Baixe fisica da terra sólida e outras Manuais, Projetos, Pesquisas em PDF para Física, somente na Docsity!
Chapter 1
THE SOLAR SYSTEM
" ... the solar system possesses several oddities .... " GAMOW, 1963, p. 63.
1.1 The Planets
Our knowledge of the solar system has made major advances in the past two decades. For many years theories of the origin of the planets have been built around the observed regularity in planetary orbits. More recently the emphasis has been on chemical considerations, with appeals to the densities of the planets and isotopic abundances in the Earth and in meteorites. It is now apparent that the Earth had a common origin with the other planets, about 4.5 x 10 9 years ago,in a cloud ofgas and dust surrounding the then youthful Sun. The abundances of the elements in the cloud were approxi- mately what would be expected from theories of nuclear synthesis, so that the formation of the solar system required no special conditions; rather we suppose that there are millions of similar systems of planets, even in our own galaxy. Densities and orbital radii of the planets are listed in Table 1.1. Reliable values of density are much more recent than the orbital data, because precise measurements of planetary diameters are notoriously difficult to make and they enter as the third power in density estimates. However, the remaining uncertainties leave no doubt about the significant differences in composition, even between the basically similar inner four (terrestrial) planets. These differences are considered in S.ection 1.5. The approximate geometrical progression of orbital radii of the planets is known as Bode's law or sometimes as the Titius-Bode law (Roy, 1967). In its original form this law gives the orbital radius Rn of the nth planet (counted outwards) as (Ll) 1
N
"" TABLE 1.1: PLANETARY ORBITS AND DENSITIES
Vl 0 15"'..., Orbit Radius (Rn) Mass Radius Estimated Density (^) ~ Relative to Earth's Rn^ Relative to Relative to Density at (^) "".....
n Planet Orbit R n_ 1 Earth Earth (gmcm- 3 ) Zem Pressure "";;::
Mercury 0.387 0.055 3 0.3820 5.47 5. 2 Venus 0.723 1.86 0.815 5 0.9506 5.24 3. 3 Earth 1.000 1.38 1.00000 1.000 5.517 4. Moon 0.01230 0.273 3.33 3.
Earth + Moon 1.01230 5.44 3.
4 Mars 1.524 1.52 0.107 0.530 4.0 3. 5 Asteroids Mean about 2.7 1.77 3.9 3.9" 6 Jupiter^ 5.203 1.92 317.9 10.97 1.
1
7 Saturn^ 9.539 1.83 95.1 9.03 0.71 Largely 8 Uranus 19.18 (^) 2.00 14.6 3.72 1.56 Gaseous 9 Neptune 30.06 (^) 1.56 16. 1 3.8 3 1. Pluto 40. (eccentric) (^) 0.09? 0.5? 4?
NOTE: There are numerous tabulations in the literature, with slight discrepancies. Important improvements in the data for terrestrial planets are by Ash et al. (1967) and for Neptune by Taylor (1968).. " Average for total mass of meteorite falls.
4 The Solar System
recent discussions of the law are influenced by von Weizsacker's (1944) model of a turbulent solar nebula, in which the planets accumulated at the boundaries
between vortices, whose size increased regularly outwards from the Sun. *
Another important aspect of the orbital motions of the solar system is the· distribution of angular momentum. With three apparently related exceptions, all of the planets revolve about the Sun and the satellites about the planets in the same direction and the orbits are approximately circular and coplanar. The exceptions are Pluto, whose orbit is inclined at 17° to the ecliptic (Earth's orbital plane) and is so elliptical that it crosses the orbit of Neptune, and the two satellites of Neptune, Triton, which has a reversed orbital motion about Neptune, and Nereid, whose orbit is highly elliptical. It is possible that all three were once satellites of Neptune, but suffered a dramatic gravitational interaction, throwing Pluto into an independent solar orbit. For this reason Pluto is not counted as one of the numbered planets in Table 1.1. The axial rotations of the Sun and planets are also in the same sense as the orbital motions, except for Uranus, which has a reversed rotation, and Mercury and Venus,t whose rotations have been virtually stopped by tidal friction of the solar tides (see Section 2.4). Thus with the axial rotation of Uranus as the only difficulty, we can envisage the development of the Sun and its planets from a disk-shaped nebula of gas and dust, all rotating in the same sense. Hartman and Larson (1967) and Alfven (1967) pointed out that, except for Venus and Mercury, the planets and asteroids have approximately equal rotation periods. One of the detailed problems is then to explain how the Sun itself acquires nearly 99.9 %of the mass ofthe solar system but only 2 %of its angular momentum. Alfven (1954) emphasized the necessity for an outward transfer of angular momentum from the contracting Sun to the outer parts of the cloud. He assumed that the proto sun had a very extensive magnetic field, which exerted a drag on the ionized gas of the surrounding nebula, accelerating the outer parts of the nebula and slowing down the Sun.t Of the planetary satellites the Moon is by far the largest in relation to its primary, the Earth; so much so that we may be justified in regarding the Earth-Moon system as a double planet, rather than as a planet plus satellite. For comparison of density and composition with those of other planets it may therefore be more appropriate to consider values for the Earth and Moon together, rather than the Earth alone, and this possibility is allowed for in Table 1.1. However, the Moon is similar in both size and density to the inner
- Reviews of the subject are given by Spencer Jones (1956) and Ter Haar and Cameron (1963). t Radar observations of Venus (Dyce et aI., 1967) indicate a very slow reverse rotation. The dense atmosphere of Venus prevents optical observation of the solid surface. The rotations of Venus and Mercury are now explained in terms of tidal resonances (Goldreich and Peale, 1966; Bellomo et aI., 1967).
