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are constant. Figure 3.15(b) shows certain abundance ratios that can be measured today, for example, for two mineral grains A and B in a component that differ in their initial endowments of rubidium and strontium. The subscript'0' denotes zero time - the time when the component became isolated. (N0 (86Sr) does not change.) The arrowed lines show the increase in radiogenic 87Sr relative to 86Sr as 87Rb decays. The time elapsed since isolation is t. The crucial feature is that the slope of each dashed straight line shown is (et/r - 1). Thus, knowing r we can get t from the slope. Because each line in Figure 3.15(b) is for a given value of t, it is called an isochron. Question 3.12 gives you the opportunity to prove that the isochron slope is (et/r - 1).

Many radioactive isotopes are used to date meteorites. The 87Rb-87Sr decay has been used here for illustration because the decay to the stable isotope end point is particularly simple (equation (3.2)). In contrast, the decay of 238U to the 206Pb stable isotope end point involves many stages, as does that of 235U to 207Pb. The half-lives of these decays are 4470 Ma and 704 Ma respectively, and are known to higher precision than the 87Rb-87Sr half-life.

The oldest radiometric ages that have been obtained from any body in the Solar System are for the CAIs and chondrules in meteorites, 4570 Ma. This age has been established from 238U-206Pb and other decays. It is taken to be the age of the Solar System. The chondrules are near to 2 Ma younger than the CAIs. To establish such a small age difference between two such large ages use is made of short-lived isotopes. For example, 26Al decays to 26Mg with a half-life of only 0.73 Ma, much faster than the decay of 238U. So, by comparing the lead and magnesium isotope contents of the CAIs and chondrules we can get the age difference with reasonable precision. The details will not concern us. Note that the presence of short-lived isotopes, as inferred from their daughter products, indicates that the CAIs separated within a few million years of the short-lived isotope being created in stars. Furthermore, the CAIs and chondrules could not have survived in isolation for more that a few million year, and so the formation of meteorite parents must have been fairly rapid. This is consistent with the time scale of the formation of planetesimals in Chapter 2. Some separation ages are younger, but very few are less that 1600 Ma. These younger ages are the result of some later melting or vaporisation that reset the radiometric clock.

Space exposure ages

The time for which a meteorite has been exposed to space is obtained from the action of cosmic rays on the parent meteoroid. Cosmic rays are atomic particles that pervade interstellar space, moving at speeds close to the speed of light. They are primarily nuclei of the lighter elements, notably hydrogen. When a cosmic ray strikes a solid body it will penetrate up to a metre before it stops, leaving a track, and creating unstable and stable isotopes via nuclear reactions. The quantities of these isotopes increase with the duration of the exposure, and so, by measuring the quantities among the tracks, and knowing the cosmic ray flux in interplanetary space, the cosmic ray exposure age can be calculated.

Many meteorites have exposure ages considerably shorter than their chemical separation (solidification) ages - strong evidence that solid bodies larger than the metre or so cosmic ray penetration depth have been disrupted in space long after they solidified. Most exposure ages are 10-50Ma, far too long to trace meteorite origins. Some stones have particularly short exposure ages, as little as 0.1 Ma. This is presumably because stony materials are less strong than iron, and are thus more readily broken in collisions and eroded by dust. This gives a constant supply of unexposed material for cosmic rays to lay their tracks in.

Question 3.12

By obtaining an equation for N(87Sr)/N0(86Sr), show that the isochron slope in Figure 3.15(b) is (e'/T — 1). (This needs good facility with algebra.)

Question 3.13

If a certain meteorite is a piece of a larger body, how could it nevertheless have an exposure age far greater than the time ago that it was liberated from the larger body? Why could its calculated exposure age never exceed its solidification age?

3.3.4 The Sources of Meteorites

As well as the Tagish Lake parent's orbit (Section 3.3.2), a clue to the sources of the meteorites is in the few known orbits of the parent meteoroid, which resemble the orbits of the NEAs (Section 3.3.1). □ What does this suggest is the source region of these meteorites?

