SP-345 Evolution of the Solar System



Special Problems





There are a large number of theories of the origin of the Moon and of the evolution of the Earth-Moon system. A review is given by Kaula (1971). Neglecting those which obviously are dynamically impossible (unless a number of improbable ad hoc assumptions are introduced) we are left with two alternatives:

(1) The Moon accreted as a satellite of the Earth.

(2) The Moon was originally an independent planet that was later captured by the Earth.

If we confine our analysis to the Earth-Moon system a decision between these two alternatives is very difficult to make, indeed just as difficult as determining the origin of the planetary system from an analysis confined to the planetary system alone. As we have found, a clarification of the evolution of the planetary system is made possible only by comparing it with the satellite systems. This "hetegonic principle" is, indeed, what has made our analysis possible. Similarly, we can expect to understand the evolution of the Earth-Moon system only by comparing it with the other satellite systems.

We have found that accretion of secondary bodies around a primary body is a regular process, which can be described in detail and is summarized in the matrix of table 23.8.1. If these semiempirical laws are applied to the Earth, we see that satellites would be expected to form around this planet. Hence on a qualitative basis alternative (1) is reasonable. However, from a quantitative point of view we find that natural satellites of the Earth should have a mass three or four orders of magnitude smaller than the lunar mass (sec. 24.3). Hence it would, on this basis, seem highly unlikely that the Moon was accreted in the surrounding of the Earth. The fact that the Moon is definitely not a normal satellite has long been recognized.

The capture alternative brings the Moon into the same category as six other satellites (Jupiter 8, 9, 11, and 12, Saturn's Phoebe, and Neptune's Triton). The capture mechanism should be discussed with all these seven bodies in mind. Of these, five are very small and Triton is the only one which is comparable to the Moon in size. Hence the Earth-Moon system [454] is to some extent analogous to the Neptune-Triton system. We can regard both systems as "double-planet" systems.

The reason why we find double planets in these two places in the solar system is obvious from our analysis of the emplacement of the A, B, C, and D clouds (Fig. 21.11.2). In both cases two adjacent clouds overlap, the A and B clouds because of the closeness of the corresponding critical velocities and the C and D clouds because the high T/ [Greek letter] tau value in the planetary system makes the C cloud extend further out than in the satellite systems. Hence we find that the A cloud is emplaced so close to the B cloud (which has produced Mercury, Venus, and the Earth) that the innermost member of the A cloud, the Moon, comes very close to the outermost member of the B cloud, the Earth. Similarly, the innermost member of the D cloud, Triton, was produced very close to Neptune, the outermost member of the C cloud.



We know several examples of systems of secondary bodies encircling a primary body: The planetary system, the Jovian, Saturnian, and Uranian systems which are all well developed with five or more secondary bodies. The Martian system with only two satellites may perhaps also be included as a fifth system.

As discussed in previous chapters, the formation of secondary bodies encircling a primary body depends upon the critical velocity effect (ch. 21) and the transfer of angular momentum from a massive primary which rotates and possesses a magnetic dipole field (sec. 1.2, chs. 17 and 23). We have found (ch. 21, fig. 21.2.1) that the bodies in the solar system can be grouped as a function of gravitational energy. We see in fig. 21.2.1 three bands in which all the secondary bodies fall. Whether the tiny satellites of Mars indicate the existence of a fourth band is doubtful. We find further that whenever a band is located far enough above the surface of a central body (beyond the synchronous satellite orbit), we have a formation of secondary bodies in the region.

There are three exceptions to the general validity of the diagram: Venus has no satellites, probably because of its extremely slow rotation and lack of a magnetic field. Further, we find no satellite systems of the normal type around Neptune and the Earth. The reason for this seems to be straightforward. Both these bodies might very well have once produced normal satellite systems but they have been destroyed by the capture of Triton and of the Moon. Mercury has a very slow rotation, probably no magnetic field, and is probably also too small for satellite formation. Whether Pluto has any satellites is not known.



