Origin of the Moon

Ever since mankind worked its way through various ideas and beliefs concerning the ancestry of life, he has sought answers to beginning of the Universe. While that question will be discussed in detail later in the Cosmology Unit, this page looks at theories describing the origin of the Moon. When scientists first met to discuss possible lunar origins, three theories emerged:

Please be sure to watch the video that accompanies this page. It takes time to load, but it is excellent.

Capture Theory - states that the Moon was formed elsewhere in the Solar System and was passing by Earth when captured by Earth's gravity. The chief trouble with this theory is obvious from walking the "scale model of the solar system." The planets are so incredibly small compared to the vastness of space that it seems nearly impossible for something big to be captured instead of either missing us or striking us. The mathematical model for the capture of such a large body make this theory imposingly difficult to accept. However, the fact that the gas giant planets like Jupiter and Saturn have captured moons makes this scenario at least remotely possible for Earth.

Coaccretion, or Sister Theory - states that the Moon was formed at the same time as the Earth, from the same accreting material in this neighborhood, and that the two bodies never coalesced into one. This theory has the greatest observational support. Stars are most commonly found in double systems with one star having more mass than another. Indeed, Jupiter appears to be a "star" than never gained anough material to form helium by nuclear reactions, and thus became a mere gas planet. Why would it not be possible for local material in the early solar nebula to form two rocky bodies instead of one larger one.

Fission theory - states that the Moon spun out of a rapidly spinning Earth in a giant blob of material which later rounded into the Moon. The problem with this theory is that such a rapidly spinning earth is not supported by evidence from any other planet. Why would Earth spin so much faster than anything else?

What is significant of these theories is that the astrnomers, geologists, and cosmologists all applied the scientific method to determine which of the three theories might be correct. By getting an exact measure of the chemicals in earth rocks, scientists could create a baseline of data to which extraterrestrial rocks might then be compared. The experimental design then required the collection of rocks from the moon and analytical comparison to earth rocks. If the rocks from the moon and earth are identical, then either the co-accretion or fission theory would be supported. If the rock samples had distinctly different composition, then the capture theory would be supported. After the Apollo astronauts returned with rock samples from the Moon, geologists were able to make careful comparisons. What they discovered was surprising. The rock samples matched the rocks from Earth's crust and mantle, but bore no resemblence to the Earth's interior rock. The result of the analysis demonstrated that all three leading theories were unsupported and a new theory would need to be advanced to explain the moon's origin.

Giant Impact Theory - states that a Mars-sized object slammed into the Earth, knocking off a huge piece of the planet. The debris first formed a ring that quickly coalesced into the Moon, while the impactor probably crashed later into the Sun. The theory was put forward by Dr. William K. Hartmann and Dr. Donald R. Davis in a 1975 article in Icarus. Little attention was given to this theory just because it seemed so improbable to the astronomers prior to the Apollo missions.

Creation Theory - states that a supreme being made the Moon exactly as it appears in the sky and put it in its present orbit. While many cultures worldwide have religious beliefs about the origin of the Moon, only one group is trying to apply scientific methodology to a study of the Moon's origin. You can connect to their website, written by Dr. Hugh Ross.

Four of the five theories listed above can be tested. As stated earlier in the course, it is impossible to test for a Creation Theory, but possible to test for a more youthful Moon than the other theories propose. When Neil Armstrong and Buzz Aldrin returned from the Moon with actual rock samples, scientists were finally able to compare the rocks of the Moon with those of Earth. Depending on similarities or dissimilarities, it would now be possible to make the best choice among the competing four origin theories.

Video that depicts the giant impact and the formation of the Moon. This is a longer video clip, takes time to load, but is excellent as a teaching tool.

Result of the Scientific Study

The Giant Impact Theory, proposed by Hartmann and Davis is the most supported by scientists today. The fact that the Moon lacks iron is the result of the Mars-sized object striking Earth at a glancing angle, knocking out huge quantities of mantle and crustal rock, but missing the expulsion of portions of the iron core. The shattered debris would form a huge ring around the Earth and gradually coalesce into the Moon. The Earth would have been remelted, rehomogenized, and become a molten ball again. The interior would soon fill with the most dense material while lighter rocks would float to the surface, and the Earth would soon restratify with core, mantle, and crust. Interestingly, the Moon would be orbiting significantly closer to Earth than it does today, generating high and violent tides that not only moved the primitive oceans well over the land, but also moved the land itself, generating massive volcanoes and large volumes of steam and ash. It is theorized that the close Moon and strong tides would generate so much volcanism that water trapped in the rocks would be vaproized and collect as steam clouds, only to rain back down onto the planets.

Extra Reading

Two sites are available for your perusal, one of which is more in bullet-point format (Lunar Origin Lesson from UW-Madison), and the other, that is reproduced below. Both conclude the along same lines of reasoning based on the evidence from rock comparisons.

