If one wants to study the physical characteristics of individual asteroids, he must first find them and be prepared to track them accurately during observation. To make the necessary predictions, the positions of asteroids are measured in reference frames defined by stars of known coordinates as the input information for calculation of orbits and ephemerides. Continuation of positional observations over lengthening arcs provides the basis for improvements of orbits and increased accuracy of ephemerides.

The Minor Planet Center at the Cincinnati Observatory is engaged in three kinds of activities: (1) the publication and distribution of the Minor Planet Circulars (MPC’s), (2) the collection and maintenance of a complete file of minor planet observations, and (3) the computation of orbital elements and ephemerides.

This report does not attempt to review all past and present work using asteroids for determinations of planetary masses and other fundamental constants. This would be a very large undertaking, and too extensively outside of the scope of a colloquium devoted to physical studies of minor planets. It seems preferable to concentrate more on principles involved, while mentioning only some of the various results obtained. At the same time, it will be appropriate to take note of the changed situation resulting from the recent development of certain modern methods and facilities that make it possible to determine some of the constants more accurately in other ways, thus partly eliminating the once dominant role of the minor planets.

Direct optical measurements of asteroid diameters obtained by telescopic observations are scarce. Although several adequate instrumentations and techniques are available for the purpose, they have not been used. The importance of these determinations should be stressed for the attention of observers.

The filar micrometer was used only by one observer during the last century, and no additional measures have been made since. This was in 1894 and 1895 when E. Barnard (1902) used the 90 cm refractor of Lick Observatory, and the 100 cm refractor of Yerkes Observatory. The results are as follows:

Ceres: apparent diameter at 1 AU: l˝.060, or 770 km (28 nights)

Pallas: apparent diameter at 1 AU: 0˝.675, or 490 km (5 nights)

Juno: apparent diameter at 1 AU: 0˝.266, or 195 km (5 nights)

Vesta: apparent diameter at 1 AU: 0˝.531, or 390 km (21 nights)

Before 1966, when Hertz (1966) published his first direct determination of the mass of Vesta, all our knowledge on asteroid masses was based on estimates. The masses of the first four minor planets resulted from the measured diameters by Barnard (1900) (see the paper by Dollfus in this volume) and from estimated mean densities. The diameters of the smaller objects were derived from their brightness and an estimate of their reflectivity (usually the reflectivity of the Moon was adopted). In 1901, Bauschinger and Neugebauer (1901) derived a value for the total mass of the first 458 asteroids. All the diameters were computed from the brightness with an assumed value for the reflectivity. The diameter of Ceres found in this way is very close to Barnard’s (1900) value. The mean density of the 458 asteroids was put equal to that of Earth, and their total mass resulted as 3 X 10-9 solar mass. Stracke (1942) used the same method with an increased material, but the addition of more than 1000 faint asteroids did not bring a significant change in the estimate of the total mass. The report on the McDonald asteroid survey (Kuiper et al., 1958) does not contain another estimate of the total mass of the asteroid ring, but it points to the possibility of a very rapid increase in the number of asteroids with decreasing absolute brightness. If this increase is strong enough, each interval of 1 mag in absolute magnitude can contribute the same amount to the total mass. In the range of magnitudes covered by the Palomar-Leiden survey (PLS) (van Houten et al., 1970), there are no indications for such a strong increase.

Over the past decade, largely because of the pioneer work of F. J. Low in Tucson, it has become possible to make accurate and reliable astronomical measurements at infrared wavelengths as long as 20 µm. At such wavelengths we see solar system bodies not by reflected sunlight but by their own thermal emission. The larger asteroids, though subtending small angles, give signals at 10 µm comparable in intensity with those from the brightest stars. It is now possible to determine the absolute flux from such asteroids to an accuracy of about 10 percent. Because an asteroid might reasonably be expected to have no atmosphere and no internal source of heat, the thermal radiation it emits must just balance the solar radiation it absorbs, and the measured flux will depend only upon its size. Infrared measurements therefore provide an opportunity to determine the diameters of the brighter asteroids.

This paper is a brief preliminary report about a program of reconnaissance photometry designed to study the thermal radiation emitted from asteroids. Observations of thermal radiation, and their subsequent interpretation, can provide new knowledge that presently cannot be gained by any other method. The emitted thermal power is by and large that portion of the insolation which is absorbed. Part of the asteroid’s emission spectrum can be observed through windows in Earth’s atmosphere. With the aid of models for the details of energy transfer at the asteroid’s surface, and accurate visual photometry, reliable estimates can be made for some of the important parameters in the models. Of particular interest are Bond albedo, size, emissivity, and thermal inertia.

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 µm 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.

The optical properties of the asteroids are compared with those of the Moon and various terrestrial, lunar, and meteoritic materials. It is concluded that the surfaces of most of the asteroids are covered with at least a thin layer of unconsolidated, fine-grained powder similar to lunar soil. None of the asteroids appear to have compositions corresponding to pure nickel/iron meteorites.

The question of what information about an asteroid's surface is contained in a measurement of the phase coefficient between phase angles of 10° and 30° is examined in detail. Contrary to some past claims it is shown that absolute reflectivities cannot be derived from phase coefficients. Furthermore, typical asteroid phase coefficients cannot be interpreted unambiguously. This is because the observed phase coefficient may depend as much on the photometric properties of an individual surface element as on the degree of large-scale surface roughness, and these two effects are impossible to separate if only disk integrated measurements are available. The wavelength dependence of asteroid phase coefficients should be small and should contain little information about the surface. In the case of irregular asteroids with macroscopically rough surfaces, the importance of large-scale shadowing, and hence the observed phase coefficient, will depend on the aspect of the asteroid. In such cases, therefore, phase coefficients must be carefully defined to be meaningful It should be possible, in some cases, to estimate the relative surface roughness of two quasi-spherical asteroids by combining photometric and polarimetric observations. For example, if the two asteroids have almost identical polarization curves but quite different phase coefficients, it is likely that the asteroid with the larger phase coefficient has a macroscopically rougher surface.