The regularity of the diagram (fig. 21.2.1) can be used as a basis for reconstructing the normal satellite systems of Neptune and Earth.

As Neptune has a mass which is only about 20 percent larger than that of Uranus, we expect its satellites to be rather similar to the Uranian satellites, but with orbital radii 20 percent larger (see eq. (21.10.2)). Such a system may have existed once, but when Triton was captured and slowly spiraled inward due to tidal interaction (McCord, 1966) it destroyed the original satellites which had masses of only a few percent of the mass of Triton. As McCord suggests, Nereid may be the only survivor (with a strongly perturbed orbit), the other satellites having collided with Triton.

The extrapolation from Uranus to the Earth (table 24.3.1) is more precarious because the mass ratio is as large as 14. The main effect should be a reduction of the orbital radii of the satellites by a factor 14. This would bring the counterpart of Oberon down to an orbital radius of 6.34 Earth radii, and that of Miranda to 1.37 Earth radii, the latter well inside the Roche limit of the Earth.

The accumulation of matter close to the surface of the Earth is likely to have been rather similar to the inner Saturnian satellite group (Rhea Janus). In fact, the orbital radius of Rhea is 8.7 times the radius of Saturn. A reasonable guess would be that the Earth should have formed about hall a dozen satellites (and perhaps also a ring).


TABLE 24.3.1. Earth Satellite Regions (Transposed From Uranian and Martian Systems.


Orbital radius

Radii of orbits with equal energy in Earth's gravitational field


109 cm

109 cm

Earth radii


Martian satellites










Uranian satellites





















( ) Indicates orbits within the Roche limit of the Earth. (From Alfvén and Arrhenius, 1972a.)



[456] If the Martian system is extrapolated we should in addition expect a group of satellites at a distance of 13.5 to 34.2 Earth radii. The inferred normal satellites of the Earth would not be expected at the exact positions shown in table 24.3.1, but rather in the general regions indicated.

For an estimate of the masses of the Earth's satellites we plot the total mass of the secondary bodies as a function of the mass of the central body (fig. 24.3.1). We see that the total masses of the planets, and of the Jovian, the Saturnian, and the Uranian satellites all lie on a straight line; the extrapolation of this to the Earth gives 2 X 1023 g for the total mass of the Earth's normal satellites.

If we take the Martian system into consideration, the curve should bend downward and give a value of about 1022 g for the Earth. This means that the individual satellites may have had masses in the range 1021-1022 g. Even....


FIGURE 24.3.1.- Total mass of secondary body systems as a function of central body mass.

FIGURE 24.3.1.- Total mass of secondary body systems as a function of central body mass. Both Triton and the Moon have much larger masses than expected of normal satellites. Two possible mass estimates for a normal Earth satellite system are shown, one based on an extrapolation from the systems of Jupiter, Saturn, and Uranus, and the other, an interpolation also including the Martian satellite system. (From Alfvén and Arrhenius, 1972a.)


[457] ....the highest value is only a small fraction of a percent of the lunar mass (0.73 X 1026 g).

The structure of a system of secondary bodies depends not only on the mass of the central body as indicated by fig. 21.2.1, but also on its axial rotation. (This is the main reason why the bands in fig. 21.2.1 have a slope (sec. 23.9.2) instead of being horizontal, as would be expected from an extrapolation which assumes that the gravitational energy of a specific cloud is constant for all central bodies.) Spin of the central body is essential for the transfer of angular momentum to the surrounding plasma which condenses and later accretes to secondary bodies.

The relevant parameter in this case is mathematical symbol, where [Greek letter] tau is the spin period of the central body and Tion is a characteristic orbital period of the group of secondary bodies defined in sec. 23.5. Figure 24.3.2 shows the number of secondary bodies as a function of mathematical symbol
for the different groups of satellites. Although the curve is purely empirical, theoretically we expect the....


