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promising instruments, in the breadboard stage of development, to determine composition by time-of-flight mass spectroscopy (Grün, 1970; Roy and Becker, 1970). The small-particle population can provide diagnostic evidence for phenomena currently going on in the asteroid belt, as well as data on hazards to spacecraft. To facilitate this discussion, figure 2 represents a model synthesized by Kessler (1970, and in this volume”). It is assumed here that the small particles and subvisual asteroid population can be represented by a power-law spectrum in mass in which N is the cumulative space density per cubic meter and the exponent is 0.84. The curve at the high-mass end represents the contribution of visual asteroids and the low-mass cutoff is at 10-9 g. Also shown is Kessler's model of the cometary meteoroid population. The horizontal bars represent the range of practical applicability of various instruments and techniques. The power-law exponent can provide clues to the collisional and possibly accretive processes currently taking place (Dohnanyi, 1969, and in this volume? Hellyer, 1970; Piotrowski, 1953). The small-particle cutoff yields information on the interaction of particles to radiation, presumably the Poynting-Robertson effect. It is evident that the sensors have a capability of determining both the small-particle cutoff and the power-law exponent, if a particle population of this nature exists. Moreover, data may be obtained regarding jetstreams, the subject appearing in several titles in this colloquium.

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Figure 2. —Kessler model. Cumulative space density in ecliptic plane at 2.5 AU. Curve A, asteroid population; curve C, cometary population.

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Of course, cometary meteor streams are well known, and these are also accessible to the sensors. The curves in figure 2 apply to points in space in the ecliptic plane at the solar distance of 2.5 AU. To obtain similar curves at other points, the Kessler model provides radial and latitude functions by which the curves are simply multiplied. This, of course, assumes that the curves are functionally separable from each other and from possible mass dependence. Kessler's radial curves are particularly interesting in their own right (fig. 3). The asteroid curve A is obtained by computer calculation, employing the orbital elements of all numbered asteroids, with correction for observational selection, and represents the sum of the contributions of each asteroid to the local space density. The effect of Jupiter is to concentrate the perihelia close to Jupiter's perihelion. The location of perihelia and aphelia of Earth, Mars, and Eros are shown. Off scale to the right would be Jupiter at 4.95 and 5.25 AU. The effect of the planets in depressing the local space density is noticeable. (See also Williams.19) The cometary curve, of course, is not so well known; but to the extent it can be believed, it represents a young population with moderate to large eccentricities, whereas the asteroid curve represents an old population with small eccentricities (Marsden, 1970). From the point of view of mission analysis, Eros is a prime target for rendezvous, landing, or even sample-return missions (Bender and Bourke;" | Mascy and Niehoff,” Meissinger and Greenstadt”) because of its orbital

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Figure 3.-Kessler model. Asteroid and cometary radial functions. Also shown are regions swept out by Earth, Mars, and Eros. f(r) is the log of the ratio of the asteroid spatial density at distance r to the spatial density at the center of the asteroid belt. Broken lines show the asymmetry of distribution in heliocentric longitude: upper and lower curves correspond to longitudes of Jupiter's perihelion and aphelion, respectively.

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characteristics and low gravity. There is great scientific interest in Eros. Does its shape imply that it is a fragment of a larger parent body? Is it solid iron (Anders, 1964)? Is it a potential source of stony meteorites, in the sense that eventually it will be scattered by Mars into Earth-crossing orbit (Wetherill and Williams, 1968)? Is it, despite its shape, a defunct cometary nucleus with possibly an associated non-Earth-crossing meteoroid stream (Marsden, 1970)? Is it, as Alfvén and Arrhenius suggest (1970a,b, and in this volume!"), a very ancient body and a possible source of primordial grains and gently treated meteoroidal material?


This report presents results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract no. NAS7-100.