Below is a webpage, constructed by R. Bugiolacchi, and copied here strictly for the purposes of education for this course, and because I found the article to be complete in explanatory detail. Because I was fearful that the page might somehow disappear from the internet, I copied it into my course. You can access the original material, complete with illustrations and formulae by clicking on the author's name.

Introduction and background.

Until Apollo 11's 380,000 km long journey the geological history of the Moon was totally based on conjectures and observational records. Overall the Apollo mission recovered 382 kilograms of moon material from six sites and established an array of seismic stations around the landing areas.

G. Jeffrey Taylor and William K. Harman in 1984 organized a conference to discuss the first findings on the new lunar data. By the time the conference was over, a general consensus was reached about the most plausible origin of the Moon: the 'giant impact theory'. This theory was not entirely new: Baldwin and Wilhelm had suggested in 1946 that the Moon formed as a result of the glancing impact of a planet-size object against the Earth. Even before that Lord Kelvin had asserted that "when two great masses come into collision in space, it is certain that a large part of each is melted" (1908).

In 1975 Davis and Hartmann had been investigating the population of planetesimals close to the early Earth's orbit and realized that numerous large bodies, possibly of the size or even more massive than Mars, might have been wandering near our young planet. Because of one or more of such collisions, some debris would have been ejected into orbit around the planet. Within as little as 100 years this debris could have coalesced into a planetary body.

To date this theory satisfied more than any other the various astronomical and geo-chemical constraints required by the observed facts about the Moon. Since then an interdisciplinary research effort has been directed towards putting this theory into a rigorous scientific framework. Notably Cameron, Ward, Benz, and many other researchers have tried to tackle various problems in this model especially the problem posed by the angular momentum budget. Making use of increasing computer power and more accurate software models, scientists have started simulating the various dynamic scenarios of a number of collision hypotheses answering some questions but also posing some challenging new ones.

The notion of the Earth-Moon system being special and unique considering its almost double-planet nature(1) may be born out of lack of suitable comparisons.

1. Mercury and Venus were probably affected in their formation by solar tides.

2. The rock and ice component of Jupiter to the ratio of its satellite system mass is not much less than the Earth and Moon ratio.

Before taking a detailed look into the alternative models of lunar origin, it is worth summarizing the latest observational data on our satellite.

Bulk Chemistry

It is very likely that the earliest history of the Moon included the formation of a magma ocean and the subsequent development of anorthositic cumulates. This anorthositic crust was then intruded by mafic magmas which crystallized to form the lunar highlands magnesian suite(2).

*The upper mantle of the Moon is probably chemically uniform and may be composed of pyroxenite containing 0.5 - 2 mol.% of free silica(3).

*As we will see in more detail later, the bulk silicate composition (mantle + crust) is significantly enriched in FeO, SiO2 and refractory elements (Ca, Al) compared to chondrites.

*The lunar heat flow is consistent with similar mean abundances of U and Th existing in the bulk Moon and the Earth's mantle.

*About 'half of the Moon' and the 'Earth's mantle' is (by weight) composed of oxygen (16O, 17O, 18O)(4). The O isotope composition of both lunar and terrestrial basalts are identical. In contrast the O in most classes of meteorites possesses distinctly different proportions of the 16O-rich component.

*The most striking geo-chemical difference between the Earth and the Moon is the depletion of iron in the latter. This fact has been suspected from gravitational data for a long time before the direct sampling of lunar material. The Fe/Si atomic ratio is equal to 0.22 as a whole (crust + mantle + core), the lowest known Fe/Si ratio of any object in the solar system(2).

For a body the size and density(5) of the Moon, the inferred mass should be at least 10% less than one of a similar sized sphere formed from the assumed cosmic Mg/Fe and Mg/Si ratios. Even varying the ratio of combined oxygen and taking into account the different forms of iron, i.e. metal, oxide or substituting for Mg in silicates, it is still apparent that the Moon was formed either in an anaemic environment(6) or directly from material already depleted in iron.

*Palaeointensity data concerning the ancient lunar magnetic field, the center of gravity center of figure offset and other physical signs indicate a core formation about 4.1 Ga ago. Unlike the Earth, the Moon's core formed some Ma after its origin and this represents a very significant boundary condition for theories of the Moon's origin(7).

*Lithner and Marti (1974) and Leich and Niemeyer (1975) found that some lunar rocks have trapped Xenon possessing a terrestrial isotopic composition. If proven indigenous and not originally from terrestrial contamination (this gas is only released at temperatures exceeding 1000ºC), this would also indicate a close genesis of our two planetary bodies.

*The current model of the formation of the Moon at a time when the Earth's core had already formed, would be reinforced if the age of Moon's rocks would be younger than some differentiated bodies such as chondrites. Indeed the single stage lead-isotope growth curve both for the Moon and the Earth mantle give a model age of 4.4 - 4.45x10e9 years against the age obtained from some meteorites of around 4.55x10e9 years.