FIGURE 24.3.2

FIGURE 24.3.2.- Number of bodies in a satellite group is a function of mathematical symbol
(where [Greek letter] tau
is the spin period of the central body and Tion is a characteristic orbital period of the bodies in the group (sec. 23.5)). The groups of satellites are the outermost Saturnian satellites (Saturnian D cloud), Galilean satellites (Jovian C cloud), Uranian satellites (Uranian D cloud), inner Saturnian satellites (Saturnian C cloud), and innermost Jovian satellites (Jovian B cloud). Assuming that the Earth's satellite system would fall into the pattern established by these groups of satellites, the Earth may once have had just a few or as many as 9 or 10 normal satellites. (From Alfvén and Arrhenius, 1972a.)


[458] ....number of satellites to drop to zero as mathematical symbol
approaches unity (ch. 23), and this is clearly indicated in fig. 24.3,2. As there are no observational points between mathematical symbol
= 1.6 and 8.4, the shape of the curve in this region remains uncertain. A lower limit to this part of the curve is obtained by placing the maximum of the curve at 8.4 (the point corresponding to inner Saturnian satellites), while an upper limit may be estimated by a freehand extrapolation with a maximum as high as 9 or 10 before the curve drops toward zero.

If we want to make a conjecture about the number of normal satellites of the Earth, we need to know the value of T/[Greek letter] tau for the Earth. Using the present value of the Earth's spin period, which is 24 hr, we obtain T/[Greek letter] tau
= 0.36. Obviously, we should use instead the spin period of the Earth before the Moon's capture resulted in tidal braking of the spin. There are various ways of estimating this period. Gerstenkorn (1955) found a precapture spin period for the Earth of about 2.6 hr. If we assume the Earth once had the entire angular momentum of the present Earth-Moon system, a value of about 4.1 hr is obtained.

Yet another way is to use the empirical observation that the quantity mathematical symbol
is constant for the planets, where [Greek letter] capital theta is the average density of a planet (see sec. 13.4). Applying this relation to the Earth and Jupiter we obtain a period of about 4.7 hr, while the value of 3.4 hr is indicated by applying it to the Earth and Saturn instead.

All these considerations indicate a value of the original spin period of the Earth somewhere in the range 3-5 hr, thus placing the value of T/[Greek letter] tau
in the range of about 2-3. Unfortunately, this falls in the uncertain interpolation region of the curve in fig. 24.3.2. We cannot be sure if the number of original satellites was 2 or 3 or as high as 8 or 9.

Furthermore, if the Martian satellites, which are excluded from the scheme of fig. 24.3.2, are included, we may expect another group of perhaps four or five more satellites for the Earth.

In conclusion we see that if we apply the principle that the Earth should be treated in the same way as the other planets, we arrive at a satellite system which, even if we cannot at present reconstruct it in detail, in any case is very different from the Earth-Moon system.



According to Kaula (1971), the capture hypothesis (Alfvén, 1942, 1943a, 1946, 1954) "is an improbability, not an impossibility." However, he does not clarify why a lunar capture is improbable. In reality both observations and theoretical evidence indicate the contrary.

In the solar system there are six retrograde satellites (see table 2.1.3). [459] There is general agreement that all of them must have been captured. Figure 24.4.1 shows their orbital inclination and distance rsc, with the radius Rc of the planet they encircle as unit. (If instead the distance to the closest Lagrangian point, which may be more relevant to the capture process, is chosen, a rather similar diagram is obtained.)

The diagram shows that the orbits of the small retrograde bodies are situated in the region rsc / Rc = 200-350 and i = 145°-175°. We can well imagine that Triton originally was located in the same region but that tidal interaction has brought it closer to Neptune. The reason for this is that Triton is much larger than the other retrograde satellites, which are much too small to produce significant tidal effects. Hence observation indicates that a capture mechanism exists which results in wide capture orbits, subsequently contracting if the captured body is large enough to cause tides.

A body like the Moon may very well be captured in this manner. Furthermore, mechanisms exist (Gerstenkorn, 1955) by which the body can be transferred from such a shrinking capture orbit into a prograde orbit of the present lunar type. Therefore there could be no fundamental objection to the capture theory.


