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As discussed in these earlier reports, it may be expected that there will be a relationship between the distribution of orbits from which meteorites impact Earth and the orbit of their source. At the time the meteorite was fragmented from a larger body, its initial orbit was approximately that of the larger body, because the large unshocked fragments surviving the fragmentation event will have a low velocity in the center-of-mass reference frame. However, these initial orbits will not be identical; and, with the passage of time, they will evolve into a distribution of orbits, some of which will be Earth crossing ones from which meteorites will be derived. The approach that has been taken is to consider various source orbits or “initial orbits” and see which, if any, of these evolve into orbits distributed in such a way as to correspond to the observed data. It is also necessary that the time interval between the fragmentation event that starts the “cosmic-ray clock” and Earth impact be in agreement with cosmic-ray-exposure ages, and furthermore, that any acceptable source provide a mass yield in accord with the observed meteorite flux.

The observed data consist of the time of fall of several hundred meteorites, the apparent radiants and exposure ages of about 100, and a very few complete orbits, only two of which can be considered well determined, Příbram and Lost City. Only for the most abundant class of meteorites, the chondrites, are these observed data sufficiently complete to be useful. In addition, orbits have been determined for a large number of bright fireballs falling within the Prairie Network. (See McCrosky, 1967.) These data for chondrites and fireballs are shown in figures 1 through 4.

In my previous studies (Wetherill, 1968a,b; 1969), I have considered initial orbits corresponding to those of the Moon, the Earth-crossing Apollo asteroids,

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observed TIME of FALL (hours)

Figure 1.-Observational data for time of fall of chondritic meteorites. Dotted area indicates daytime falls, when social biases are of lesser importance.

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the Mars-crossing asteroids, typical ring asteroids, Hilda and Trojan asteroids, various short-period comets, and long-period comets. The evolution of these orbits was calculated by use of a revised version of the Monte Carlo method developed by Arnold (1965a,b), and the distribution of the observable quantities calculated from those orbits terminating with Earth impact. Comparison of the calculated and observed data showed that none of these sources yielded data that agreed with the observed data. In fact, it was shown that only an initial Earth-crossing orbit with perihelion near Earth, aphelion near Jupiter (i.e., "4.5 AU), and low inclination would be satisfactory. Calculated exposure ages for such a source are shown in figure 5. The difficulty

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Figure 4.—Observed distribution of geocentric velocities and radiants for Prairie Network fireballs (circles) and the better determined meteorite orbits (squares). The curve marked ~ is the boundary between elliptic and hyperbolic orbits; the other curve is the locus of relatively low-inclination orbits with aphelia at 4.5 AU.

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Figure 5.-Calculated distribution of exposure ages for a starting orbit resulting in Earth impacts corresponding to the low-velocity component of the Prairie Network flux. Aphelion = 4.50 AU, perihelion = 1.01 AU, inclination = 2°. This dynamically determined distribution is very similar to that observed for chondrites, except for those few with exposure ages greater than 50 million yr. These will probably be removed by collisional destruction.

with this orbit is that no family of bodies with such orbits is known. It was suggested (Wetherill, 1969) that a more plausible model would be one in which the observed data were augmented by a component of higher velocity bodies that fail to survive passage through Earth's atmosphere.

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RECENT DEVELOPMENTS

Work done on this problem during the last 2 yr has confirmed and extended these earlier conclusions. In particular, no satisfactory way has been found for removing from the principal belt of asteroids a significant quantity of relatively unshocked material on the necessary time scale. Other asteroidal sources continue to appear unsatisfactory. The principal new developments during the last 2 yr are the recognition of the fact that the Prairie Network fireball data agree very well with the results predicted for short-period comets of Jupiter's family (and not for other possible sources) and the experimental work of Gault (1969) showing that finite-sized bodies can be broken into fragments much more readily than semi-infinite targets.

It now appears very likely that the Prairie Network fireballs are derived from short-period comets or possibly from related bodies having the same orbital history but less visible as a consequence of containing a smaller fraction of volatile matter. In any case, the identification of the fireballs with these comets shows that objects hundreds of kilograms in mass are associated with these bodies, only a small fraction of which mass can be volatile matter. Consequently, in at least this sense there must be “dead comets,” as discussed by Öpik (1963).