This suggests an ultimate origin in the asteroid belt. The short cosmic ray exposure ages of the stones supports this conclusion, the ages being consistent with the high rate of collisional disruption expected in the asteroid belt, continuously liberating unexposed material, and the relatively short times before many of the meteoroids so generated will collide with the Earth. Many meteorites show evidence of collisional disruption, notably in minerals that have been shocked, and in structures indicating broken fragments that have been cemented together. Sometimes the fragments seem to have come from different bodies, or to have been subject to different processes. To get a meteoroid from an orbit within the asteroid belt into a near-Earth orbit, it is usually necessary for its orbit to be perturbed by Jupiter, or sometimes Mars, when the meteorite encounters an mmr. Such encounters continually occur because of orbital migration caused by the Yarkovsky effect (Section 3.1). Of the more than 30 000 meteorites known, very nearly all seem to be asteroid fragments.

Further support for the view that meteorites are derived from the asteroids comes from comparing the reflectance spectra of the various classes of asteroid with those of the various classes of meteorite. As noted in Section 3.1.6, a clear correspondence exists between the CCs and the abundant class C asteroids. The CCs are presumably collisional fragments of an asteroid that never became sufficiently heated to lose its carbonaceous materials and hydrated minerals, and was far too cool to differentiate. The parent asteroid might itself have been a fragment of a larger unheated body. In the outer belt we see class C asteroids in abundance, indicating that this is where the large asteroids avoided differentiation, perhaps because of weaker magnetic induction heating (Section 3.1.6), and lower proportions of rocky materials and iron, which would give less accretional and radioactive heating. From their position in the outer belt there could well be a low probability of transfer to a near-Earth orbit, which would explain why class C asteroids are common, but the corresponding meteorites, the CCs, are rare.

There is also a clear correspondence between irons and the rare class M asteroids. As pointed out in Section 3.1.6, early in Solar System history the larger asteroids (a few hundred kilometres across, or larger) could have become warm enough to differentiate fully or partially. Figure 3.16 shows the resulting layered structure in the partially differentiated case. The Widmanstatten pattern in irons is indicative of the slow cooling that would occur in the iron core of a large asteroid. Fragmentation of the asteroid can expose the core, which itself could subsequently be fragmented. The core, or its fragments, are the class M asteroids, and the smaller fragments are the parent meteoroids of the iron meteorites. A complication is that the magnesium-rich silicate called enstatite could be mixed with iron-nickel without betraying its presence. Therefore, some class M asteroids might be a mixture of iron-nickel with this type of silicate. Radiometric dating of irons indicates that the parent asteroid formed, in the main, early in Solar System history, just 5-10 Ma after the CAIs.

Stony-irons show some correspondence with S class asteroids. □ What is a possible origin of such asteroids?

These asteroids could come from the interface between the iron core and the silicate mantle of (partially) differentiated asteroids, where silicates and iron are mixed.

There are only a few asteroids that match the achondrites. The largest achondrite subgroup comprises the howardites, eucrites, and the diogenites, called the HED subgroup. These are

Some ordinary

Some ordinary

100-500 km

Figure 3.16 A partially differentiated asteroid, showing regions from where various sorts of meteorite could originate.

100-500 km

Figure 3.16 A partially differentiated asteroid, showing regions from where various sorts of meteorite could originate.

composed of silicates like feldspar and pyroxene (Tables 2.3 and 6.1). In an asteroid these would be produced by the melting of parent silicates, notably olivine and pyroxene (Table 6.1) followed by differentiation, with the new silicates rising to the top, where they constitute basalts (= feldspar + pyroxene), and the metallic iron sinking to form a core. This requires an asteroid more than a few hundred kilometres across, a necessary (but not sufficient) condition that differentiation is (nearly) complete, so that the achondrite silicates are at the surface and the metallic iron is in a core. The HEDs show a good spectral match with the rare class V asteroids, which includes Vesta, 256 km mean radius, and a handful of small asteroids, presumably collision fragments. HST images of Vesta show a big impact crater (Figure 3.6(a)) that could have supplied a huge number of HEDs, a view supported by the few known HED orbits being similar to that of Vesta. The high density of Vesta (Section 3.1.5) is consistent with a considerable iron core. Radiometric dating of the HEDs indicates core formation within 4 Ma of CAI formation.

