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Figure 6.-Calculated distribution of geocentric velocities and radiants for Earth impacts resulting from a starting orbit equivalent to the observed short-period comet Neujmin 2. Aphelion = 4.79 AU; perihelion = 1.32 AU; inclination = 10.6°; and Earth impact efficiency = 0.24 percent. Earth impacts requiring more than 30 million yr have been removed because these bodies would probably be destroyed by collisions in the asteroid belt. Inclusion of these events would not affect the distribution very much.

calculations for several other comets are being published elsewhere (Wetherill, 1971). From this work it is believed that not only are most of the smaller meteors of cometary origin, as has been known for a long time, but also the massive objects observed by the Prairie Network. Consequently, essentially all of the extraterrestrial flux on Earth is derived from comets. There remains the question of whether the meteorites and the chondrites in particular can be identified with this source. It would not be expected that objects with initial atmospheric velocities greater than about 20 km/s would survive passage through the atmosphere unless they are unusually large. Therefore it may be anticipated that only the lower velocity component of the data shown in figure 4 would be represented in the material reaching Earth. From figure 4 it may be noted that almost all of these low-velocity bodies have elongations of the radiant less than 90°. This is in accord with the observational data for chondrites (fig. 2) and also leads to the correct distribution of fall times (fig. 1). The calculated exposure ages would also be similar to those of figure 5. The interpretation of the exposure age for a cometary source depends on the comet model employed. If it is thought that chondrites are buried within the volatile matter of the comet and become separated following the loss of the volatile matter, then the exposure age would start immediately after this loss. As mentioned above, the time (~1000 yr) required for loss of the volatile matter is small compared to the exposure age and can therefore be neglected. On the other hand, it could also be that the cometary core is a solid piece of chondritic material hundreds of meters in dimension, the interior of which will be initially shielded from cosmic rays. This model then is in many ways equivalent to an Apollo asteroid source in that the meteorites are derived from a dense, nonvolatile body in an Earth-crossing orbit. Unlike the observed Apollo asteroids, these bodies will predominantly have aphelia near 4.5 AU. As discussed elsewhere (Wetherill and Williams, 1968), it is quite likely that Apollo asteroids with large aphelia have escaped detection, and as Öpik (1963) has argued, it is also probable that even the observed Apollo asteroids are cometary cores. If these statements are accepted, therefore, this model of the cometary source becomes identical to an Apollo asteroid model for the origin of chondrites and would also be acceptable as the source of Prairie Network fireballs. There is evidence that at least the present flux of chondrites is derived from a small number of sources. The most compelling evidence of this kind is that a large number of hypersthene chondrites appear to have experienced a common shock impact within the last 500 million yr (Heymann, 1967). As discussed elsewhere (Gopalan and Wetherill, 1971), this event is not well dated and could have occurred during the last 50 million yr. Therefore, these data are not in themselves strong evidence against a cometary origin of chondrites, but do support the second alternative discussed above; i.e., derivation of chondrites from large comet cores rather than from many small pieces. In summary, when one includes the effect of the atmosphere as a velocity filter, it turns out that short-period comets satisfy the dynamical requirements for chondrites as well as for fireballs. Probably the principal difficulty in identifying the chondrites with the fireballs is that the typical fireball apparently has a density lower than that of chondrites and tends to disintegrate in the atmosphere more readily than expected for chondrites. The Lost City meteorite had an aerodynamically determined density higher than that of a typical fireball; on the other hand, Příbram was a typical fireball, with a calculated density, if anything, lower than average. Some evidence for associating typical fireballs with at least one class of chondrites is provided by Revelstoke, a type I carbonaceous chondrite recovered following the disintegration of a very large fireball corresponding to an incident mass of hundreds of megagrams, most of which failed to penetrate the atmosphere. The question of the association of more dense stones with the more friable material of a typical fireball remains open. The identification of possible sources for the highly differentiated meteorites, the achondrites and irons, is more difficult because of the paucity of dynamical data available for these bodies. The high exposure ages of iron meteorites are probably indicative of an asteroidal origin, although a completely satisfactory theory of their mode of derivation from the asteroid belt remains to be developed.