COMETS AS SOURCES OF FIREBALLS AND CHONDRITES

In figure 4, the Prairie Network results are plotted on a diagram where the ordinate is the geocentric velocity and the abscissa is the elongation of the geocentric radiant (corrected for zenith attraction). The scale on the ordinate at the left is the geocentric velocity prior to acceleration by Earth's gravitational field; that at the right is the actual velocity at which the body enters the atmosphere with its velocity augmented by Earth's gravitational field. Values of the elongation of the radiant near 0° correspond to objects of low inclination that are near their perihelion, when they are moving more rapidly than Earth and are overtaking Earth. Values near 180° correspond to the opposite situation: bodies near their aphelion; i.e., with orbits within that of Earth. The curve marked oo is the boundary between elliptic heliocentric orbits and hyperbolic orbits not bound to the solar system. The other curve bounds the regions for which objects of low inclination (i.e., 315°) have their aphelia greater or less than 4.5 AU. Orbits plotted to the right of this curve have aphelia less than 4.5 AU and have escaped Jupiter's “sphere of influence” but nevertheless are still subject to strong perturbations by Jupiter. The exact position of this boundary is slightly dependent on the inclination, but for the values of the inclination actually observed, this is not significant.

The Prairie Network fireball points are seen to be displaced along the 4.5 AU curve over a wide range of geocentric velocities. This is characteristic of bodies whose orbital evolutions have been primarily determined by proximity to Jupiter. In contrast to this, a body crossing only Earth's orbit will tend to preserve a constant geocentric velocity as a consequence of the approximate conservation of its kinetic energy in geocentric coordinates at the point of close approach to Earth. Such a body will evolve horizontally on a diagram of this kind, resulting in frequent high values of the elongation of the radiant. On the other hand, the Jupiter perturbations tend to conserve the same quantity in Jupiter's frame of reference, resulting in a wide spread of geocentric velocities, as exhibited by the Prairie Network fireballs. This is the essential reason why predicted data for bodies with initial Earth-crossing orbits well inside Jupiter's orbit, such as most asteroidal sources, fail to agree with the Prairie Network data. There are several possible meteorite sources whose orbital evolution is dominated by Jupiter. These are the short-period comets of Jupiter's family and collision ejecta from the Hilda (a - 4.0 AU) and Trojan (a - 5.0 AU) families of asteroids. Ejecta from the latter two sources that are not stabilized by the commensurability stabilizing the asteroid orbits themselves will be strongly perturbed by Jupiter but will seldom achieve perihelia within that of Earth. The low Jovicentric velocity of these bodies may lead to Jupiter capture; more probably, interaction with the eccentric components of Jupiter's velocity will accelerate the object into Saturn crossing, and ultimately to ejection from the solar system. The orbits of the short-period comets will evolve in a somewhat different way. If their perihelia are initially not too distant from Earth's orbit (i.e., 1 to 2 AU), Jupiter perturbations acting near their aphelia will frequently move the perihelia just inside Earth's orbit. Following this, close approaches to Earth will occasionally move the aphelia within 4.5 AU. Escape from Jupiter's sphere of influence may also be aided by nongravitational accelerations, as discussed by Marsden (1968). Although most cometary orbits will suffer the fate of ejection from the solar system (as was the case for the Hilda and Trojan asteroidal ejecta), a small but significant fraction of short-period comet orbits will evolve so that their aphelia are ~4.5 AU and their perihelia ~1 AU. From such orbits, meteoroids with the orbital characteristics of the Prairie Network fireballs are derived. If, as proposed by Öpik (1963), there is a residual nonvolatile portion of the comet remaining after the volatile gases, which cause the comet to be visible, have evaporated after ~1000 yr, this nonvolatile component will comprise a “dead comet” that will still have, in many cases, a dynamical lifetime of 10° to 107 yr. This model fits the observed dynamical and physical properties of the Prairie Network fireballs, and no other source has proven to be satisfactory. Predicted data calculated by the Monte Carlo method for residua from comet Neujmin 2 are shown in figure 6, and are seen to resemble closely the distribution found observationally for the fireballs (fig. 4). Similar results are found for any orbit with aphelion within Jupiter's orbit and perihelion less than about 2.0 AU. About 10 percent of the observed short-period comets fulfill these criteria; the remainder will give similar points but with greatly reduced mass yields. The results of similar Monte Carlo

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