Some of the achondrites that are not HEDs could have come from the interiors of partially differentiated asteroids (Figure 3.16) that were collisionally disrupted. The rare basalt meteorite (NWA011) might be from the asteroid Magnya which seems to have a basalt surface, in which case Magnya is a differentiated body.

Ordinary chondrites

The most common class of meteorite is the ordinary chondrite, OC (Figure 3.14), in which the silicates are composed largely of pyroxene and olivine, and (excluding volatile substances) with elemental composition similar to the Sun. This indicates that they originate from undifferentiated asteroidal material. In spite of their abundance, it was only in 1993 that an asteroid was discovered that provided a good spectral match. This is Boznemcova, and it is only 7 km across. Other candidate asteroids are the Q class, though these are few in number. A particularly promising candidate is the S class asteroid Hebe, with a semimajor axis of 2.43 AU that places it in the inner main belt. It has a mean radius of about 90 km, and in 1996 its surface spectrum was shown to match that of the H-type subclass of OCs that accounts for about 40% of them. Moreover, Hebe orbits near to the 3:1 resonance with Jupiter (Figure 3.1), and so chips off its surface would readily find their way to the Earth. Some other OCs could originate from the outermost zone of a partially differentiated asteroid (Figure 3.16).

Other S class asteroids could well be copious sources of OCs too. The S class constitutes about 80% of the inner main belt (Figure 3.8), from where there is ready access to the Earth. These asteroids have spectra that in a few cases are a good match to the OCs, but in many cases display only muted and reddened spectral features of pyroxene and olivine. However, it has been shown that space weathering by solar UV radiation, micrometeorite bombardment, and perhaps cosmic rays, darken and redden OC materials in just the right way, and that the pristine surface of an S class asteroid should be a close spectral match to the OC interiors. NEAR's mission to the S class asteroid Eros has shown that it has the same composition as the OCs.

Martian and lunar meteorites

By mid 2006, there were 34 meteorite finds in which oxygen isotope ratios throughout the group are distinctly non-terrestrial, and sufficiently similar to suggest a common origin. Each one contains minerals of volcanic origin with solidification ages in the range 165-1360 Ma

(except for one, ALH84001, which has a solidification age of 4500 Ma). We thus seek an extraterrestrial parent body that could have produced molten rock at its surface by volcanic processes 165-1380 Ma ago. It also has to be relatively nearby, and with at most a thin atmosphere so that a huge meteorite impact could throw surface materials into space. Amongst our neighbours, only Venus and Mars could have had volcanic processes so comparatively recently.

Venus has a very thick atmosphere, inhibiting the escape of rocks. Also, the impact on Venus would have to be so violent that either the rocks would be vaporised completely, or they would bear telltale signs of extreme violence, and these are not seen.

Mars is thus the only candidate. That Mars is indeed the parent body is strongly indicated by gases trapped within one of the meteorites, EETA 79001 - in the mid 1980s these were shown to have a composition similar to the Martian atmosphere, and unlike any other plausible source. Recently, the Mars Exploration Rover, Opportunity, found a rock with a mineral composition very similar to EETA 79001. Other meteorites in this group have now also been shown to have Martian characteristics. The Martian meteorites provide us with important information about Mars, as you will see in later chapters.

What sort of impacts on Mars are required to provide the Martian meteorites? Computer models show that an impact that would produce a crater about 3 km across would eject millions of bits of the Martian crust into space large enough to constitute meteoroids rather than dust, and with negligible impact melting. After the heavy bombardment, which ended about 3900 Ma ago, a Martian crater about 3 km across would have been created at average intervals of 0.2 Ma, leading to an estimate of a few meteorites per year landing on the Earth, certainly enough to account for the small sample that has been found. But at least half of the Martian crust had formed by about 4000 Ma ago, so why are the meteorite ages predominantly much younger? One explanation is that the older Martian crust, having been exposed longer to meteorite bombardment, has developed a thick coat of loose rubble and dust (regolith) that has cushioned the larger impacts. Additionally, or alternatively, the widespread presence of sediments on the older terrain could provide a cushion.