*Our satellite completely lacks any water-bearing minerals.

*There is a depletion of heavy REE(8) in the lunar crustal rocks (usually due to fractionation caused by the crystallization of garnet at very high pressures below the liquidus).

On Earth the pressure at depth of 200-300 km in the primitive magma ocean (at 70-100 kbar) would have caused garnet to co-precipitate with olivine causing depletion of heavy REE. REE relative enrichment(9) in the maria indicates that their magma formation originated under highly reducing conditions and that plagioclase was absent from their source regions. The prior removal of a plagioclase component from the source region of maria basalts explains why the REE europium is instead seriously depleted(10). Differences in the composition of the lower mantle of the Moon indicate a higher FeO and SiO2 contents than the Earth's mantle. The source regions of mare basalt may also have a higher proportion of MnO and Cr2O3

Possible explanations:

On the Earth the early formation through differentiation of the core caused strong convection in the mantle and its melting to a depth of 200-400 km forming a deep ultramafic magma ocean. Several impacts by planetesimals before extensive crystallization (hence soon after the formation of the Earth's core) would have evaporated and ejected material over the Roche(11) limit to form moonlets and ultimately the material constituting the highlands system (following fractionation). Consequently this terrestrial ultramafic magma ocean would have been dominated by fractional crystallization resulting in the separation of olivine; this would have led to a composition richer in FeO, SiO2, MnO and Cr2O3 and significantly poorer (by half) in Ni. A large impact at this stage would have led to the formation of a significant moon nucleus with a similar inferred composition of the source regions of mare basalts. This large nucleus would than attract and consolidate the other earlier moonlets to form the lunar upper mantle. Then it would have taken around 100 years for the upper mantle to melt and differentiate, leading to the formation of the lunar crust.

Volatile Depletion

The Earth's upper mantle is depleted in volatiles in comparison to the primordial composition of the disc-like nebula of dust and gas. Nevertheless the Moon's depletion pattern extends to many volatile elements in relation to C1 chondrites, ordinary chondrites and the Earth's mantle. Take for instance the relative abundances of selected volatile and refractory elements in terrestrial and lunar basalts(12) (Table 2):

Table 2.

What appears quite clearly is that generally the Moon is depleted in volatiles and enriched in refractory elements. Any hypothesis that can stand up to scrutiny on the origin of the satellite requires the Moon to have selectively recondensed from the original material in circumstances under which volatiles were lost. The size of the Moon and its limited gravitational pull have to be discounted as reasons for this process in view of newly acquired geo-chemical knowledge of similar sized planetary bodies (i.e. Io has a substantial volatile component(13)). The depletion of some elements such as Sb and Ge in the Moon can be modeled by the absence of metallic iron during the volatilisation-recondensation phase. Current research and newly acquired data indicate that the estimates of the degree of volatile depletion might be incorrect due to the possibility of volatiles enriching the deep lunar interior. Moreover estimates based on the picritic glasses infer a higher Li/Be ratio for the bulk Moon than estimated from the lunar basalts. This would indicate that the bulk Moon is less refractory than previously calculated from Li/Be data and approaches the bulk composition of the Earth(14). In the whole both highlands and maria rocks have similar ratios of volatile/involatile elements (such as K/Zr).

Siderophile elements(15).

The abundance of siderophile elements Fe, Ni, Co, W, and P are similar (within a factor of about two) in low-Ti mare basalts, parental (PLC) magma in the lunar crust and in terrestrial oceanic tholeiites. Cu, Ga, S and Se where also found to share the same similarities in these three different environments (after having taken into account depletion caused by volatility). Depletion of W and P in the Earth's mantle, and of most of the other siderophile elements in comparison to the PSN, can be explained by their preferential entry into a metallic iron phase which segregated to form the core. However, several siderophile elements - Ni, Co, Cu, Au, Ir and Rh - are present in the mantle in much higher concentrations than expected(16) (according to the model which advocates partition under equilibrium conditions and low pressures into a Fe-rich metallic phase). These discrepancies may be the product of a number of processes, the two most important ones being the changes in metallic/silicate partition coefficients due to the presence of an element of low atomic weight (possibly oxygen or sulfur) within the segregating core and the high pressures deep within the Earth(17). This process is difficult to apply to the Moon in view of its iron depletion; the core of the Moon, if present at all, is only 2% of the lunar mass against 32.5% on the Earth. Moreover the required pressure fields on the Moon are only 47 kbar as compared to 3900 kbar within our planet.

At this point the similarities of siderophile ratios both in the Earth and the Moon become quite significant in helping to understand the origin of the latter. There is not a workable model which envisages the partitions and fractionations of these elements within the primordial nebula. We must conclude that these type of relative abundances of siderophile elements are typically terrestrial in origin.