This is a brief report on the present status of asteroid polarimetry. A detailed paper is in preparation jointly with T. Gehrels.

The first polarization measurements of asteroids were made by Lyot (1934), who photographically determined the polarization curves of Ceres and Vesta. These curves are reproduced by Dollfus (1961). Unfortunately, because of the low sensitivity of the photographic method, they do not agree very well with recent photoelectric measurements.

The first photoelectric polarization measurements of asteroids were made by Provin (1955) (details of this work are given by Dollfus, 1961), and in recent years this work has been extended by Gehrels (unpublished) and by Veverka (1970). To date, fairly complete polarization curves for about a dozen asteroids have been obtained, and at least partial data are available for twice that number.

Curves of polarization are available at present for asteroids Vesta, Ceres, Pallas, Iris, Flora, and Icarus. These curves are compared with those of the satellites of Jupiter and Mercury, the Moon, and Mars. Laboratory simulations had already proved that the Moon's surface behaves like a powder of pulverized basalts; the recent confirmation by direct exploration is proving the significance of the method for remote determination of the surface properties of celestial bodies. The simulation of the Martian surface is found on small grained powders oxidized by ferreous limonite or goethite. New laboratory measurements were conducted to prepare the simulation of the asteroidal surfaces. Samples of the lunar surface returned to Earth provide impact-generated regolith and bare rocks superficially pitted and etched by impacts of the types suggested to be found on asteroidal surfaces; they were analyzed polarimetrically.

Preliminary interpretations show that Vesta departs significantly from the other asteroids and cannot be covered by frost deposits or by aggregate cosmic dusts; a regolith-type surface generated by impacts or a coating of cohesive grains is indicated.

Ceres, Pallas, and Iris are darker, and their polarizations do not suggest a pure regolithic surface, but cohesive grains or aggregates of dust are indicated.

Icarus is 108 times smaller in mass; its polarization authorizes a fluffy, loosely aggregated dust deposit; however, a cometary model with stones embedded in ice is perhaps not ruled out on the basis of the present data.

The way in which deep-space missions near the asteroidal belt can improve these results is discussed.

The brightness-time variation (the lightcurve) of an asteroid is observed to obtain the rate of rotation, some indication of the shape, and the orientation of the rotation axis in space. The brightness-phase relations are observed for the study of surface texture.

This paper deals specifically with observing routines and reductions, including discussions of lightcurves, rotation periods, absolute magnitudes, phase coefficients, opposition effects, and pole determinations. This paper supplements the review chapter by Gehrels (1970). Only photoelectric techniques are considered because the visual and photographic ones are, nearly without exception, not precise enough.

To evaluate the precision of the previously determined coordinates of the rotation axes (table I) we should review the methods (originally developed for 433 Eros) and logic of the various authors. Table II contains pole coordinates of Eros and the sources of these data. A critical summary of the work will enable us to make some conclusions concerning the poles presented.

There is general agreement that greatest rotational amplitude is observed when an asteroid is viewed equatorially, and we can detect three approaches to the determination of the Eros pole: the micrometer position angles observed by van den Bos and Finsen (1931); the graphic presentations used by Watson (1937), Stobbe (1940), and Rosenhagen (1932); and the mathematical model developed by Krug and Schrutka-Rechtenstamm (1936). These initial attempts yielded only approximate values, but the approximations were sometimes refined by analytical methods.

A simplified lightcurve inversion method is applied for the special case where observations are taken in the equatorial plane of the asteroid The solution is obtained in terms of a spotted two-surface model using Lambert’s law and geometrical reflectivities.

Photometric lightcurves of about 50 asteroids have been obtained over the past 20 yr, yet very little is known about the shape of these objects. Perhaps 100 lightcurves (including photographic ones) of 433 Eros have been obtained with amplitudes up to 1.5 mag. Some authors have attempted to calculate the dimensions of Eros assuming it to be a three-axis ellipsoid. The most recent determination (35 km, 16 km, 7 km) was given by Roach and Stoddard in 1938. In the case of 624 Hektor, amplitudes up to 1.1 mag were observed on lightcurves in which the primary and secondary maxima differed by less than 0.04 mag. Van Houten (1963) noted that for lightcurve amplitudes greater than 0.2 mag, the two maxima were about the same level and differed by 0.04 mag on the average.

Dunlap and Gehrels (1969) have published lightcurves of the Trojan asteroid 624 Hektor. They proposed a conventional explanation in which Hektor is regarded as having the shape of a cigar. Two circumstances suggest, but do not prove, that Hektor is a binary asteroid. (1) The cigar shape at the conventional density of stony meteorites (3.7 g-cm-3) appears to produce stresses that may well exceed the crushing strength of meteoritic stone. (2) The lightcurves exhibit an asymmetry changing with time that suggests librations of two ellipsoidal components. Observations are clearly required to look for these periodicities when we shall again be nearly in the plane of Hektor’s revolution (or rotation) in 1973. An additional supporting lightcurve is desirable in 1972 and also in 1974. The periods of libration are probably nearly 1 day, if they exist, so that observations should be made from more than one geographic longitude in 1973. The present paper is an exposition on these considerations.