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REFERENCES

Alfvén, H. 1969, Asteroidal Jet Streams. Astrophys. Space Sci. 4, 84-102.

Brouwer, D. 1951, Secular Variations of the Orbital Elements of Minor Planets. Astron. J. 56, 9–32.

Brouwer, D., and Clemence, G. M. 1961, Methods of Celestial Mechanics, p. 527. Academic Press, Inc. New York.

Houten, C. J. van, Houten-Groeneveld, I. van, Herget, P., and Gehrels, T. 1970, Palomar-Leiden Survey of the Faint Minor Planets. Astron. Astrophys. Suppl. 2, 339–448.

Kresák, L. 1967, The Asymmetry of the Asteroid Belt. Bull. Astron. Inst. Czech. 18, 27–36.

Kresåk, L. 1969, The Discrimination Between Cometary and Asteroidal Meteors. II. Orbits and Physical Characteristics. Bull. Astron. Inst. Czech. 20, 231.

DISCUSSION

VAN HOUTEN: Kresåk argues that the number of asteroids found in the PLS is larger than the average value for a field of equal size along the ecliptic. This conclusion is based on a combination of the following points:

(1) There is a preferential orientation of asteroid perihelia in the direction of the perihelion of Jupiter's orbit.

(2) The PLS was taken in the direction of the perihelion of Jupiter's orbit.

(3) Asteroids are usually discovered near perihelion.

In his figure 1, Kresák shows that, indeed, there is a pronounced asymmetry in the distribution of perihelia for asteroids found in the PLS. This may give the impression that there is a large excess of PLS objects compared to those of the general field, supporting Kresák's conclusion mentioned above. But before this conclusion can be safely made, the PLS distribution of perihelia should be compared with that of the numbered asteroids. This comparison is shown in table D-I. The PLS material of 980 first-class orbits is compared with the data of Bauschinger (1901), who used the numbered minor planets 1 to 463, and Kiang (1966), who used 791 asteroids with mo « 15. The material is divided into four intervals; the first interval is centered on Jupiter's perihelion.

The results of Bauschinger and Kiang are practically identical; and they show that in the PLS there is a small excess, about 2 or 3 percent, of orbits oriented in the direction of Jupiter's perihelion. This excess is so small that it hardly influences the number statistics. Accordingly Kresåk's result of a ratio of 1.26 of the asteroids near the vernal equinox compared so those near the autumnal equinox is far too large.

KRESAK: A ratio of 1.26 of the two extremes corresponds to an excess of 12 percent in the direction of the PLS, and 10 to 11 percent in the first interval of table D-I, as

TABLE D-I.—Comparison of the Distribution of Perihelia

Distributions, percent

Intervals, J 4 so PLS Bauschinger Kiang 330° to 60° 40 38 38 60 to 150 23 24 24 150 to 240 11 14 15 240 to 330 26 24 23

compared with the average abundance along the ecliptic. Table D-I suggests a relative excess of 2/38 (i.e., 5 to 6 percent) in the first interval, and the differences in the ratios of the first to the third interval (3.6 for the PLS and 2.5 to 2.7 for the samples of numbered asteroids) appear rather significant. Thus the disagreement is not as bad as it appears to be at first glance. Moreover, the predicted ratio is based on the assumption that the actual degree of alinement is the same for bright and faint asteroids, which cannot be verified by a one-directional survey. The correlation between eccentricity and inclination, producing an additional latitudinal dispersion of asteroids in the direction of Jupiter's perihelion, might remove the remaining discrepancy. Anyway, a definitive solution of this complex problem can be obtained only from a comparison sample taken in the opposite direction.

DISCUSSION REFERENCES

Bauschinger, J. 1901, Tabellen zur Geschichte und Statistik der kleinen Planeten. Veröff.
Königi. Astron. Recheninst. Berlin no. 16.
Kiang, T. 1966, Bias-Free Statistics of Orbital Elements of Asteroids. Icarus 5,437–449.

PART ||

ORIGIN OF ASTEROIDS

INTERRELATIONS WITH COMETS, METEORITES, AND METEORS

ASTEROIDAL THEORIES AND EXPERIMENTS

GUSTAF ARRHENIUS AND HANNES ALFVéN
University of California, San Diego

Theories on the origin and evolution of asteroids are confronted with three types of experimental tests. The first refers to the dynamic state of the asteroids and consists of orbital and in some cases spin data for bodies as small as about 1 km. (There are reasons to assume that the size spectrum extends to very small objects but nothing is known about them.)

The second type consists of observations of the chemical and structural properties of objects fallen to Earth from space. Here the relationship to asteroids is much more tenuous. Nevertheless, the study of meteorites has provided important insight into the chemical evolution of small bodies in space. As long as one realizes that such data refer only to bodies of special structure, composition, velocity, and other orbital characteristics, they can be useful also for conjectures about asteroids.

The third source of information, also bearing indirectly on the structure and evolution of asteroids, is the lunar surface, which provides for the first time a display of the dynamic interaction between the surface of a celestial body and the space environment. To be applicable to the asteroidal environment, these results have to be scaled in a way that remains somewhat hypothetical.

BREAKUP AND ACCRETION IN THE ASTEROIDAL REGION

The mass in the asteroid region is small (fig. 1) and has not been collected into a small number of bodies as in the planetary regions. A similar situation seems to prevail in the satellite systems of Jupiter, Saturn (fig. 2), and Uranus, where analogous mass gaps are observed.

It is sometimes claimed that the present asteroid distribution has resulted from the explosion of one or a few larger bodies. Such an assumption meets with serious mechanical difficulties; some of these are examined below.

The distribution of particles in collectives such as the asteroidal and cometary jetstreams would appear to be a result of the two opposing processes of accretion and fragmentation. For reasons that are mainly historical, the emphasis has been placed mostly on the fragmentation process, which no doubt is important, but which alone cannot account for the observed distribution of bodies. One of the reasons for the biased interpretation is that

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