Different Models of Moon Origin

A number of models had been worked out prior to the latest theory of a giant impact. Most of them fitted a number of direct and indirect observations but also left too many questions unanswered. It is important to keep in mind that as we acquire new data and refine existing models, we have to take into account so many variables and different scenarios that involve complex dynamic planetary interactions and geo-chemical processes; ultimately any new and old hypothesis have to explain all the actual and future physical realities on Earth and on the Moon. We are going to have a look at a number of different theories on the origin of the Moon and we will pay particular attention to the Single Impact Hypothesis, the model most agreed upon in the scientific community.

CAPTURE HYPOTHESIS

The most problematic of the older models was the capture hypothesis. The idea is that the early Earth had seized a fully formed moon that come too close to our planet. It was soon realised that two fundamental problems undermined this model: first the extreme unlikeness that the correct dynamic and gravitational circumstances would have occurred; second, lunar samples showed that the Earth and the Moon have similar quantities of oxygen isotopes, suggesting a close kinship. Early in the formation and harmonic condensation of the solar nebula, objects up to of a mass similar to Mars were being accreted and captured by the more massive proto-planets. However both theoretical models (Safronov) and computer simulations show the extremely unlikeness of a capture scenario for a body of the mass of the young Earth (around 2/3 of modern size when the Moon came into being).The main theoretical obstacle is the high encounter velocity (typically a few kilometres per second) and the required dissipation of the satellite's kinetic energy.

One possible scenario involves a gradual and progressive slowing down of the proto-satellite's velocity. This is extremely unlikely because it does not take into account the violent environment at the time, where other more or less massive bodies would have caused incoherent and widespread scattering. This would ultimately have lead to an increase in velocity rather than decrease. Nakazawa et al (1983) suggested that gas drag would have helped to gravitationally join the two bodies, but again, this model too requires a very small encounter velocity. Besides, this thick gas envelope would have to be lost very quickly otherwise the moon would have finally spiralled inward and accreted onto the Earth. Ultimately this model fails to explain the similar geo-chemical evidence (such as similar d 18O ratio) of the Earth and the Moon which points to a common origin within the solar nebula, suggesting a close kinship.

FISSION HYPOTHESIS

The fission hypothesis presented fewer but still fundamental problems. According to this theory, first proposed 100 years ago by George Darwin, after forming its core the early earth was spinning so fast that it formed a prominent bulge at the equator. Eventually a sizable chunk of material was thrown off into orbit. Unfortunately calculations showed that for the Earth to have the necessary centrifugal force it would have been rotating once every 2.5 hours. The slow accumulation of dust grains in the early stages of the earth's origin cannot account for such spin. Even the continuous bombardment of planetesimal would averaged themselves out in the long run. Moreover the inclination of the Moon's orbit is not in the equatorial plane of the Earth (although some researchers do not rule out a successive 'migration' to the present orbit). This model takes into account the lower density of the Moon, implying a small metallic core (if at all). A fissioned moon would be composed mainly of the earth's mantle. It also seems to explain the siderophile element depletion placing "the moon's nickel in the earth's core" (Ringwood, 1979). Nickel, being more siderophile than iron, if accreted from the cosmic component, would have to be enclosed within the moon's core radius. This is at odds with the density values and inertia constraints which restrict a metal core to a radius of less than 400 km.

Also if the Moon would had come into being just as a 'lump' of mantle material, its rocks would have had to contain more nickel and less of the other siderophile elements due to the fact that when the Earth formed it had not attained full equilibrium. Moreover, apart from the similar oxygen isotope abundance, the Earth and the Moon are different in many other geo-chemical properties. For instance not only has the Moon a much lower concentration of many volatile elements in respect to the Earth's mantle, but it is also seriously depleted of certain fundamental volatiles such as potassium and sodium (see bulk chemistry above for more details). On the other end it appears that refractories such as aluminum, calcium, thorium, uranium and the REE are present in the Moon in concentrations up to 50 percent higher than in the Bulk Silicate Earth. An additional difficulty of this model is the discrepancy between the ratio of iron oxides to magnesium oxide, about 10 per cent higher in the moon than in the terrestrial crust and mantle.

Altogether if the lunar interior and the mantle of the Earth share a common origin we would expect the lava extruded from the mantle (in comparable tectonic environments) to be very similar. The many distinctions observed make this hypothesis very objectionable.

The Precipitation Hypothesis

This hypothesis tries to remove some of the difficulties associated with fission by combining elements from both the double planet and the fission theories. According to this model the Earth began to accrete within a short time from the solar nebula with the an overall CC1 composition. As the Earth grew in size, gravity started playing a major role on the energy release of the impacting bodies. On this assumption the surface temperatures approached 2000ºC in the final stages vaporizing any incoming objects. As this point reduction of iron from oxide to metal released massive quantities of hydrogen and carbon monoxide resulting in a thick atmosphere which also included between 10 and 20% of volatilized silicates. These would have condensed and formed a ring around the Earth. Volatiles and gases would have been swept away by the early intense solar radiation. A residual material enriched in refractory elements (from which a metallic phase might have already been separated) and depleted in volatiles and siderophile elements would be left behind.