t See also Hoyle (1960).
1.2 METEORITES AND THEIR COMPOSITIONS 5
satellites of Jupiter and Saturn. In particular 10, a satellite of Jupiter, is very close in size to the Moon but has a mean density of about 4.06, which is even greater than the mean lunar density, 3.33. In composition 10 is almost certainly very similar to the terrestrial planets. A comparison of the masses ' and diameters of planetary satellites (which are conveniently tabulated by Blanco and McCuskey, 1961, Table VII pp. 288-289) shows that the satellites of Jupiter and Saturn follow a pattern of decreasing density outwards, similar to the outward decrease in uncompressed densities of the planets. It is probable that the same process of segregation of the elements occurred in the Jovian and Saturnine satellites as occurred in the solar system as a whole. The obvious division of the planets into two groups can be made equally well on the basis of size or density. The four major planets, Jupiter to Neptune, are more remote from the Sun and larger but less dense than the four smaller terrestrial (Earth-like) planets, Mercury to Mars, with which must be grouped also the asteroids. The terrestrial planets and meteorites are composed mainly of nonvolatiles, especially iron and silicon in varying states of oxida- tion, whereas the major planets have densities which are so low that they must be composed largely of light, volatile materials, especially hydrogen, with the nonvolatiles in much smaller but unknown amounts.
1.2 Meteorites and Their Compositions
Meteorites are iron and stone bodies, which arrive on the Earth in small numbers and quite randomly, apparently from within the solar system. The study of these objects has become a science with its own name, meteoritics, and has been comprehensively reviewed by Mason (1962), Wood (1965) and Anders (1964). Meteorites should not be confused with meteors, which are the transient luminous trails in the sky produced by small particles, known as meteoroids, many of which can be identified from their orbits as fragments of comets. There is no association between the arrivals of meteorites and the occurrences of meteor showers, which are observed when the Earth passes through bands of orbiting comet debris, although it must be expected that a few of the sporadic meteors h[lVe the same origin as the meteorites (Jacchia, 1963). The total number of observed falls from which the recovery of meteorites has been documented is about 700, although the number offinds, which were not seen to fall but are certainly meteorites, rather more than doubles the total number available for study. It is therefore not surprising that only one fall has been observed with sufficient scientific control (by photographing the trail from two well separated points) to allow a reliable calculation of its orbit. This occurred at Pribram, Czechoslovakia, in 1959 and the fall was one of the familiar type known as chondrites. The orbit calculated by Ceplecha
1.2 METEORITES AND THEIR COMPOSITIONS 7
A lower limit to the size range is imposed by the Poynting-Robertson effect (Section 1.4). Opik (1966) has drawn attention to a mechanical difficulty which arises in the conventional theory of meteorites as asteroidal collision fragments. Asteroids orbiting in a common direction within the main asteroidal belt do not have velocity differences great enough to project impact fragments into Earth-crossing orbits. However, the asteroidal origin remains acceptable if the source of meteorites is restricted to the asteroids in elliptical orbits and Wetherill (1968) has pointed out that afternoon falls of chondritic meteorites are twice as frequent as morning falls. This requires the chondrites to be orbiting substantially faster than the Earth when intercepted and their orbit aphelia must be near to Jupiter. Although meteorites are, for convenience, classified into several structural and chemical types, there are no clear lines of demarcation and slightly different systems of classification have been in favor at different times. The four groups listed by Mason (1962, p. 52) are chondrites, achondrites, stony- irons, and irons. A convenient checklist of their properties is given by Kaula (1968, pp. 380-382). The irons are predominantly metallic iron, with nickel in solid solution
averaging about 11 %. Smaller amounts of sulphide and graphite are found
and there are occasional inclusions of silicate. Two metal phases occur, the body-centered cubic rx form (kamacite) with about 5.5 % nickel, and the face-centered cubic y form (taenite) with variable nickel content, generally
