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Figure 4.—Infrared flux as a qualitative function of visible flux for a rotating, spherical minor planet with uniform albedo and zero obliquity.

dark asteroids. 313 Chaldaea was obtained near the end of the program when a small number of objects that were thought to be too faint for detection were observed. Considering this bias, it seems likely that there exist small, dark asteroids comparable in size and albedo to Phobos. Infrared observations of Phobos are extremely important. This control point will help to remove distortion in the radius and albedo scales due to differences in surface morphology between large and small asteroids. At the other extreme of the albedo range is type II bias. Here objects are unduly favored by observational selection. It is surprising that more of them were not discovered. This implies that they are not particularly abundant in the time and space regions sampled. At this time 20 Massalia and 39 Laetitia are the asteroids with the highest albedo. Their data are dispersed because of their lightcurves. In this reduction, their albedo is in the same class as 4 Vesta and perhaps J3, using Johnson's (1970) lunar-model values for the Bond albedo. For the large bodies without atmospheres, the trend in the inner part of the solar system is one of low albedo. The Moon, Mercury, and perhaps J4 can be thought of as part of a branch of large, dark objects. The light objects appear to be singular with no trend except for the sheer size of the Galilean satellites of Jupiter. At a radius of about 100 km the dark asteroids continue but they are now joined by objects with higher albedos. Considering the errors in the model and in the data, it would be risky to draw conclusions about any of the smaller features of figure 3. Infrared observations also have other applications that are not related to the main thrust of this project. For example, they can aid in the study of rotating asteroids. Consider a rotating, spherical asteroid with an absolutely uniform albedo. Figure 4 shows how the visible and infrared fluxes will be related. Before opposition, warm material is still seen after it crosses the evening terminator. After opposition, the morning terminator of the asteroid is viewed and cool material on the night side contributes only a small amount to the infrared radiation.

ACKNOWLEDGMENTS

The author thanks Bruce C. Murray for suggestions, encouragement, and discussions throughout the course of this project. Gordon Hoover assisted with all of the observations and was indispensable to the program. A special thanks goes to the staff of the Hale Observatories for the many courtesies that they rendered. This work was supported by the National Aeronautics and Space Administration Grant NGL 05-002-003.

REFERENCES

Allen, C. W. 1963, Astrophysical Quantities. Athlone Press. London.
Allen, David A. 1970, Infrared Diameter of Vesta. Nature 227, 158-159.
Gehrels, T. 1970, Photometry of Asteroids. Surfaces and Interiors of Planets and Satellites
(ed., Dollfus), ch. 6, pp. 317-375. Academic Press, Inc. New York.
Gehrels, T., Roemer, E., Taylor, R. C., and Zellner, B. H. 1970, Minor Planets and Related
Objects. IV. Asteroid (1566) Icarus. Astron. J. 75, 186-195.
Johnson, Torrence Vano. 1970, Albedo and Spectral Reflectivity of the Galilean Satellites
of Jupiter, p. 58. Ph. D. Thesis, Calif. Inst. of Tech.
Matson, D. L. 1971, Ph. D. Thesis, in preparation.
Smith, Bradford A. 1970, Phobos: Preliminary Results From Mariner 7. Science 168,
828-830.
Veverka, J., and Liller, W. 1969, Observations of Icarus: 1968. Icarus 10,441-444.

DISCUSSION

ANONYMOUS: What happens to the albedo as the size decreases?

MATSON: As the slide showed, we continue to get dark objects but we also seem to be seeing lighter objects at a model radius of about 60 km. Although we say there are some lighter objects, I could not really say which ones because I am worried about the extent of the lightcurve variation of these small objects.

ANONYMOUS: It would seem to me that the type of model that you consider should take into account the scattering properties of the surface material. Is this being done?

ALLEN: This is fairly ineffective. I think one cannot as yet try to arrive at any conclusions. Roughness and shape are the most important things and if we ultimately get accurate diameters, from some other method, and we only have two unknowns left, then eventually it can be solved—but not yet.

ANONYMOUS: What if the emissivities are not unity?

MATSON: For the brighter objects there are things that can be done (using observations at three wavelengths), and I am running models for Vesta that are fairly sophisticated in order to check. But for those asteroids with radii of less than 100 km I do not have much hope for improving the situation with the present data. For the smaller objects there is currently data at only 11.6 um. With future observations we may be able to work out some of the difficulties.

A REVIEW OF SPECTROPHOTOMETRIC STUDIES
OF ASTEROIDS*

CLARK R. CHAPMAW, TORRENCE V. JOHNSON,
A/VD THOMAS B. McCORD
Massachusetts Institute of Technology

It has long been realized that studies of the colors of asteroids provide useful clues to their composition. However, only since the development of photoelectric photometry have measurements of asteroid colors proven to be reliable. Recently, with advances in sensors and data systems, it has become possible to measure precisely the spectral reflectivity curves of asteroids from 0.3 to 1.1 pm with higher spectral resolution than that of the UBV system.