Öaut;pik (1955) formulated a model which predicted the condensation of the Moon from such a ring. As the Moon grew in size, it gravitationally swept up larger objects which would have caused the heavy cratering in the upper uplands. The last stage would have accomplished the final capture of the larger objects (50-100 km) which would have impacted on the newly formed lithosphere and produced the giant ringed basins. The Precipitation hypothesis still does not offer a satisfactory answer to the dynamic problem.

DOUBLE PLANET (accretion) HYPOTHESIS

Lastly the double planet hypothesis states that the Earth and the Moon formed concurrently from a cloud of gas and dust. Ruskol (1960) elaborated that when two planetesimals collide within the Hill sphere of a planet some of the debris end up in orbit due to their high angular momentum and low intrinsic energy. Eventually this debris forms a disk in the equatorial plane that is fed by particle collisions from incoming planetesimals. When the main showering phase ended, satellites of various sizes could form beyond the Roche limit. Unfortunately these newly accreted bodies would be following the same thermal evolution as the Earth, i.e. temperatures would never be hot enough to allow for total melt of at least the lunar mantle (forming the modeled primordial 'magma ocean'). Moreover there is a basic problem with the critical quantity and mass of the planetesimals (Stevenson et al, 1986) for this model to work.

This model fails to explain the present 5º 09' inclination of the lunar orbit to the plane of the ecliptic. If the Moon had formed close to the Earth, it would have orbited the equatorial plane. On the other hand if it had formed further away it should orbit the plane of the ecliptic. It is also difficult to explain why the Earth is 1.6 times denser than its moon(18) given that the two bodies had formed at the same time from the same area of the solar nebula. The apparent problem given by the lunar Fe depletion could be addressed by modeling the orbiting ring of material as a compositional filter. The heavy metallic particles would have 'rained' down to the Earth. Unfortunately this idea does not offer a proper explanation for the differences in volatiles and refractories. Besides we have to call upon additional selective fractionation of silicates in order to explain the fact that the lunar interior is different in composition to the terrestrial mantle. Most unsatisfactory is the lack of explanation for the angular momentum that the Earth ought to have had to keep a spinning ring of material and the present 24 hours rotation.

GIANT IMPACT HYPOTHESIS

Physics of Large Impacts

The physics of large impacts are very difficult to model and simulate mathematically because of the quantitative scale well beyond current computative capabilities. Nevertheless especially in the last few years a number of scientists and engineers(19) have tried to use powerful workstation computers to recreate a silicon model of the outcome of impact on a planetary scale. The fate of the debris generated by an impactor after hitting a planetary body is governed by the r-1 gravitational potential (Keplerian trajectory). If its total energy (gravitational plus kinetic) is positive then debris escapes on a hyperbolic trajectory; otherwise it traverses a closed elliptical orbit destined to re-impact the planet's surface. In order to eject enough material over the Roche limit there must be a mechanism by which even debris with negative energy is given a 'second burn' and finally pushed into orbit.

Two possible processes(20):

pressure gradients near the impact site increase the angular momentum of material ejecting it into orbit.
The proto-moon gains the angular momentum necessary to escape a re-entry by gravitational torque exerted by the bulge or discrete body on the planet.

Thermodynamics of Impacts

Irreversible entropy production is achieved when the impact material is subjected to very rapid high pressure and temperature shock. It then expands approximately isentropically(21) from the peak pressure stage(22). The temperature at which vaporization occurs is sensitive to pressure and is conventionally modeled at a nominal 1-bar pressure. Because of the size of the suggested impactor (³ Mars!) energy release from the rain-out of debris has to be accounted for when assessing vaporization. Various mathematical models have been used to try and quantify the entropy production upon shock compression. One of the most widely used are based on this expression entropy production: *(23); after a number of assumptions and derivations we end up with this final expression:

*(24)

It is apparent(15) in this expression(19) that D S is only a weak (ln) function of impact velocity. This is because at very high impact velocities a volume much larger than the projectile volume is at least vaporized and it is the integral over all this volume that is relevant(25). This model also takes into consideration that the temperature of the Earth's surface at the time of the impact was around 1800 K and molten (magma ocean, Rigden & Ahrens, 1981). Applying these constraints to the expression(18) we see that material subject to a 10 km s-1 impact is about 20% vapor, 80% liquid by mass at P = 1 kbar (T~4000K). Eventually as expansion proceeds even the liquid boils producing more vapor.

Other calculations were carried out and a figure of 3 ´ 10e38 erg(26) was estimated for the energy release of a Mars-sized projectile impacting at 10 km s-1. This injection of energy would be sufficient to raise the average temperature of the Earth by ~ 5000 K. This would have formed a deep magma ocean with a surface that merges continuously with a thick vapor atmosphere. Assuming an atmospheric temperature Te of ~ 2000 K and applying the formula = t cool (cooling time) » 103-104 yr. This proves that such a giant impact would have enormous consequences for the development and geological history of the Earth.