exceeding 27 %. Normally both phases occur in close association, evidently
as a phase separation from solid solution after solidification as a single phase from the melt. The metal crystals are commonly very large, up to a meter. or so across, indicative of extremely slow cooling. Quantitative evidence of the cooling rate has been obtained from the variations in composition across the kamacite-taenite phase boundaries. The phase separation usually forms a characteristic pattern, which is rendered obvious by etching, and is known as the Widmanstatten structure. A good example is shown in Fig. 1.3. The mutual solubility of iron and nickel decreases with falling temperature, but the rate of atomic diffusion also decreases. Thus, as cooling proceeds, the compositions of kamacite and taenite cannot maintain mutual equilibrium, except at the phase boundary itself, and a diffusion zone is formed. The kamacite (nickel-poor phase) is depleted in nickel near to the boundary and the taenite (nickel-rich phase) is further enriched. The width of the diffusion zone has been used to estimate cooling rates by Short and Anderson (1965) and Goldstein and Short (1967). The rates of cooling were variable from O.4°C to 40°C per 10 6 years through the critical range from 650 to 350°C, in which the diffusion was effective. These slow rates are in keeping with the large crystal sizes and coarse Widmanstatten structures of iron meteorites and
8 The Solar System
Figure 1.3: Widmanstatten structure of the metal phase in the Glorietta Mountain pallasite (stony-iron meteorite). The scale line is 1 cm. Photograph courtesy of J. F. Lovering.
suggest burial in parent bodies 100 km or more in radius. However, the wide range of cooling rates appears not to be compatible with a single parent, but rather with several of different sizes. Chondrites are the most common of the four types of meteorite, comprising
85 % of observed falls, although iron meteorites are generally larger and the
mass of meteoritic matter in space is probably less than 85 % chondritic. The characteristic feature of chondrites is the occurrence of chondrules, spherical grains of silicate with diameters of about 1 mm, which ar~ distributed through the matrix of silicates and nickel-iron (Fig. 1.4.). Chondrules do not occur in any of the terrestrial rocks accessible to us and they indicate that a large fraction of meteoritic material underwent a special process, of which we have no direct evidence on the Earth. The principal theories of chondrule formation have been reviewed by Anders (1964), but none avoid what appear to be improbable stages in meteorite evolution. Wood (l963b) argued persuasively that the chondrules condensed as in- dependent objects in the solar nebula and that they were subsequently incorporated in the accretion of the meteorite parent bodies. Evidence in favor of this hypothesis includes the enrichment of the isotope Xe 129 , observed by Merrihue (1963), in chondrules relative to the groundrnass in the chondrite Bruderheim. Xe 129 is the key isotope in discussions of the very early history
of the solar system (Section 8.5). It is the decay product of r^129 , whose
10 The Solar System 17 million year half-life is so short that its incorporation ina meteorite, and the subsequent enrichment of the meteorite in Xe 129 , implies that the meteorite both formed and cooled within a few hundreds of millions of years of the cessation of nuclear synthesis. Greater Xe 129 enrichment of the chondrules therefore implies that the chondrules formed first. Most other authors (especially Ringwood, 1966b) have favored chondrule formation by rapid crystallization from a melt, after accretion of one or several parent bodies of substantial size, perhaps, but not necessarily, as large as the Moon. Dodd and Teleky (1967) found evidence of alignment of olivine crystals within chon- drules, such as is observed in terrestrial rocks which have flowed as partially crystallized magma. They concluded that this observation is compatible only with a volcanic origin of chondrules. The subsequent mixing of chondrules with silicate groundmass presents no problem, but it is difficult to envisage a chondritic parent body reaching the stage of volcanism while still retaining near to its surface the free metal which is an integral constituent of the chondrites. Much less frequent than chondrites are the achondrites, which are essen- tially similar to terrestrial rocks, being crystalline silicates with virtually no metal phase. The stony-irons hardly merit separate classification, being merely about halfway through the continuous range between