FIGURE 74.4.1.- Possible evolution (dashed lines) of the orbits of Triton and the Moon.

FIGURE 74.4.1.- Possible evolution (dashed lines) of the orbits of Triton and the Moon. These bodies are massive enough for tidal effects to modify their orbits from the typical large semimajor axis, retrograde orbit characteristic of the smaller, presumably captured satellites shown in the diagram. (From Alvén and Arrhenius, 1972a.)



[460] Capture requires that the body approach the planet in an orbit with parameters within rather narrow limits. Thus if a body approaches a planet in a random orbit, the chance that the approach will immediately lead to capture is very small. The most likely result of the encounter is that the body will leave the region of the planet with its orbit more or less changed. It is probably this fact which is behind objections to the capture theory.

However, we learn from Kepler that if the body leaves the neighborhood of the planet after an encounter, it will move in an ellipse which brings it back to the vicinity of the orbit of the planet, once or twice for every revolution. If the body is not in resonance, it will have innumerable new opportunities to encounter the planet (fig. 24.4.2). Hence even if at any specific encounter capture is "horrendously improbable" as Kaula puts it, subsequent encounters will occur a "horrendously" large number of times, so that the probability of a final capture becomes quite large, and may approach unity.

In fact, we can state as a general theorem (with specific exceptions) that if two bodies move in crossing orbits and they are not in resonance, the eventual result will be either a collision or a capture. (By "crossing" we mean that the projections of the orbits on the invariant plane intersect each other. There are some special cases where the theorem is not valid; e.g., if one of the bodies is ejected to infinity at an encounter.)


FIGURE 24.4.2.- If initially the orbits of the Earth and the planet Moon intersected, there would have been frequent encounters between the two bodies.

FIGURE 24.4.2.- If initially the orbits of the Earth and the planet Moon intersected, there would have been frequent encounters between the two bodies. capture at any given encounter is unlikely. The most probable result is a deflection leading to a new orbit. However, this new orbit would also intersect the Earth's orbit so that a large number of new encounters would occur. The most probable final result is capture. (From Alfvén and Arrhenius, 1972a.)


[461] Because celestial mechanics is time-reversible, a capture cannot be permanent unless orbital energy is dissipated. For small bodies the main sink of energy is likely to be viscous effects or collision with other bodies. For large bodies like the Moon or Triton, tidal interaction may make the capture permanent and will also produce drastic changes in the orbit after capture

So far there is no detailed theory which explains the capture of the individual retrograde satellites. If a theory consistent with present-day, conditions in the solar system is not forthcoming, it may be fruitful to turn to suggestions (e.g., Kaula, 1974; Kaula and Harris, 1973) that capture occurred during an accretionary phase of the hetegonic era. Satellite capture during accretion of a planet is indeed dynamically possible.



Having discussed the Earth-Moon system by comparison with other satellite systems we shall now consider earlier studies of lunar orbital evolution which investigated tidal effects. To sum up the most important steps in this extensive discussion, Gerstenkorn (1955) concluded that the Moon was captured in an almost hyperbolic retrograde ellipse with an inclination i = 150°. It was shown by Goldreich (1968) that, because of a complicated transitional effect, the calculations were not altogether correct This caused Gerstenkorn (1968; 1969) to make a new calculation which indicated a capture from a polar or even prograde orbit with a very small perigee. Independently Singer (1968; 1970) made calculations with simile' results.

Furthermore, it was pointed out (Alfvén and Arrhenius, 1969) that the tidal theory which is used in all these calculations is highly unrealistic Especially at close distances, a number of complicating effects are likely to arise so that calculations which are mathematically accurate do no represent reality. Resonance effects of the Allan type (Allen, 1967) ma, also interfere, preventing the Moon from ever coming close to the Roche limit and considerably prolonging the duration of the close approach. This would explain the long immersion of the Moon in the Earth's (possibly enhanced) magnetosphere, indicated by the natural remanent magnetization of lunar rocks in the age range 4-3 Gyr (e.g., Fuller, 1974; Alfvén and Arrhenius, 1972a; Alfvén and Lindberg, 1974).