Viscosity of Ejecta

In order for some of the material ejected from the surface of the Earth to make an orbital injection (after only one orbital period) we have to consider its viscous properties. Viscosity acts on the material by increasing its angular momentum. By applying physics of accretion disks(27) in a steady state we have F[dh/dr] = [dg/dR]*(28) Solving this equation (with g = 2p R3n s W) we found that we need a viscosity n ³ 0.01 R2W or n ³ 10e14-10e15 cm2s-1 in order to raise the periapse of outer material in the disk in one orbital period. This value is very high, comparable to glacier ice on Earth; nevertheless this kind of viscosity can be produced by fluid dynamic instabilities.

Dynamics

Most of the mass which is likely to end in orbital injection is in the state of vapour. For the periapse to lie above the Earth: where x º h/RÅ, and B and A relate to the vertical and horizontal velocities. A second burn (non-ballistic processes) must to be taken into account to approximate values for x and Vt so that injection is possible. This is achieved by pressure-gradient acceleration up to a significant fraction of the Earth's radius.

Starting from the Euler equation , which after a number of assumptions can be expressed as ~ 3(Mproj/MÅ)1/3(Vimp/14 km s-1)2/3 or as the predicted value of x. This equation predicts a very weak dependence of injection efficiency on projectile mass15. This result also suggests that all impacting bodies with mass ³ 10-3 MÅ are capable in theory to eject material both from the target and the impactor into orbit. To recap, substantial vaporization is achieved by a hot projectile of the size of Mars or greater hitting either a hot or molten surface at a speed ³ 10 kme-1.

Numerical simulations

Since 1986 Cameron and Benz investigated the problems in the mechanics of ejection of vapor into orbit. Using a method called the smooth particle hydrodynamics (SPH) Cameron(29) investigated three cases of collisions. All of them using a program based on the simulation of a Protoearth and an Impactor made up of 5000 particles of equal mass and fixed smoothing lengths. The ratios at the hypothetical impact were (Protoearth/Impactor) 5:5, 6:4 and 7:3. The temperatures of the impacting bodies were set to 2000 K which is an agreed value for an early Earth's surface temperature. Each of these collisions took into account an angular momentum slightly over the modern Earth-Moon system.

The simulations agreed with a rather simple scenario. When the Earth was hit by the Impactor, a very hot magma ocean was formed. This molten surface underwent extensive evaporation to hot rock vapor. An atmosphere, both hydrostatically and centrifugally supported, formed around the planet and it stretched to up to 8 Earth radii (with temperatures >4000 k) and over 20 Earth radii (T > 2000 K). Theoretically this scenario would have worked because it offers an explanation to the lunar iron depletion (the Impactor core being 'swallowed up' by the Earth) and its enrichment in refractory material. Unfortunately the amount of mass available in this scenario over the Roche limit is far too little to form a sizable moon.

Initially it was thought that pressure gradients were instrumental in giving the ejected vapor the extra boost necessary to end up orbiting the Earth. Following the computer simulations it became apparent that gravitational torques are the main forces acting on the expanding vapor. Indeed a scenario which can be successfully simulated requires high-angular-momentum Earth/Moon collision with a mass ratio of at least 8:2 (in agreement with Can& Esposito, 1996). The problem with dissipation of this high-angular-momentum collision can be solved if we imagine the impact to have taken place when the Earth was only some 50 to 90% accumulated.

It is clear that much more software simulation of collision has still to be carried out, and indeed Cameron et al are already at work on simulations involving Impactor/Protoearth ratios of around 0.3 to 0.5 and with the Earth mass a fraction of the present.

Lunar Accretion from the Impact-generated Disk

As we have mentioned before, the possible consequence of a planetary impact is the formation of an orbiting disk rather than the direct formation of a body. Most models at present predict a circumterrestrial disk of around 2.5ML(30) stretching from near or interior to the radius aR of the Roche limit. The angular momentum of the impact would have been 1-2 JEM(31). Canup and Esposito (1995) argued that according to their models many small moonlets are initially formed instead of a single massive one. In order to simulate the formation of a single moon sized body one needs to begin with at least a lunar mass outside the Roche limit. However their modeling of the velocity evolution, accretion and rebounding of disk particles failed to take into consideration non-local effects such as radial migration of the disk material and the gravitational interaction of the moonlets and the disk32.

Ida et al (1997) showed that, allowing for the possible formation of moonlets at different orbital levels, using 27 N-body simulations to model accepted initial conditions and constraints, only a single moon would form. It would only take 100-1000 orbital periods to finally accrete. Its mass would be determined by a function of initial mass and angular momentum of the disk. Whether colliding particles accrete or rebound depends on their orbital positions. Within ~ 0.8 aR tidal forces preclude accretion. In the transition zone (0.8 - 1.35 aR) limited accretion could take place. Outside the Roche limit tidal forces would not effect the vapor disk. Clearly in order for the particles to accrete their rebound velocity must be smaller than some critical value of mutual escape velocity.