stones and irons. However, there is an important class of chondrites which deserves special mention, the rare carbonaceous chondrites (for a review of their properties see Du Fresne and Anders, 1963). Their rarity in meteorite collections is _ probably due more to their extreme friability and lack of strikingly meteoritic features than to an absolute rarity in space. As the name implies, they contain several percent of carbon and carbon compounds. Metal phases are virtually absent, the iron occurring in silicate, oxide, and sulfide phases. Substantial amounts of volatiles, especially water, are present, so that these chondrites can never have been strongly heated. Of all of the materials available for laboratory examination, the subclass of carbonaceous chondrites known as type I must be nearest to the primitive dust from which the terrestrial planets were formed. Types II and III are more like ordinary chondrites. No listing of meteorite types would be complete without mention of the tektites, although they cannot strictly be classed with the other groups. Tektites are rounded pieces of silica-rich glass which have been found in tens of thousands in limited areas, notably the Philippines and South East Asia, Southern Australia, and Czechoslovakia. Their shapes clearly indicate rapid flight through the atmosphere, although none has been observed to fall. For each geographical group the ages determined from potassium and argon isotopes agree and coincide with the age of the geological formations in which they are found, although their compositions are unrelated to their environ- ments. The range of ages (time since fusion) of the several groups is 0.3 to
1.3 COSMIC RAY EXPOSURES OF METEORITES 11
35 X 10 6 years,* many orders of magnitude less than the meteorite ages, which exceed 4 x 10 9 years. Metallic (nickel-iron) spherules have been found in some tektites. The favored, but not universally accepted theory is that each geographical group was formed as a fused splash by a major meteorite impact on the Moon, so that the tektites are fused lunar surface material with traces of meteoritic matter. O'Keefe (1966) has reviewed the tektite problem with emphasis on a variation of the lunar origin. The other serious possibility is that tektites were produced by meteorite impacts with the Earth.
1.3 Cosmic Ray Exposures of Meteorites The "age" of a meteorite normally means the time elapsed since it was formed as solid material. More specifically, this is the solidification age, deter- mined by the methods used for dating rocks which are discussed in Chapter 8. The principal methods, based on the decay of uranium to lead, rubidium to strontium, and potassium to argon, are all applicable to stony meteorites, which contain the parent elements of these decay schemes. Iron meteorites contain negligible amounts of the parents and can be dated only from lead isotope ratios by presuming that the ultimate source material is the same as for the stones (and for the Earth). The numerous age determinations indicate that the meteorites underwent a major process of chemical evolution 4.5 x 10 9 years ago, simultaneously with a similar process in the Earth. In considering meteorites we are also interested in the cosmic ray exposure ages, the intervals of time which have elapsed since the meteorites were broken down into meter-sized pieces and exposed to bombardment in space. by cosmic radiation. It is only the outer 1 m or so of each independent body that is exposed to cosmic radiation, so that each fragmentation event exposes fresh material. From the abundances of certain short-lived cosmogenic (cosmic ray produced) nuclides (Ar 39 , C 14 , C1 36 ) a terrestrial age can also be estimated. This is the time since a meteorite arrived on the earth and cosmic radiation was thus" switched off." Extremely energetic cosmic ray protons cause violent disruption (spallation) of the atomic nucleii in exposed meteorites. Anders (1962, 1963), who reviewed the whole subject of meteorite ages, used the following example to illustrate the spallation process:
Fe 56 + Hl ----+ Cl 36 + H3 + 2He 4 + He^3 + 3H 1 + 4n (1.3)
Many products can arise from numerous similar reactions and in principle the total cosmic ray exposure can be estimated from the content of a particular
* Tektites fall into distinct age groups, which show that they were produced by four, or at
most five events in the past 35 million years (see tabulation of ages by Kaula, 1968). It must, however, be admitted that there may have been earlier tektite-producing events, but that the tektites produced have been lost geologically.
