al., 2001). Hewins and Herzberg (1996)have proposed that this is reflected in the Earthsnonchondritic Si/Mg (Figure 8).9.02.7 Dynamics of Planet FormationIn broad terms the rates of accretion of planets fromdisks are affected by the amounts of mass in the disksthemselves. If there is considerable nebular gas pre-sent at the time of accretion the rates are faster (e.g.,Hayashi et al., 1985). If gas is present then it is impor-tant to know what Jupiter is doing at the time ofterrestrial planet accretion. At present this is under-constrained and model dependent. The absence ofnebular gas is also calculated to lead to eccentricorbits (Agnor and Ward, 2002). Recently however,it has been shown that accretion in the presence ofswarms of planetesimals also decreases eccentricity(OBrien et al., 2006).The most widely accepted model of terrestrialplanet formation is the planetesimal theory(Chambers, 2004). In the simplest terms accretion ofterrestrial planets is envisaged as taking place in fourstages:1. settling of circumstellar dust to the midplane ofthe disk;2. growth of planetesimals up to $1 km in size;3. runaway growth of planetary embryos up to$103km in size; and4. stochastic growth of larger objects through late-stage collisions.Stage 1 takes place over timescales of thousands ofyears if there is no turbulence but much longerotherwise. It provides a relatively dense plane ofmaterial from which the planets grow. The secondstage is poorly understood but is necessary in order tobuild objects that are of sufficient mass for gravity toplay a major role. Planetesimals would need to beabout a kilometer in size in order for the gravitation-ally driven stage 3 to start. Although we do not knowhow stage 2 happens, somehow it must be possible.Fluffy aggregates of dust have been made in thelab but these are typically less than a centimeter insize (Blum, 2000). Larger objects are more proble-matic. One obvious suggestion is that some kind ofglue was involved. Volatiles would not have con-densed in the inner solar system, however. Not onlywere the pressures too low, but the temperatureswere probably high because of heating as materialwas swept into the Sun (Boss, 1990). Organic materialor molten droplets such as chondrules (Wiechert andHalliday, 2007) may have played an important role incementing material together. An alternative to gluesthat has long been considered (Ward, 2000) is thatwithin a disk of dust and gas there is local separationand clumping of material as it is being swept around.This leads to gravitational instabilities whereby anentire section of the disk has relatively high gravityand accumulates into a zone of concentrated mass(Goldreich and Ward, 1973; Weidenschilling, 2006).This is similar to some models envisaged by some forJupiter formation (Boss, 1997).Once stage 2 has occurred, runaway growth buildsthe 1-km-sized objects into 1000-km-sized objects.This mechanism exploits the facts that: (1) largerobjects exert stronger gravitational forces, (2) thevelocity dispersion is small so the cross-section forcollision can be much larger than the physical cross-section for the largest bodies in the swarm, (3) colli-sions resulting in growth are favored if the material isnot on an inclined orbit, and (4) larger objects tendnot to take inclined orbits. The net result is that thebigger the object the larger it becomes until all of thematerial available within a given feeding zone orheliocentric distance is incorporated into planetaryembryos. This is thought to take place within a fewhundred thousand years (Kortenkamp and Wetherill,2000; Kortenkamp et al., 2000; Lissauer, 1987, 1993).The ultimate size depends on the amount of materialavailable. Using models for the density of the solarnebula it is possible that a body of the size of Mars($0.1 ME) could originate in this fashion at its cur-rent heliocentric distance. However, in the vicinity ofthe Earth the maximum size of object would beMoon-sized ($0.01 ME) or possibly even smaller.Building objects that are as large as the Earth isthought to require a more protracted history ofThe Compositon and Major Reservoirs of the Earth 23collisions between the 1000-km-sized planetaryembryos. This is a stochastic process that is hard topredict in a precise manner. The Russian thoreticianSafronov (1954) proposed that, in the absence of anebula the growth of the terrestrial planets would bedominated by such a history of planetary collisions.The late George Wetherill (1980) took this modeland ran Monte Carlo simulations of terrestrial pla-netary growth. He showed that indeed some runsgenerated planets of the right size and distributionto be matches for Mercury, Venus, Earth, and Mars.He monitored the timescales involved in thesesuccessful runs and found that most of the masswas accreted in the first 10 My but that significantaccretion continued for much longer. Wetherill alsotracked the provenance of material that built theterrestrial planets and showed that, in contrast torunaway growth, the feeding zone concept wasflawed. The planetesimals and planetary embryosthat built the Earth came from distances thatextended over more than 2 AU. More recent calcula-tions of solar system formation have yielded similarresults (Canup and Agnor, 2000).Planetary collisions of the type discussed abovewould have been catastrophic. The energy releasedwould have been sufficient to raise the temperatureof the Earth by thousands of degrees. The mostwidely held theory for the formation of the Moon isthat there was such a catastrophic collision between aMars-sized planet and the proto-Earth when it wasapproximately 90% of its current mass. The putativeimpactor planet sometimes named Theia (themother of Selene who was the goddess of theMoon) struck the proto-Earth with a glancing blowgenerating the angular momentum of the EarthMoon system.These dynamics models can be tested with geo-chemistry and petrology, which provide six principalkinds of information relevant to the earliest history ofthe Earth:1. Isotopic heterogeneity in the solar system can beused to trace the sources of the components thatbuilt the Earth and Moon.2. Timescales for accretion, volatile loss, and coreformation can be determined from short- andlong-lived decay systems.3. Conditions of core formation can be determinedfrom metal-silicate partitioning behavior of