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Figure 1.-Conceptual view of conditions governing minimal asteroid magnetospheres caused by dipole field, as seen in noon-midnight meridian plane. (a) A solar-wind pressure of density nm grams per cubic centimeter and at velocity vow from the left of the diagram is balanced by energy of stopping field B, (n is the proton number density and m is the proton mass.) (b) Proton gyroradius p is at least commensurate with magnetospheric diameter. (c) Balance takes place far enough, at stopping distance approximating geometric mean of proton and electron gyroradiip and e (in field B.), to keep particles from hitting surface.

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Figure 2.-Dependence of stopping field B, stopping distance L, and proton gyroradius p in field B, on heliocentric distance r for quiet solar wind. Asteroid number distribution at bottom; dimensions and orbital semimajor axes of selected asteroids shown above on p, r scales, respectively. Dimensions of elongated Eros are from Roach and Stoddard (1938).


satisfy to guarantee a magnetopause standing away from the surface. For smaller asteroids, the field of equation (2) must provide the minimal transverse dimension, the diameter of the body being too small; the condition for minimal stopping distance is then automatically satisfied, because L “p always.


Figure 3 shows the dependence of minimal surface field Bo on asteroid radius R for the quiet conditions defined above at selected heliocentric distances. The distinct behavior of the two sets of curves reflects the distinction between criteria of stopping distance and lateral dimension for magnetosphere maintenance. The shaded area representing acceptable combinations of R and B, PBO is bounded by curves corresponding to the range of most common asteroid aphelia, 2 < r < 3.5 AU. Values of R corresponding to

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Figure 3.-Dependence of minimal equatorial dipole surface field Bo on assumed asteroidal radius R (curves), defining values of R and surface field Ba (shaded) capable of maintaining magnetosphere. Local fields measured by Apollos 12 and 14 indicated at right; radii of Ceres and Eros at bottom. R increases to the left.


Ceres and to Eros, a proposed destination for an asteroid mission, are indicated at the bottom of the figure. The range of dimensions of ellipsoidal Eros was obtained from Roach and Stoddard (1938). The lines designated Apollo 12 and Apollo 14 will be discussed in a later paragraph. The scale of minimal fields Bo covered in figure 3 is well within the range found for naturally occurring objects on Earth and in the solar system. Minimal surface fields as low as a few tens of gammas are sufficient to form an identifiable magnetic cavity around the largest asteroids. Fields on the same order as Earth's, Bo = 50 000), on the other hand, would be necessary for bodies of radii a few tens of kilometers to maintain magnetospheres against the pressure of the undisturbed solar wind at normal asteroid distances. The requirement on Eros' field is somewhat more lenient because of its smaller semimajor axis, but depends on which dimension is chosen to represent it in this application. In any case, minimal surface fields above 1000Y to 10 000) do not seem so unlikely that asteroids of radius 20 to 30 km or less should be excluded from consideration as magnetically potent objects on the basis of Bo alone. Larger bodies are perhaps more easily envisioned as likely to display the small surface fields required of them, however.


Equivalent Magnetization

In the preceding paragraphs, specification of fields was limited to “surface” values. Induced fields involving plasma sheaths or conducting materials are, of course, potential sources of Ba. For this discussion, however, the source of Ba will be attributed to hypothetical asteroidal magnetization to relate Ba directly to lunar and meteoritic measurements. In this context, minimal equivalent uniform magnetizations for spherical asteroids having radii corresponding to the Bo curves for r = 2.8 AU in figure 3 run between 6 × 10−3 and 2.5 × 10−' emuscn”. At an assumed density of 3 g/cm3, magnetizations might also be expressed as 2X 10-8 to 8.34 X 10-2 emulg. Because many asteroids are apparently not spherical, these figures can only serve as order of magnitude approximations.

If the conditions on Bo are thought of in terms of equivalent magnetization, what are the prospects that these conditions will be met by any asteroid? The evidence on which to base an answer to this question is sparse, being limited to a few data on meteoritic and lunar materials.

Meteorite Magnetizations

Magnetic characterizations of meteoritic material have led to the inference that the samples examined had been naturally magnetized in fields of extraterrestrial origin. Remanences of several samples of about 5X 10-3 to 4 × 10−3 emuscim” were attributed by Lovering (1959) to cooling in the

presence of a magnetic field. Stacey et al. (1961) investigated the thermomagnetic properties of chondritic meteorites and concluded that measured magnetizations resulted from cooling in extraterrestrial fields of 0.15 to 0.9 Oe. Additional results of a similar nature were reported by Stacey and Lovering (1959). The source of meteorite magnetizations was credited by the authors to cooling in the crust or mantle of a primary meteorite body with a fluid core generating an appreciable field much like Earth's. Insofar as the results cited apply to material that may be representative of objects in the asteroid belt, the presence there of small planetary bodies with magnetizations comparable to those required for minimal magnetospheres is not ruled out and would be consistent with the meteorite data.