1.3 COSMIC RAY EXPOSURES OF METEORITES 13
to conclude that they were produced simultaneously by disruption of a single parent body or by the collision of two parents. However, the concentrations of spallation products are highly variable and indicate a more complex history. Nearly half of the exposure ages for stony meteorites are closely grouped around 23 x 10 6 years, but others cover the range from 2.8 x 10 6 to 500 X 106 years (Anders, 1962, Table III), with a tendency to minor groupings of different types also at 4.5 x 10 6 and 10 x 10 6 years. Some of the lower estimates are probably invalidated by diffusion losses because the same meteorites have small potassium-argon ages. Iron meteorites have generally had much greater exposures, lip to a maximum of 1500 x 10 6 years with groupings at 550 x 10 6 and 900 x 10 6 years but not at 23 x 10 6 years (Anders, 1962, Table IV). There is a wide scatter and, in many cases, very imperfect agreement between the alternative methods. Nevertheless, it is evident that the meteorites suffered a multiplicity of fragmentation events which were very much more recent than their solidifications. The measurements do not preclude the possibility of a primary fragmenta- tion of one or two parent bodies, because the large number of asteroids requires that we assume many more recent collisions of small bodies, although few major collisions of large ones. However, if collisions are occurring at a rate such that the interval between them, for anyone fragment, is short compared with the time since the suppose primary fragmentation, then the cosmic ray exposures will indicate the more recent fragmentations. The fact that stony meteorites are more easily broken up, and are on average signifi- cantly smaller than the irons, is consistent with their shorter cosmic ray exposures. Furthermore, the exposed surfaces of stones are eroded more quickly by impact of small dust particles than are the surfaces of irons, an additional reason why stony material with very prolonged cosmic ray ex- posures may not be available for measurement (Fisher, 1966). We are there- fore faced with a sampling difficulty and must regard the evidence as inconclusive. A more important reason for entertaining the hypothesis that the asteroids are collision fragments of planetismals which have never accreted to form a planet arises from the difficulty of devising a satisfactory mechanism for the break-up of more than a very modest (i.e., sublunar-sized) planet. The grouping of exposure ages suggests that the irons and stones were produced by different events and therefore that the bodies from which they came were chemically different. However, measurements of isotopic ratios of lead and strontium, which have been used to date the meteorites (Section 8.4), show that the meteoritic parents differentiated from a common source and, if they are of asteroidal origin, then the asteroids had a history of chemical differentiation before the break-up of those sampled as meteorites. It is this differentiation process which is dated at 4.5 x 10 9 years ago.
14 The Solar System
1.4 The Poynting-Robertson Effect
Solar radiation has an important influence on the orbits of small particles whose ratio of surface area to mass is large. Its effects on the meteor streams have been studied in detail and a historical and physical discussion is given by Lovell (1954). Particles up to about 10 cm diameter are affected on a time scale of 10 9 years. It is convenient to distinguish three effects of solar radiation pressure, although they are not really independent. First, there is a simple outward force from the Sun. For particles with diameters of a few thousand Angstroms or less this force may exceed the gravitational attraction of the Sun and blow them out of the solar system. This problem is complicated by the fact that the critical particle size is comparable to the wavelength of the radiation and the effective optical cross section is not the simple physical cross section. Weare concerned here with much larger particles. Second, the solar radiation received by a particle is Doppler-shifted to cause an increase in radiation pressure if the particle is approaching the Sun and a decrease if it is receding; elliptical orbits are thus reduced to nearly circular orbits. Third, the angular momentum of an orbiting particle is progressively destroyed by the fact that it receives solar radiation, which has only a radial momentum from the Sun (neglecting the solar rotation), and reradiates this energy with a forward momentum corresponding to its own motion about the Sun. This is the essential feature of the Poynting-Robertson effect, which is most conveniently analyzed as a problem in relativity. We consider the special case of a spherical particle of mass m and diameter d in a circular orbit at radius r. Its orbital velocity is
M is the mass of the Sun and G the gravitational constant, so that the total orbital energy is
GMm 1 2 GMm E=---+-mv =---
r 2 2r
It is convenient to consider separately the processes of absorption and re- radiation of the energy. " In time dt the particle receives energy dE as solar radiation, and this causes an increase in mass
16 The Solar System
which, for a spherical particle of density p, becomes
(
ro)2 ( r )2 6S rE - r E = dpc^2 t (1.16)
where (r/rE) is the radius of a particle orbit, expressed in astronomical units (AU). We are interested in the time taken by particles, of diameter d, originating in the asteroidal belt at 2.7 r (^) E , to reach the Earth's orbit, r (^) E • Assuming a particle density of 4 gm/cm 3 and d in centimeters, this is