COLLISIONAL DESTRUCTION

The other major development in the last few years has been the experimental work of Gault (1969) on the fragmentation of finite-sized targets. It has long been recognized that meteoritic bodies will undergo collisions with asteroidal debris and cometary meteors and will thereby be reduced in mass. Earlier calculations (Wetherill, 1967) showed that “space erosion” by micrometeorite bombardment was probably of minor importance. However, these same calculations showed that total destruction by a single impact of the meteorite in space might be sufficiently probable to play a minor role in limiting the observed exposure ages of chondrites to a few tens of millions of years. This higher probability for total destruction is in large measure a consequence of the fact that fragmentation of a finite-sized body can result from hypervelocity collision with much smaller masses. Cratering experiments indicate that collisions in the asteroid belt between small and large bodies should produce craters on the larger body, the mass ejected from the crater into space being about 100 times the mass of the projectile. However, for somewhat larger projectiles, additional damage to the target results from shock waves traversing the body and reflecting from the bounding surfaces. In the earlier calculations (Wetherill, 1967) it was estimated that this effect might increase the ratio of ejected mass to projectile mass to about 10° for the case when this additional damage was just sufficient to fragment the target into a number of pieces. The experiments of Gault have now shown that ratios of ejected to projectile mass as high as 10° are possible. The effect of this new result on cosmic-ray-exposure ages has been evaluated by computing the probability of destruction of bodies in various orbits by collision with a population of objects with orbits distributed similarly to the observed asteroids and periodic comets. Several assumptions were made regarding the total mass and population index of the colliding asteroidal and cometary bodies, based on meteor observations and theoretical studies of fragmentation in the asteroid belt (Dohnanyi, 1970). The effect of the relative velocity of the two colliding bodies was taken into consideration not only insofar as it affects the probability of collision, but also in accordance with its effect on the strength of the collision by use of Gault's experimental result that kinetic energies of 10° to 10° J/kg (10° to 107 ergs/g) will suffice to completely fragment finite-sized bodies. The results of these calculations are that total destruction by asteroidal fragments and cometary meteors are of comparable importance and that either may predominate, depending on the exact assumptions made regarding the flux of the colliding bodies. For fragmentation energies of 10° J/kg (10° ergs/g), a body 50 cm in radius will have a mean lifetime of about 10 million yr. This result is not very sensitive to the orbit assumed for the body. Uncertainties in the flux could easily cause the quantity to be in error by a factor of 10. Fragmentation energies of 10° J/kg (107 erg/g) will increase the lifetime to about 100 million yr. In addition, it is possible that meteorite lifetimes may be limited by rotational bursting (Paddack, 1969). The consequence of these results is that it now seems likely that total destruction by collision will prevent meteorites from having very large cosmic-ray-exposure ages. For the calculations based on the cometary source, this is a secondary effect. In this case, the cosmic-ray-exposure ages will be primarily controlled dynamically; the probability of these objects surviving ejection from the solar system by Jupiter perturbations for more than ~25 million yr is not large anyway. The effect of collisional destruction will be to cut off the high exposure age “tail” on figure 5 and bring the calculated results into even better agreement with the observed data. For asteroidal sources, the effect is greater because for collision lifetimes as short as 107 yr it is no longer possible to obtain the long exposure ages calculated for meteorites derived from Mars-crossing asteroids and, to a lesser extent, from Earth-crossing Apollo asteroids. This does not, however, increase the plausibility of deriving asteroids from these sources. Fragments of objects moving in orbits similar to the observed Mars-crossing or “Mars-grazing” asteroids will have their initial perihelia barely within Mars' aphelion. Multiple perturbations involving elapsed times of the order of 10° yr will be required to perturb this initial orbit into an Earth-crossing orbit. By this time, collisional destruction will have eliminated all of the fragments. If the initial distribution of Mars-crossing orbits were a random one, about 1 percent of the fragments would be perturbed into Earth-crossing orbits sufficiently rapidly to avoid destruction. However, as pointed out above, the distribution of initial orbits is a very special one, and a distinct delay on the order of 10° yr is involved prior to appearance of the fragments in Earth-crossing orbits. This difficulty of survival can be avoided by theories in which chondrites are derived from Apollo asteroids as a result of partial or complete fragmentation of the asteroid as it passes through the asteroid belt. In this case, the fragments are produced directly in Earth-crossing orbits and no delay of the type discussed above occurs. As discussed earlier in this paper, the most plausible cometary model is a theory of this kind in which the “Apollo asteroids” are cometary cores with aphelia near 4.5 AU. Alternative Apollo asteroid theories in which they are derived from ring asteroids or from Mars-crossing asteroids are less satisfactory. A short lifetime for collisional destruction removes the objection to theories of this kind raised previously (Wetherill and Williams, 1968) that predicted exposure ages are far too long. At the same time, this makes it more difficult to reconcile the other observations with the results predicted for such a model. The large observed excess of radiants less than 90° requires that most Earth impacts occur while the meteorites are near their perihelion. This fact in turn requires that a large fraction of the meteorites be produced immediately after the Apollo asteroid is perturbed into Earth crossing. With the passage of time, the Apollo asteroid will be perturbed by Earth and Venus into orbits for which its aphelion is near Earth as frequently as its perihelion. This tends to produce a symmetric distribution of radiants for low-velocity bodies, and an excess of radiants greater than 90° for higher velocity bodies. This has always been a problem with theories of this kind. Short collisional lifetimes aggravate this difficulty by relatively deemphasizing fragments produced when the Apollo asteroid first becomes Earth crossing in favor of those produced later after the perihelion of the source has become randomized.

SUMMARY

These calculations indicate excellent agreement between observed and predicted orbits of Prairie Network fireballs, if it is assumed that fireballs are derived from remnants of short-period comets of Jupiter's family. No such satisfactory agreement has been found for any other proposed source. The distribution of radiants and time of fall observed for chondrites will also be reproduced by this source, provided that consideration is given to the fact that Earth's atmosphere will permit low-velocity bodies to survive but will destroy high-velocity bodies. Again, no other proposed source has been found to be adequate.

It now appears likely that the mean lifetime of chondrites is limited to ~107 yr by the high probability of complete fragmentation following impact by smaller bodies. This improves the agreement between the observed cosmic-ray-exposure ages and those predicted for a cometary source. This also requires some modification of the earlier discussions of alternative sources but does not result in their becoming more satisfactory.

Note added in proof. Recent work by P. Zimmerman and the author shows that it is possible to inject fragments of the size of small asteroids into the 2:1 Kirkwood gap. Although the resulting libration will enable the body to avoid Jupiter, a meteorite-sized fragment ejected at a velocity of about 200 m/s as a result of a collision can escape the libration region and be in an orbit similar to those of the short-period comets, as discussed in this paper. This mechanism has not yet been sufficiently quantitatively evaluated in order to learn its importance as a source of meteorites.

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