Ida et al simulations showed how, initially, the disk compacts in the z direction and diffuses radially by angular momentum transfer. Eventually the disk scale height becomes so small that the disk's own gravity becomes predominant, due to density waves in the denser regions of the disk. These waves, which simulations display looking like spiral arms, increase momentarily the angular momentum transfer and extend disk material outwards. These transient waves are instrument in forming large bodies near the Roche limit which start to effect the whole gravitational system of the disk, hence stopping the gradual and smooth disk evolution before it "converges to some common geometry"(26). A large body with up to 90% of its final mass takes form near the Roche limit within 150 - 250 days of the impact. Due to its substantial mass the entire disk is perturbed by the moon's gravity. Most of the disk particles are then destined to either be captured by the Moon, scattered onto the Earth or sent into hyperbolic orbits.

The final position of the moon would depend on the recoil of the accreted disk particles and tidal interaction with the Earth. This would result in a outward migration which would cause the moon to accrete most of the disk material outside its original reach. The final mass of the moon can be predicted by applying a derived formula of the conservation of angular momentum: , where M¥, Mdisk are the mass of the largest moon. As we can see the final mass of the moon is strongly proportional to the disk's angular momentum and the mass of the proto-moon and disk. Moons with masses similar to our satellite can be obtained by impacts with ³ 2JEM. Unfortunately this model still leaves us with problems about the dissipation of this initial excess angular momentum. It also fails to take into account the unsatisfactory modeling of the coalescence of the multiple moons.

Chemistry of the Impact Hypothesis

As it has been mention in more than one occasion, the bulk composition of the Moon either originates from the projectile(33) or from both the target and projectile(34). Ringwood (1966, 1979, 1986) advocates the mixed terrestrial/extraterrestrial origin unless the Impactor (as seems very likely) was massive enough to have undergone similar differentiation and processing as the Earth's mantle. Ultimately the Impactor should have a mass ³ Mars, not only as we have seen because of dynamical constraints, but also to account for the necessary presence of an iron core. Planetary bodies of this size undergo preferential core formation thus forming a suitable mantle as a source of Moon-forming material. Indeed the Moon's anaemia remains one of the most intriguing factors when we are trying to model a correct lunar forming scenario. Liquid iron, if present in the disk system, would form a sub-layer at the equatorial plane of the disk but it would spread at the same rate as the rest of the disk(15).

Iron is also comparably volatile to the silicates (as FeO) and Hashimoto (1983) suggested that the iron oxide would have evaporated away. There is also the possibility that the Impactor's core would have merged into the Earth's mantle(35). Recent analysis of lunar rock samples have found high Hf/W non-chondritic ratios but also a chondritic W isotopic signature consistent with the Moon post-dating the formation of the Earth's core(36). This findings have therefore put the putative giant impact and formation of the Moon to have taken place between 4.515 and 4.500 Ga.

The loss of certain compounds can be predicted comparing the escape energy Eesc(37) at 4RÅ with; kinetic energy Ekin(@ 3/2 (kT)): *(15), Hydrogen can clearly escape, but MgO, O2 and SiO cannot.

Accepted models for the formation of the Earth's core during the first 90% of accretion history are difficult to reconcile with the W isotopic data unless the proto-Earth was re-homogenised by a major impact(38). Indeed a massive impact event might have triggered the formation of the Earth's core and the degassing of Xe from the terrestrial mantle. Otherwise the Hf-W data may define the age of a core that formed as a result of another impact shortly prior to that which formed the Moon. Present day amounts of xenon, krypton and argon in the atmosphere can be explained following deposition of thermal energy by a giant Moon-forming impact(39). Water brought into the outer edge of the disk by silicate droplets would be disassociated by the environmental temperature and pressure(40). The hydrogen would eventually escape and the oxygen combine with silicates. Stevenson (1987) concluded that the disk acted as a closed system with neither loss of material (except for H and H2O) or differentiation. Ultimately the lunar composition has to be compared and modeled on the colliding bodies' geo-chemical make-up and dynamics.

Conclusion

Despite the amount of direct and inferred evidence for the giant impact hypothesis the reality is that there is still a lot of research and modeling necessary to explain too many theoretical and physical problems. The alternative theories that were discounted in 1984 are far from being dead and buried. Especially the fission and binary accretion hypothesis which may one day resurface as possible scenarios. Three-dimensional hydrodynamic simulations are still quite basic approximations even when using the most modern computers and N-point modeling software. In particular the role of pressure gradients in the post-impact flow is not yet understood(15). A hot silicate vapor atmosphere requires a global terrestrial magma ocean. Evidence or traces of this has still to be found.