All the possible schemes for the evolution of the lunar orbit discussed above should be taken with a grain of salt. They may describe the general type of evolution, but an exact treatment appears futile as long as the important secondary effects are not well understood. Hence the formal objections to Gerstenkorn's original model do not necessarily mean the this is less likely to describe the general type of orbital evolution.

[462] Calculation of the time and duration of the close encounter also remains uncertain because of the poorly understood resonance and dissipation effects. For this reason the actual record in the Earth, meteorites, and the Moon would provide the most direct information on time and type of encounter.

In Gerstenkorn's original model the close approach would necessarily lead to large-scale heating, exceptional but possibly localized tidal effects, and possibly bombardment of both bodies with lunar debris if the Moon came within the Roche limit (Kopal, 1966). Combining amplitude indications from tidally controlled sediments and reef structures with the evidence for culminating breakup of meteorites at about 0.9 Gyr, we suggested as one of two likely alternatives that this may mark the time of closest approach if a development of this type actually occurred (Alfvén and Arrhenius, 1969). There is, however, some doubt about the preponderance of tidal sediments in this period and about the reliability of stromalites as tidal indicators when extended into the Precambrian. Nor does the high incidence of meteorite breakup in itself provide a compelling argument for a lunar interaction.

The second alternative (Alfvén and Arrhenius, 1969) (namely, an orbital evolution modified by resonance phenomena) would result in the Moon's residing in the Earth's environment for a considerable time and at a distance of the order 5-10 Earth radii (fig. 24.5.1); hence energy dissipation would take place at a more modest rate. This alternative is supported by the results subsequently obtained by exploration of the Moon.

Assuming that the generation of mare basalts on the Moon ranging from 3.7 to 3.3 Gyr (Papanastassiou and Wasserburg, 1971a) or perhaps as low as 3.0 Gyr (Murthy et al., 1971) was caused by collisions during the contraction of the Moon's capture orbit (see sec. 24.6), the closest approach to the Earth would have occurred in the range of 2.8-3.3 Gyr. The paucity of preserved sediments on the continents dating from this period and earlier could possibly be the result of the extensive and long-lasting tidal effects associated with this proposed lunar orbital evolution. However, it is difficult, given our present state of knowledge, to distinguish such an effect from the cumulative effects of damage incurred continually during geologic time.



In sec. 24.3 we discussed the possibility that the Earth originally had a satellite system with properties of other normal, prograde systems. If such a normal system existed, the only likely possibility for its destruction would be by the Moon as its orbit evolved after capture. With its orbit slowly contracting due to tidal dissipation, the Moon would sweep out the space....



FIGURE 24.5.1.- Noncatastrophic alternative; spin-orbit resonance prevents the Moon from reaching the Roche limit.

FIGURE 24.5.1.- Noncatastrophic alternative; spin-orbit resonance prevents the Moon from reaching the Roche limit. The retrograde lunar capture orbit contracts due to tidal dissipation until resonance between the lunar orbital period and the spin period of the Earth locks the Moon in a slowly expanding orbit. Since the Moon never comes very close, no breakup or autoejection of debris occurs and the tides do not reach catastrophic heights. When the orbital inclination has decreased below a critical angle (suggested in the diagram at about 25°), the resonance locking is broken and the Moon recedes to its present orbit at 60 Earth radii. The dotted curve represents the catastropic alternative (Moon reaching the Roche limit). (From Alfvén and Arrhenius, 1969.)


...occupied by the normal satellites and either collide with them or eject them from their orbits; collision with the Earth or ejection to infinity could result from the latter type of perturbation. Such a development has already been proposed by McCord (1966) to explain the absence of a normal satellite system around Neptune; i.e., the satellites have been swept up by Triton after its capture by Neptune.