Until recently, attempts to determine asteroid composition by comparing color indices for asteroids with spectral reflectivities or color indices for meteorites and terrestrial rocks have not been fruitful (Kitamura, 1959; Watson, 1938). It has been noted that the mean color indices for asteroids fall within the range for rocks and meteorites. However, there are far too many minerals for a one-dimensional characterization of asteroid color (color index) to suggest even a compositional class, let alone a specific composition. But when the full spectral reflectivity curve is well defined, for instance in the 24 narrowband interference filters we have been using, the measurements are considerably more diagnostic. Especially diagnostic are well-defined absorption bands as have been found for Vesta (McCord et al., 1970) and a few other asteroids. For instance, the position of the center of the prominent band near 09 um due to Fe?" is dependent on mineralogy. Spectral reflectivity measurements of rocks and meteorites that have been published show a variety of spectral features ranging in strength from a percent to a few dozen percent that are repeatable for different rocks of identical mineralogy. An understanding of the basic physics of the production of absorption bands in solids is well developed, and it is possible to infer mineralogy from spectra containing such bands with considerable confidence. On the other hand, some solids show relatively featureless spectra, characterized only by their sloping trend and perhaps a few inflection points. Obviously such spectra cannot be uniquely diagnostic, but they can certainly rule out many possible compositional classes. A complete catalog of spectral reflectivities for all common rocks and meteorites has not yet been assembled, though many measurements have been made (Adams, unpublished; Adams and Filice, 1967; Hunt and Salisbury, 1970; Hunt and Salisbury, 1971). Once such a catalog is constructed it should be possible to determine much about the mineralogical composition of measured asteroids, particularly those with absorption bands in their spectra. Of great interest is the possibility of relating the many distinct classes of meteorites to specific asteroids, asteroid families, or portions of the asteroid belt, and of extending the many results of meteoritics to the asteroids. It is significant that the first conclusive identification of asteroid composition (McCord et al., 1970) shows that Vesta has a composition very similar to the Nuevo Laredo basaltic achondrite. It should soon be possible to relate the common classes of meteorites to specific asteroid families or parts of the belt, which will be a test of our understanding of the processes that transport asteroidal fragments into Earth-crossing orbits. Because the gross characteristics of most asteroid orbits probably have not changed substantially during the age of the solar system, what understanding has been achieved of the thermal and chemical environments where meteorites were formed (Anders, 1971) can then be tied to a specific location in the early solar system. Even when unique compositional identifications are not possible, spectral reflectivity measurements permit a sorting of asteroids into classes of similar composition. Asteroids with similar reflectivities may well be genetically related, especially when the asteroid population is examined statistically. Thus we will attempt to correlate asteroid colors with orbital characteristics, size, and lightcurves. We now describe some kinds of correlations that should be searched for and some implications such correlations might have if found. Correlation between color and semimajor axis a or the Jacobi constant (Tisserand invariant) may well be indicative of differences in the condensation of the solar nebula as a function of distance from the Sun. To the extent that it may be possible that ices could be stable over long durations in the outer parts of the asteroid belt (Watson, Murray, and Brown, 1963), some correlations with a could reflect on-going processes or conditions in the asteroid belt integrated over the age of the solar system. Asteroids with unusual inclinations or eccentricities have orbited the Sun in a different space environment than have most asteroids. In particular, the spatial density of small asteroids, meteoroids, micrometeoroids, and interplanetary dust is probably substantially lower away from the main part of the asteroid belt. On the other hand, the relative impact velocities against such space debris will be higher for asteroids in inclined or eccentric orbits. The glasses produced by hypervelocity micrometeoroid bombardment of the lunar regolith modifies spectral reflectivity curves for the Moon, primarily by lowering albedo and diminishing absorption band intensity (Adams and McCord, 1971). Also, it seems possible that there could be a greater meteoritic component (i.e., a contamination of the original asteroidal composition by material not originating on that asteroid) in asteroidal regoliths than the few percent determined for the lunar mare regolith. In fact, depending upon the mass-frequency relation for the population of impacting particles to which an asteroid is subject, a substantial regolith may never form on some asteroids. Any correlation of asteroid spectral reflectivity with variables correlated with an asteroid's impact environment may shed light on these processes. Several dozen Hirayama families, possible families, or jetstreams of asteroids with similar orbital elements have been recognized (e.g., see Arnold, 1969). It is particularly interesting to examine the colors of asteroids as a function of family. Though it is widely believed that members of a family are products of a collision or collisions, alternative hypotheses have been proposed. Fragmental family members might generally be expected to have identical colors, but differences within a certain family could be interpreted in terms of a highly differentiated asteroid being broken up or of the collisional fragmentation of two asteroids of similar size. Some asteroids have unusual rotation periods that may result from collisions. Other asteroids have large-amplitude lightcurves, suggesting either a markedly nonspherical shape or great differences in surface albedo on different sides of the asteroid. Either might result from initial conditions or from a major collision. Correlations between such characteristics and color might prove valuable, especially if these asteroids can also be related to particular meteorite groups. It is clear that studies of asteroid spectral reflectivities have great promise for shedding light on the origin, history, and current processes and state of the region of the solar system between 2 and 4 AU. But it is also clear that there are many variables to consider and hence much data are required for definitive conclusions. Future programs should take into account the following requirements: (1) It is imperative that the largest possible number and variety of asteroids be observed. This means that very faint (hence small) asteroids must be observed as well as the major ones. Several members of each asteroid family should be observed and of unusual | . classes of asteroids such as Apollo asteroids, Trojans, and dead * COmetS. (2) Asteroids should be observed at as many wavelengths throughout the visible and as far into the infrared (where most absorption bands occur) as possible. Ability to recognize reflectivity features at the 1 percent level would be desirable, and ability to measure band positions to 0.01 pum would be valuable. (3) Individual asteroids should be observed over a complete rotation and at a variety of solar phase angles. Reflectivity curves undoubtedly vary with phase angle and probably differently for different asteroids. Some small variation of color with rotation has been detected for at least one asteroid.

*Contribution No. 30 of the Planetary Astronomy Laboratory, Dept. of Earth and Planetary Sciences, MIT. A more complete treatment of this subject is found in Chapman (1971).

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