t = 8.6 X 107 d years (1.17)
A more complete analysis (Lovell, 1954, pp. 402-409) shows that a particle in an elliptical orbit is first reduced to a nearly circular orbit, just inside its initial perihelion distance. Since this process also depends upon the Doppler shift of radiation due to motion of the particle relative to the Sun, the time required is similar to that for the spiraling effect. The Poynting-Robertson effect thus ensures that any small particles in the common meteoroid range (less than 1 cm diameter), which originated in the asteroidal belt about 10 8 years ago, would have passed the Earth's orbit and spiraled into the Sun. McKinley (1961, pp. 169-171) has pointed out that very few meteors appear to be due to particles having the density of stone or rock.·" They are envisaged as loose, dusty aggregates, similar to the supposed struc- tures of comets and quite different from the meteorites. The relative rarity of very small meteorites is consistent with the conclusion that they must be products of recent asteroidal collisions. Further, we can see that if a primary asteroidal fragmentation had occurred very early in the history of the solar system, say 4 x 10 9 years ago, then all primary fragments smaller than 50 cm would have spiraled into the Sun and the terrestrial collection would be strongly biased toward the shorter cosmic ray exposures of more recent, secondary fragmentations. Thus the currently available exposure age data do not permit us to decide whether the meteorites originated in one or two fairly large or many smaller parent bodies. Although the complexity of the chemical evidence appears to demand at least four parent bodies, semi-independent physical evidence is very desirable.
1.5 Compositions of the Terrestrial Planets In spite of their uncertain mechanical histories, meteorites have had a pro- found influence upon our ideas about the composition, internal structure, and history of the Earth. They provide us with samples of the compositions of the terrestrial planets which are far more representative of the planets as as whole than are the rocks to which we have access near the surface of the Earth. Chemical considerations now dominate the discussion of the nature and
1.5 COMPOSITIONS OF THE TERRESTRIAL PLANETS 17
origin of the Earth. Important reviews, although with somewhat divergent views, are given by Urey (1952, 1957, 1963) and Ringwood (1966a); MacDona:Id (1963a) has reviewed the physical aspects of studies of internal constitutions of the terrestrial planets. Meteorite compositions are in satisfactory accord with spectroscopic esti- mates of the solar abundances of nonvolatile elements. The dominance of Si, Mg, and Fe strongly indicates that all of the terrestrial planets are composed essentially of magnesian silicates and iron, either as metal or oxide. The average density of the Earth (Table 1.1) and its internal structure deduced from seismology (Chapter 4) agree well with the presumption that the Earth has a liquid iron core, of uncompressed density Po = 7 gm cm - 3, and a solid
silicate mantle with Po = 3.3 gm cm - 3. The proportions are estimated from
the measured radius ofthe core. In the same way we can interpret the average densities of the other terrestrial planets in terms of iron cores and silicate mantles in different proportions, although we have no direct estimates of the core sizes. Mercury, whose uncompressed density is substantially greater than that of the Earth, must have a larger core in proportion to its total volume. At the other extreme, the low density of the Moon leads us to conclude that it has virtually no core. Venus is very similar to the Earth in both size and density and is presumed to be essentially similar internally, but if we assign to Mars an iron core of radius calculated to give the observed mean density with a silicate mantle of Po = 3.3 gm cm - 3, then we run into difficulty. From the motions of its satellites the mass of Mars is well determined. The moment of inertia is also estimated, assuming approximate hydrostatic equilibrium for the surface, as in the calculations given for the Earth in Section 2.1 (Wilkins, 1967; Runcorn, 1967b)* and is found to correspond much more nearly to uniform density than in the case of the Earth. Allowing for uncertainty of the radius, the core
can be no more than 10 % of the total mass, and is probably substantially
less; moreover, a much higher density must be assigned to the mantle than in the case of the Earth. This observation gives strong support to Ringwood's (1966a, 1966c) theory of planetary evolution, which leads to different oxida- tion states for the terrestrial planets, so that in Mars virtually all of the iron has remained oxidized and therefore has not separated from the silicates. According to Ringwood the overall Fe/Si ratio in Mars is approximately the same as that in the Earth, the iron occurring as oxide, which has a density of
5.2 gm cm- 3. When added to silicate of Po = 3.3 gm cm- 3 , it brings the
uncompressed silicate density up to Po = 3.7 gm cm-3, to which only a small
core need be added to give the observed Martian density. In view of the high
* Disagreement between the observed surface ellipticity and that expected from the dynami-
cal ellipticity raises doubt about the assumption of equilibrium, but this is not sufficient to invalidate the conclusion drawn here.