It is interesting to speculate about a development of this type for the Earth-Moon system since it implies that original Earth satellites now may be buried in the surface of the Moon where it might be possible to distinguish them on a chronological and perhaps compositional basis from the majority of planetesimals that impacted on the Moon during the much earlier terminal stage of accretion (as discussed in ch.12). The late occurrence in time of the excavation of Mare Imbrium (Turner et al., 1971; Papanastassiou and Wasserburg, 1971b) and the low ages of the mare

[464] basalts have prompted several other authors to consider the possibility of a collision with a preexisting Earth satellite (Ganapathy et al. 1971, Kaula 1971). It is, however, difficult to exclude entirely the possibility that some of the planetesimals in the Moon's or the Earth's formative jet streams survived as long as 0.5 to 1 Gyr after runaway accretion. In the latter case it is possible that such material, distributed in the Earth's orbit, caused collisional perturbation of the Moon's precapture orbit, thereby contributing to the capture of the Moon (Kaula and Harris, 1973; Kaula, 1974; Wood and Mittler, 1974; Opik, 1972).

The low relative velocities suggested by some features of the near-circular basins on the Moon would also point at Earth satellite impact, as suggested by Kaula (1971). However, the accretion conditions in the parental jet stream would also lead to low relative velocities between accreting planetesimals (ch. 12).

The large near-circular basins on the Moon would seem to be features which could mark the resting places of original Earth satellites (or possibly of late, large lunar jet-stream members). Stuart-Alexander and Howard (1970) list nine such basins larger than 500 km, all located on the front...


FIGURE 24.6.1.- Size distribution of circular basins on the Moon.

FIGURE 24.6.1.- Size distribution of circular basins on the Moon. The few large basins (indicated by diagonal stripes) may be the final resting places of either large lunar or terrestrial planetesimals or of the small "normal" satellites of the Earth. (From Stuart-Alexander and Howard, 1970.)


[465] ....side of the Moon (fig. 24.6.1). Five or six of these basins contain positive mascons (Muller and Sjogren, 1969); their mass excesses are in the range 0.4-1.4 X 1021 g. By comparison, Earth's normal satellites would have had individual total masses in the range 1021-1022 g (sec. 24.3). Urey and MacDonald (1971) have brought forward a number of arguments favoring the view that the mass excesses represent the projectile materials rather than the alternative possibility that they were formed by a sequence of basalt eruptions from an interior melt reservoir as proposed by Wood (1970).

A relatively large number of mascons has already been found (12 positive and 1 negative in the surveyed region bounded by latitude ±50° and longitude ±110°) and they extend into low mass ranges (present lower detection limit ~1020 g). Hence it is unlikely that mascons are uniquely caused by impact of tellurian satellites. As has been pointed out above, however, low relative velocities must be a characteristic of planetesimals in a jet stream when t approaches tc/2. Subsonic relative velocities, which appear necessary to prevent net loss from the impact crater (Urey and MacDonald, 1971), could thus be achieved both between the Moon and its planetesimals during accretion and between the Moon and normal Earth satellites during the contraction of the capture orbit.

Only about half the large basins which possibly could contain satellites have positive mascons. Hence the presumed projectiles in some cases did not have very high density relative to the lunar crust or they impacted with supersonic velocity. Only in the case of the Imbrian impact does enough information now exist to suggest the timing and other characteristics of the event.



The magnitude of the accretion rate of a planet and the rate changes during the formative period are of particular interest since they would largely control the primary heat structure of the body. Secondary modifications of this structure may arise from buildup of radiogenic heat, from thermal conductivity, and from convection. The planetesimal accretion rate is determined by the gravitational cross section of a growing planetesimal and by the particle density in the surrounding region. This process is discussed in detail in secs. 12.9-12.11.

The accretion of the Moon was characterized by slow growth and a late runaway accretion phase (fig. 12.9.1). The greatest heating of the lunar surface due to impacting planetesimals occurred during this phase when the radius of the Moon had already attained 0.8 of its present size (fig.12.11.1). During runaway accretion planetesimal velocity at impact is high [466] enough to melt the majority of accreting material, and transient temperatures at impact probably exceed 1800K.