Nearly 100 meteorites from the Moon have also been found, a largely undisputed origin because of the compositional similarities with the lunar surface samples that have been returned to Earth by lunar expeditions. Further material from the Moon might be some of the many tektites found on Earth. These are rounded glassy objects, typically 10 mm across, with a presumed volcanic or impact melt origin.

The Moon is very much nearer to us than Mars. It is therefore a puzzle why there are not far more lunar meteorites than Martian ones - models predict a ratio of about 100:1.

Question 3.14

State a possible origin of the stony-iron meteorites, and the likely origins of the OCs, and hence account for the broad differences in their compositions.

3.3.5 The Sources of Micrometeorites

Most micrometeorites are derived from bodies that in space must have been less than a few millimetres across. The great majority of bodies of this size vaporise completely in the Earth's atmosphere and account for most of the meteors. Therefore, if we can find the source(s) of the meteors we will have found the source(s) of the micrometeorites.

If you were to go out on a clear dark night, then on most days in the year you would see on average about 10 meteors per hour. On or around a few dates, the same each year, the hourly rates are considerably greater. These enhanced rates are called meteor showers. Just how much greater the hourly rate becomes in a shower varies from year to year, but in exceptional years rates of the order of 105 meteors per hour are observed; these are called meteor storms. Observations show that the meteors in a shower very nearly share a common orbit, and for many showers this orbit is the same as the orbit of a known comet. In other cases the orbit indicates an asteroidal source. There are 19 major showers. Table 3.1 lists the six that are usually the strongest, with their dates and associated comet or asteroid.

Figure 3.17 shows how a comet gives rise to a meteor shower (the case of an asteroidal source is similar). Rocky particles are lost by the comet and initially do not get far away. They are estimated to vary in size from submicrometre dust particles, to loose aggregates up to several millimetres across, and sometimes far larger. With each perihelion passage of the comet the debris accumulates, and various perturbations gradually spread it along and to each side of the orbit. The debris moves around the orbit, and when the Earth is at or near the comet's orbit at the same time as the debris, a shower results. The year-to-year variations are the result of a nonuniform distribution of debris along the orbit. The cometary origin of many showers is further supported by estimates of the particle densities, obtained from the rate at which the Earth's atmosphere slows them down. Values in the range 10-1000 kg m-3 are obtained, suggesting loose aggregates of dust particles of the sort that comets could yield.

Micrometeorites are also loose aggregates, indicating that they are comet debris that has survived atmospheric entry. This possibility is strongly supported by the composition of the micrometeorites, which is in accord with remote observations of comets and with in situ measurements made by Giotto on dust lost by Halley's comet. Micrometeorite composition is something like that of the CCs, though sufficiently different to indicate a source other than class C asteroids. It therefore seems that most meteors, and hence most micrometeorites, originate from the rocky component of comets.

Of the meteors that do not belong to showers, most are thought to be comet debris no longer concentrated along the parent comet's orbit. A few meteors have entry speeds that are so high (> 72 ms-1) that they might have come from beyond the Solar System. This interpretation is supported by the greater fluxes of fast meteors when the Earth is at points in its orbit when it

Table 3.1 The six strongest meteor showers

Shower namea

Date rangeb

Associated parent

Quadrantids

G1-G6 Jan

96P/Macholtz 1

Eta Aquarids

G1-G8 May

1P/Halley (HFC)

Perseids

25 July-18 Aug

109P/Swift-Tuttle (HFC)

Orionids

16-26 Oct

1P/Halley (HFC)

Leonids

15-19 Nov

55P/Tempel-Tuttle (HFC)

Geminids

G7-15 Dec

Phaeton (an Apollo asteroid)

a Each name is derived from the constellation from which the shower appears to emanate. b These are the approximate dates each year on which the shower is greatest.

a Each name is derived from the constellation from which the shower appears to emanate. b These are the approximate dates each year on which the shower is greatest.

Figure 3.17 Meteor showers and the orbit of a comet.

is either travelling in the same direction through the Galaxy as the Solar System as a whole, or travelling towards nearby massive stars.

Question 3.15

Give two plausible reasons for why some meteor showers are in orbits in which no comet has been seen.

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