Alfvén, H., and Arrhenius, G. 1970a, Mission to an Asteroid. Science 167, 139-141.
Alfvén, H., and Arrhenius, G. 1970b, Structure and Evolutionary History of the Solar
System, I. Astrophys. Space Sci. 8, 338-421.
Anders, E. 1964, Origin, Age and Composition of Meteorites. Space Sci. Rev. 3, 583.
Berg, O. E., and Richardson, F. F. 1969, The Pioneer 8 Cosmic Dust Experiment. Rev. Sci.
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Dohnanyi, J. S. 1969, Collisional Model of Asteroids and Their Debris. J. Geophys. Res.
74(10), 2531-2554.
Grün, E. 1970, Massenspectrometrische Analyse von Ionen bein Aufschlag schneller
Staubteilchen. Ph. D. Thesis. Univ. of Heidelberg.
Hellyer, B. 1970, The Fragmentation of the Asteroids. Mon. Notic. Royal Astron. Soc.
148, 383-390.
Houten, C. J. van, Houten-Groeneveld, I. van, Herget, P., and Gehrels, T. 1970,
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Kessler, D. J. 1970, Meteoroid Environment Model—1970 (Interplanetary and Planetary).
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TRW, Inc.

Investigation of extraterrestrial objects is habitually accompanied by the observation of extraterrestrial magnetic fields, which often have significant effects on the solar wind in the vicinity of the objects. Should we be surprised to find this experience repeated at an asteroid?

A recent study considered the conditions that would have to be satisfied by the surface magnetic field of a small planetary body at asteroidal distances so that the field would be an obstacle capable of stopping the solar wind or deflecting it sufficiently to generate a detectable magnetic interaction (Greenstadt, 1971). Meteoritic and lunar data indicate that magnetic field levels associated with material found in, or retrieved from, the extraterrestrial environment are compatible with levels demanded by the limiting conditions for the existence of identifiable magnetospheres around the largest asteroids. The conditions for asteroidal magnetospheres in the region 1 < r < 3.5 AU, as applied to hypothetical spherical bodies of dipole magnetic signature, are Summarized below and related to measurements of meteorite magnetizations, fields detected on the lunar surface, and magnetizations of lunar samples.


The magnetic field of a small planetary body must fulfill three scaling conditions to maintain a recognizable magnetic cavity from which the solar wind is excluded. First, the magnitude B, of the stopping field transverse to the Solar-wind flow at the upwind interface, or subsolar magnetopause, must be large enough to balance the bulk flow pressure; otherwise, there can be no magnetospheric barrier as we know it. Second, the field must extend at least the order of its own proton gyroradius across the solar-wind flow direction (Shkarofsky, 1965); otherwise, the plasma will be deviated rather than halted; edge-effect instabilities will predominate; the barrier, if any, will be ephemeral; and the field and plasma will intermingle, generating electromagnetic noise in various plasma wavemodes (Bernstein, Ogawa, and Sellen, 1968; Sellen and Bernstein, 1964). Finally, the field must extend upwind from the body a sufficient distance, on the order of the geometric mean of proton and electron gyroradii, to reverse the solar-wind particles before they intersect the body's surface (Dungey, 1958, p. 143); otherwise, only the body itself will properly constitute a barrier. Figure 1 illustrates these three conditions conceptually.

The conditions just enumerated yield expressions (Greenstadt, 1971) for the stopping field,

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where vow is the solar-wind velocity in kilometers per second, r is the solar distance in astronomical units, and n1 is the solar-wind proton number density at r = 1 AU, per cubic centimeter. These quantities are plotted in figure 2 for a quiet solar wind with vow = 320 km/s, n1 = 5 cm-3. The number distribution of asteroids versus solar distance r is superimposed (Alfvén and Arrhenius, 1970), and the radii and the orbital semimajor axes of several selected asteroids are indicated in the figure. Note that except for Eros, their sizes are comparable to, or larger than, the “quiet” proton gyroradius p. If a dipolar field is assumed for an asteroid so oriented that the solar-wind velocity vsw is in the plane of the dipole's equator, i.e., the magnetic axis is normal to the solar-wind flow, then the equatorial surface field Ba must exceed the following values to permit the establishment of a magnetosphere: For the proper minimal upwind stopping distance, 3 ) 10-2 y (1)

and for an upwind standoff distance and, therefore, a lateral dimension greater than 2p,

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where R is the radius of a postulated spherical asteroid, in kilometers. Steps in derivation of expressions (1) and (2) are given by Greenstadt (1971). Figures 1 and 2 illustrate that for large asteroids, the criterion of adequate lateral dimension is satisfied by the diameter of the body itself, so that the criterion of stopping distance, equation (1), is the important one Bo must

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