The primordial heat profile of the Moon indicates that the interior of the Moon was originally at a relatively low temperature and that the maximum temperature and molten region would have been close to the surface. The evidence available to date suggests that the deep interior of the Moon is in the melting range, and hence that radiogenic heating of the interior has altered the primary heat structure.

The sustained, average temperature over the surface of the embryonic Moon is harder to predict since the rate of heat loss by radiation from, and conduction through, the surface are controlled by a number of factors for which we still lack sufficient scaling experience. Such factors are depth of implantation and mode of dissipation of energy, size and velocity distribution of impacting planetesimals, and the properties of the impact-generated atmosphere. Generalized knowledge of these parameters will hopefully be derived from continued lunar exploration. Information on some related parameters is provided by the impact waves recorded in the ringed maria (Van Dorn, 1968, 1969) and from detailed analysis of the Imbrian impact (Urey and MacDonald, 1971) in combination with direct study of returned lunar samples and field relationships on the Moon.

Since the dominant fraction of mass and energy is contributed by the larger planetesimals, the heating effects caused by them are of major importance. During and after runaway accretion each major impact must have resulted in implantation of a large fraction of the energy at considerable depth (~105 cm). This would lead, particularly at subsonic impact, to formation of molten pools insulated by the low-density fallout from the explosion clouds. In each such magma chamber differentiation would be expected to generate a sequence of heavy cumulates on the bottom and light ones on the top. At each remelting event the low-density differentiates would be transferred upward toward the new surface but with the previously settled heavy component remaining in place.

Regardless of the average sustained temperature in the outer layer of the accreting embryo, which may be low or high depending on the accretion rate, the integrated effect due to this phenomenon would be that of a heat front sweeping low-density components from the interior to form a light surface crust where the heat-generating radioactive nuclides would also accumulate. In this way it is possible to understand both the interior structure and the chemical composition and formation of the crust of the Moon and other bodies in the solar system. (See detailed discussion in ch. 12.)

The maximum value of energy flux at the time of runaway accretion tc determines the maximum temperature reached and also the extent to which simultaneous melting occurred over the entire surface. In a case like the Moon (in contrast to the Earth) this parameter is sensitive to the value [467] chosen for the duration of infall of matter to the lunar jet stream tinf, since tc and tinf here are of the same order of magnitude. For reasons discussed above we cannot yet quantitatively translate energy flux into surface temperature; hence we depend on direct observation for scaling. The most significant information now available comes from the distribution of the rubidium and strontium isotopes in lunar rocks (Papanastassiou and Wasserburg, 1971b). These results suggest that melting in the outer layer during terminal accretion was extensive enough to completely segregate Rb and Sr within individual reservoirs, but that the melt reservoirs did not equilibrate between each other.

Differentiation features on the Moon contrast in some significant respect. with those we are used to seeing on Earth. For this reason it has been suggested (Arrhenius, 1969; Arrhenius et al., 1970; Gast, 1971) that the differentiation taking place before accretion could be responsible for the lunar surface composition. Similar proposals have been made to explain the layering of the Earth (Eucken, 1944b; Anders, 1968; Turekian and Clark 1969) and could, in principle, be rationalized on the basis of partial overlap between the A and B clouds (sec. 24.8). However, it seems that the in escapable accretional heating may, in itself, satisfactorily account for currently known facts, including the loss of potassium and other volatile, elements from the Moon.

Gast (1971, 1972), in an argument for the alternative of pre-accretionary differentiation, has suggested that volatile elements such as potassiun could not be effectively removed from the Moon to the extent observed The reason would be that the slowness of diffusion would prevent evaporative losses from occurring except from the most surficial layer of lunar magma basins. With the accretional heating considered here, however, violent convection must have been caused by planetesimal impact and gas release within the melt. The impacting projectiles could furnish one source of such escaping gas. Furthermore, because of the low lunar oxygen fugacity magnesium silicates dissociate into gaseous MgO and SiO at an appreciate] rate in the temperature range of 1400-1700K, leading to the extensive frothing observed in lunar lava (Arrhenius et al., 1970). Convection an gas scavenging hence would contribute to efficient transfer of volatiles from the melt into the temporary lunar atmosphere. Such an atmosphere would be rapidly ionized and removed, as seen from the prompt ionization of the clouds caused by artificial impact on the lunar surface and by gas eruptions (Freeman et al., 1972).