Current calculations are still based more on theoretical models than on sound mathematical basis. In particular we don't have mathematical models for the formation of a orbiting disk, the actual ratio Earth/Impactor of initial ejecta over and within the Roche limit, the speed of accretion, and the real possibility that the Moon was only the last, albeit probably the largest of a few potential proto-moons.

Currently we are witnessing a resurgence of scientific interest on our satellite. After successfully using the Clementine satellite to create detailed maps of the surface of the Moon, NASA launched on 7 January 1998 the Lunar Prospector Orbiter. During its one-year polar orbiting mission this satellite will have the exciting and exacting task of sleuthing some of the Moon's remaining mysteries, including whether or not water ice is buried inside the lunar crust. Lunar Prospector will be followed by two Japanese missions: 'Lunar A', lunar Orbiter and Penetrators in 1999; this will be followed by another Lunar Orbiter, Selene, in 2003.

However, although many problems at present are still unresolved, we can predict with a certain degree of confidence that a complete model of lunar origin will probably contain many elements belonging to a giant impact scenario.

1 The lunar mass is approx. one eightieth of the Earth's mass.
2 C. R. Neal, A. N. Halliday, G. A. Snyder and L. A. Taylor, 1995
3 O. L. Kuskov, 1997
4 two different origins of variations in the ratios: a) primary isotopic inhomogeneities in the O in various regions of the solar nebula prior to accretion, due to the non-uniform distribution of a nuclear component rich in 16O, possibly injected via a supernova explosion; b) chemical isotopic fractionations caused, for example, by differing temperatures at which the solar matter which accreted to form planets and meteoritic parent bodies equilibrated and then became separated from the gases in the parental solar nebula, PSN).
5 3.344 ± 0.002 g cm-3
6 There is no direct evidence that the Moon has an iron core at all, but almost certainly, if existing, it is at most ~400 in radius.
7 S .K. Runcorn, 1996
8 Rare Earth Elements
9 In comparison to Carbonaceous Chondritic 1 (CC1).
10 Europium behaves anomalously in that it can take a divalent form (Eu2+) which is the right size to substitute for Ca in the crystalline lattice of feldspar (unlike the other REE (exp. Cerium) which are trivalent).
11The Roche limit is the orbital distance at which a satellite with no tensile strength (a 'liquid' satellite) will begin to be tidally torn apart by the body it is orbiting. A real satellite can pass well within its Roche limit before being torn apart (at 2.89 Earth radii).
12 Open University, S267 course 1994
13 D. J. Stevenson, 1987
14 C. K. Shearer, G. D. Layne, J. J. Papike, 1994
15 O'Keefe, (1972); O'Keefe and Urey (1977); Ringwood and Kesson (1977); Rammensee and Wänke (1978) et al.
16 Between 10 to > 100 times higher.
17 Ringwood (1979).
18 Allowing for the difference in internal pressures.
19 R. M. Canup, Larry W. Esposito (1995), Shigeru Ida (1997) et all.
20 D. J. Stevenson (1987)
21 Process that takes place without a change of entropy.
22 Supercritical state, neither a gas or a liquid.
23 Where Th = temperature behind the shock wave. Ts = temperature of material is compression were isentropic, Cv = specific heat.
24 g = Gruneisen parameter, b =d ln P/d ln r and V = impact velocity.
25 The integral over all this volume scales roughly linearly with peak shock pressure.
26 Defined as the work done by a force of 1 dyne when it acts through a distance of 1 cm (1 erg = 10-7 joule).
27 Lynden-Bell & Pringle, 1974
28 F = total mass flux radially outward at radius R of a disk of material with local specific angular momentum h = R2W (W is the angular velocity) and viscous couple g. (Stevenson 1987).
29 A. G. W. Cameron, 1996
30 ML is the lunar mass, 0.0123 times the mass of the Earth 'MÅ '
31 JEM is the angular momentum of the present Earth/Moon system.
32 Shigeru Ida, Robin M. Canup & Glen R. Stewart (1997)
33 Benz and all 1986a, b
34 Melosh & Sonett 1986, Kipp & Melosh, 1986
35 Benz et all 1986b
36 D. C. Lee, A. N. Halliday, G. A. Snyder and L. A. Taylor, 1997
37 Eesc = GMÄ m / 10RÄ : where m = mass of atom or molecule
38 A. Halliday, M. Rehkamper, D. C. Lee, W. Yi, 1996
39 R. O. Pepin, 1997
40 T ~ 2000 K, P(H2O) ~ or = 10-6 bar.

[ Chronology of Lunar Exploration / References ]

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You have finished your study of Phases, Features, Tides, and Origins. Time now to make some applications. A lab activity awaits you at Why Are All Lunar Craters Round, as well as a Moon Observation, that you have already looked at. When you have an idea of what you are doing for these two assignments, then move ahead to the Solar System Introduction, or return to the Moon Introduction, or the Syllabus.

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