Apollo Measurements

Direct measurements of local, steady magnetic fields have been made on the lunar surface with magnetometers carried by Apollos 12 and 14. Preliminary results from Apollo 14 indicate that a field of 100) was detected, but data were insufficient for determining the extent or character of the source (Palmer Dyal, personal communication). Apollo 12's ALSEP magnetometer, selfcontained and more elaborate than Apollo 14's, gave steady readings in the neighborhood of 36 y, together with gradient measurements that have been analyzed in some detail. The steady field was attributed to a source of moment between 1.4 x 1014 and 1 x 1023 y-cm3 located from 0.2 to 200 km from the apparatus (Dyal, Parkin, and Sonett, 1970).

The horizontal lines in figure 3 are entered at the appropriate field levels for the Apollo 12 and 14 results. The Apollo 12 measurement is shown as a line running from R = 200 km to small values of R beyond the edge of the graph. The Apollo 14 measurement is drawn as a dashed line across the graph because no dimensional inferences are available. The Apollo 12 field value is 50 percent larger and the Apollo 14 value four times larger than the Bo that would be needed to give Ceres a distinct magnetosphere. The Apollo 14 field is, in fact, about double the stopping field at the subsolar point of Earth's magnetopause. The Apollo 14 field, in contrast, is a factor of 30 smaller than the Bo necessary for Eros to balance the solar wind magnetically, even if its size were taken as large as 35 km. Neither result provides a combination of R and B, unambiguously inside the shaded region. On the other hand, neither result is confined to combinations of R and B, so far from the minimal curves of the shading boundary as to make later discovery of admissible combinations highly improbable, at least for asteroids of dimensions above 100 km. Eros would not be a candidate for magnetic opposition to the solar wind, based on these figures.

Lunar samples returned to Earth by Apollo 11 have been tested in the laboratory for their magnetic properties. A variety of results was described by numerous authors in the Moon issue of Science (Abelson, 1970). Of importance to this discussion was the measurement of a remanent magnetization of one breccia sample of 2.8 x 10-?'emulg (Strangway, Larson, and Pearce, 1970), attributable to ancient cooling in the presence of a field comparable to that of Earth and substantially within the range of equivalent minimal magnetizations imposed by the curves of figure 3. The origin of the onsite fields on the Moon and of returned sample magnetizations in lunar samples is unsettled. Interpreted at face value, the levels of field and magnetization recorded so far are on the order of those that could support the establishment of well-defined magnetic envelopes around the larger asteroids of radii greater than about 100 km.


Magnetospheric Interaction

A full-scale asteroidal magnetosphere will interact with the solar wind in a familiar way and should be detectable by conventional spacecraft magnetometers, although a close flyby will be necessary (Greenstadt, 1971). The interaction would include generation of a plasma shock ahead of the body and a magnetic tail downstream. The latter might be the most reliable indication of the existence of an asteroidal magnetic field, for a mission of limited target capability, because it would extend considerably behind the asteroid and be detectable much further from the body than would the magnetosphere proper. Transient components of Explorer 35's magnetometer measurements in the lunar wake have been attributed to the effect of asteroid-sized deposits of fossil magnetism on the Moon's surface (Binsacket al., 1970). The distance at which Explorer 35 detected these fluctuations behind the assumed lunar anomalies is equivalent to 5 to 10 Ceres radii and 20 to 40 radii of a 100 km asteroid.

Magnetospheric interaction would not be confined to simple exclusion of the solar wind from a magnetic cavity, but would include the generation of plasma waves and electromagnetic noise that would also be detectable far from the body.

Submagnetospheric Interaction

Fields less than those required for maintaining magnetospheres might still perturb the solar wind sufficiently to create measurable wave signals, as discussed by Greenstadt (1971). This type of “submagnetospheric” interaction seems the most probable, because the uniform magnetization of entire asteroids, especially the larger ones, that would be necessary to satisfy the stated conditions on Bo would be an unjustified assumption. The convenient assumptions of dipolar fields and axes normal to the solar wind are also unlikely. Especially interesting prospects would be the presence of a severely tilted or displaced dipole or a field of multipole origin in a body of nonuniform magnetization, or perhaps inhomogeneous conductivity. A hovering rendezvous

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