Hence it would seem that the separation and loss of volatile elements characteristic of the Moon (and to a lesser extent of the Earth) are a dire' consequence of an accretional heat front, differentiating the outer 300 400-km layer of the Moon and the outer core and entire mantle in t! case of the Earth.



In Laplacian types of models all the source material for planets and satellites is assumed to be present at one time in the solar nebula and to be uniformly mixed to give a "cosmic composition." Striking differences in composition (see sec. 20.5) such as among the outer planets, the satellites of Jupiter, and in the Earth-Moon system are either left unexplained or ascribed to ad hoc processes without theoretical basis. In the present theory for emplacement of matter around the central bodies (sec. 21.11-21.12), controlled by the critical velocity phenomenon and ablation of transplanetary material, the Moon and Mars would have formed from the A cloud, and the inner terrestrial planets from the B cloud, inheriting the specific and different chemical properties of these clouds. From these considerations the low density of the Moon and Mars compared to the inner terrestrial planets is understandable. The partial overlap of these two clouds may also provide an explanation for the possible inhomogeneous accretion of the Earth (sec. 24.9).



Our analysis, which is essentially a development of the planetesimal approach, leads to the following conclusions:

(1) The Moon originated as a planet ("Luna") which accreted in a jet stream in the vicinity of the Earth's jet stream. Together with Mars, it derived from the A cloud.

(2) The condensed material forming the Moon and the terrestrial planets would be derived (a) from condensable impurities in the infalling A cloud and B cloud (secs. 21.11-21.12), (b) by electromagnetic capture in the A and B clouds of transplanetary dust as described in sec. 21.12, (c) by ablation of transplanetary material in these plasma clouds (sec. 21.12), and (d) by capture of transplanetary material in the jet streams of the terrestrial planets (sec. 21.12).

The processes (a), (c), and (d) would contribute to making the jet streams of Moon and Earth chemically dissimilar. However, because of their closeness in space, temporary overlap of one or the other is possible in analogy with observations in meteorite streams (sec. 22.9.1). This could provide an explanation for layering (heterogeneous accretion) of either planet.

(3) We cannot decide at the present time whether the lunar jet stream was located outside or inside Earth's jet stream.

(4) Due to its smaller mass, the Moon accreted with a cool interior and reached a maximum temperature at about 80 percent of its present radius. In the surrounding mantle all material was processed through high transient [469] temperatures in the hot-spot front, but the entire present lunar crust was probably never all molten at the same time.

(5) The original lunar orbit intersected Earth's orbit (or was brought to intersection by some perturbation). This led to frequent Earth-Moon encounters which eventually resulted in capture.

(6) The Moon was probably captured in a retrograde orbit in the same way as the other six captured satellites were. Such a process may have taken place at a time when Earth still was accreting planetesimals. A capture by a very close encounter is less probable but cannot be excluded.

(7) From the regular distribution of secondary bodies in the solar system, one may conclude that Earth had an original satellite system. The structure of such a system depends on the mass of the central body. Extrapolation from the Uranian system to Earth suggests that Earth should have had a group of perhaps half a dozen small bodies. To this we should possibly add a group obtained by extrapolation of the Martian system to a larger central body mass. Hence Earth may originally have had a total of 5 to 10 normal satellites.

(8) During the tidal evolution of the lunar orbit the original satellite system was destroyed, as was that of Neptune. Most or all of the satellites may have been swept up by the Moon. It is possible that some of the nearcircular basins and mascons on the Moon were produced in this way, but we cannot exclude the possibility that they are due to late planetesimals.