indi-cative siderophile elements.4. Time-integrated parent/daughter ratios can bedetermined from isotopic compositions of thedaughter elements yielding insights into the(paleo)chemistry of precursor materials.5. Mass-dependent stable isotopic fractionationsprovide constraints on the prevalent processesand conditions.6. Geochemistry and petrology provide our princi-pal constraints on the state of the Earth at the endof accretion.This represents a huge area of science and a conti-nually evolving landscape as new and improvedtechniques are brought to bear on meteorites andlunar samples. The key aspects as they relate to theearly Earth are as follows.9.02.8 The Age of the EarthThe age of the Earth represents a problem that inmany respects is solved. Clair Patterson in 1956published the results of Pb isotopic analyses ofmeteorites that lay on an isochron passing throughthe composition of the silicate Earth and indicatingan age of 4.54.6 Ga (Patterson, 1956). Following thiswork many refinements to the age of the Earth weresuggested based on better estimate of the average Pbisotopic compositon of the BSE (references galore)but the essential result remains unchanged. Thesefurther studies highlight the fact that there are avariety of inherent complications to take into accountin determining an isotopic age or rate. These are veryrelevant to the issue of how well we know the exacttimescales for Earths formation. (see reviews byHalliday (2003, 2006)).In most isotopic dating one has to make allow-ance for the initial daughter isotope that was presentin the mineral, rock, or reservoir when it formed.This can be corrected for adequately or ignored incertain minerals with very high parent-element/daughter-element ratios. For example, the mostaccurate ages of ancient rocks in the continentalcrust are obtained by UPb dating of the commonzirconium silicate mineral zircon. This mineral hashigh U/Pb ratio when it forms and is resistant to theeffects of natural resetting via diffusion. Lead doesnot fit readily into the lattice when zircon grows soany initial Pb is minor and corrections can be madewith sufficient confidence that the ages are extre-mely accurate. The oldest portion of a terrestrialzircon grain thus far found yields an age of 4.40 Ga(Wilde et al., 2001).24 The Compositon and Major Reservoirs of the EarthThere are no rocks surviving from the first500 My of Earths history and no zircons from thefirst 100 My. The age of the Earth and solar system isdetermined using a different approach. Most miner-als and rocks carry a significant proportion of initialPb relative to that formed by radioactive decay. It isnecessary to monitor the initial abundance of thedaughter isotope precisely by measuring the parentand daughter isotopes relative to a nonradiogenicisotope of the same daughter element. This is com-monly done using isochrons which allow one todetermine an age without knowing the initial com-position a priori. There are two isotopes of U whichdecay to two isotopes of Pb. By comparing the Pbisotopic ratios in reservoirs that all formed at thesame time it is even unnecessary to know theparent/daughter ratios, since the ratio 238U/235U isconstant in nature (137.88). It was using these tech-niques that Clair Patterson determined that the ageof iron and silicate meteorites, and the Earth, wasbetween 4.5 and 4.6 Gy. This defines the time atwhich the major variations in U/Pb betweenU-depleted iron meteorites and (variably) Pb-depleted silicate reservoirs, such as the Earths pri-mitive mantle, were established by volatile loss andcore formation.Although PbPb dating was at one time used fordating a wide variety of terrestrial samples, thismethod is all but obsolete except for studying extra-terrestrial samples. Most chondrites contain CAIs,which, as previously explained, are enriched inelements expected to condense at very high tempera-tures from a hot nebular gas, such as U. These are theoldest objects yet identified that formed in theSolar System. CAIs from the Efremovka chondritehave been dated by 235/238U207/206Pb at4.5672 0.0006 Ga (Amelin et al., 2002) and this isthe current best estimate of the age of the solarsystem (Figure 2) which defines a more preciseslope to the meteorite isochron (called theGeochron) first established by Patterson(Figure 10).Since Patterson published his work variousresearchers have tried to estimate the average Pbisotopic composition of the bulk silicate portion ofthe Earth. This provides information on the timing ofU/Pb fractionation caused by terrestrial core forma-tion (Figure 11). The results of these variousestimates are shown in Figure 10. It can be seenthat none plot on the Geochron and this provideevidences that accretion of the Earth, or core forma-tion, or both, was either late or protracted. Theseresults need to be interpreted with caution for tworeasons. Firstly, the average Pb isotopic compositionof the bulk silicate portion of the Earth is very hard toestimate because the long-lived decay of U hasresulted in considerable isotopic heterogeneity. Allof the estimates could in principle be wrong.Secondly, converting these results into timescales isstrongly model dependent involving assumptionsabout how the Earth formed. The results of onesimple model are shown in Figure 10. In this modelit is assumed that no U/Pb fractionation took placeuntil a single point in time. So for example, this coulddescribe an Earth that formed its entire core in asingle event (Figure 12). The ages defined by thePb isotopic compositions correspond to tens ofmillions of years after the start of the solar system(Figure 10). Although such data were at one timeused to date core formation, it is now recognizedthat the processes of accretion and core formation aremore complex than can be described by such anapproach. The data do, however, provide evidenceof a protracted history of accretion and core forma-tion. To sort out that history it is necessary to useshort-lived nuclides, dynamic simulations of planetformation, and petrological constraints on likelycore-formation scenarios.15.817.0 17.562K8946D84446147109102KC9977AL89A88104Geochron = zero ageL915615.314.818.0206Pb/204Pb18.5 19.0207Pb/204PbGG91MKC03DZ79143ZH88KT97BSE lead isotopic estimatesTwo-stage model age (My)Figure 10 Estimates of the lead isotopic composition ofthe bulk silicate Earth (BS