1.5 COMPOSITIONS OF THE TERRESTRIAL PLANETS 19
core imposes two important requirements in the early chemical history of the Earth. First, carbon played an important role in the reduction process because hydrogen' would not reduce silica. Second, the mantle, which contains some magnetite, is not in chemical equilibrium with the core because iron oxide and silicon react, producing metallic iron and silica; the materials of the core and mantle could not have formed an intimate mixture at any stage. The separation of at least a major part of the core must therefore have occurred simultaneously with the reduction process which produced the metal and, since there must have been a mechanism for the escape of carbon monoxide, the reduction was probably part of the accretion itself. The occurrence of silicon in the core and magnetite in the mantle thus requires that the reducing conditions vary during the accretion of the Earth. It is possible that the
reaction Fe304 + 2Si --+ 3Fe + 2Si0 2 has subsequently occurred across the
core-mantle boundary, depositing iron in the core and leaving at the bottom of the mantle a silica-rich layer which is responsible for complications in the seismic velocity profile of this region. Alder (1966) has given an alternative explanation for the core density which avoids these consequences. He argued that at the temperature and pressure of the core-mantle boundary MgO is
soluble in iron to the extent of about 10 %and is a more likely core constituent
than Si. If this argument is correct, the core and mantle may not be in such serious disequilibrium as Ringwood requires. A complication in seismic velocities of the bottom of the mantle could then arise from depletion of MgO relative to Si0 2 • Another possible core constituent is sulfur, * which is associated with the metal phases (as troilite, FeS) in iron meteorites and chondrites. All of the important, long-lived radioactive elements, uranium, thorium, rubidium, and potassium, are strongly oxyphile and remained with the silicate during the process of reduction and melting which produced the iron meteor- ites and metal phases of the chondrites. Similarly, the iron core of the Earth can contain no significant radioactive material, so that radioactive heating cannot be invoked as a source of power to maintain the geomagnetic dynamo (Sections 5.4 and 9.4). In the Earth the fractionation of these elements is even more marked because they have large ionic radii and are expelled from the close-packed spinel structures to which silicates transform at the pressures of the lower mantle. The concentration of radioactive elements in continental rocks is the most striking evidence of the chemical differentiation of the mantle whereby the continents were formed. The age zones of the continents (Section 8.3) indicates that the differentiation was not a sudden process at an early stage in the Earth's history, but has occurred progressively, or possibly spasmodically, since.
* O. L. Anderson has drawn the author's attentIon to the fact that this is an old idea and
that it appears to be demanded by the cosmic abundance of sulfur.
Chapter 2
ROTATION AND THE FIGURE OF THE EARTH
" ... consider the wobble induced by a chula dancer of mass m on the geographic north pole ... " MUNK AND MACDoNALD, 1960b, p. 55.
2.1 Figure of the Earth
The centrifugal effect of the Earth's. rotation causes an equatorial bulge, which is the principal departure of the Earth from spherical shape. If the whole Earth were covered with a shallow sea, then, apart from minor dis- turbances due to wind, etc., the surface would assume the shape determined by hydrodynamic equilibrium of the water sUbjected to gravitation and rotation; the sea level equipotential surface is the geoid or figure of the Earth.* Tidal effects are superimposed upon the mean geoid by gravitational gradients of the Moon and Sun, but are very small in comparison with the n:itational ellipticity with which we are concerned here. Crustal features, continents and mountain ranges, are significant departures of the actual surface of the Earth from the geoid, but mass compensation at depth (the principle of isostasy discussed in Section 3.3) reduces the influence of surface features on the geoid., Jhe-ferm.ef the geoid has been determined from astrogeodetic surveys~6ver several extended continental survey arcs, the vertical, or direction of the local gravity vector, being determined at each point of observation by reference to stars. The process is described in detail by Bomford(l962) and is indicated in Fig. 2.1. Values of the ellipticity of the geoid deduced in this way from surveys completed between 1900 and 1960 are within the range 1/297 to 1/298.3 and deductions from gravity observations (Section 3.1) cover the same range.
* For a physical idea of the geoid in continental areas, picture canals cut through the
continents and connected with the oceans, so that the water level is the geoidal surface. 20
I,
