BOX 2.1 Asteroid Magnitudes and Sizes

The absolute magnitude H of an asteroid is a constant that represents its intrinsic brightness due to reflected sunlight in the V spectral band (the yellow-green region centered near the peak of the solar energy spectrum). The observed magnitude V of an asteroid depends on H and on the asteroid's distance from Earth (Δ), its distance from the Sun (r), and the angle (α), between the lines of sight to Earth and the Sun as seen from the asteroid:

H is determined from observations of V at times corresponding to specific values of Δ* and r (in astronomical units); f(α) is the phase function (a function of α that can be estimated in various ways).

The absolute magnitude depends on the size of the asteroid and its albedo (its reflectivity in a given spectral band). Thus, the asteroid's size can be estimated from H if the albedo can be measured or inferred from other observations (e.g., its spectral type). At absolute magnitude 18, an average S-type (relatively bright) asteroid is about 0.8 km in diameter, and an average C-type (dark) asteroid is about 1.6 km in diameter. There is, however, a factor-of-three uncertainty in the measured albedos of S-type asteroids and a similar uncertainty for C-type asteroids. Thus, the 0.8-km object cited above could reasonably be anywhere between 0.5 and 1 km in diameter. This factor-of-three uncertainly corresponds to a factor-of-eight uncertainty in volume.

decades-long interval during which no additional close approach will occur. Fainter-magnitude limits being achieved by CCD surveys conducted to discover NEOs are reducing the bias toward discovering objects only when they are in the near vicinity of Earth.

Prospects for progress in measuring NEO physical characteristics, especially their spectral properties, are illustrated in Figure 2.2, which shows the apparition circumstances for known near-Earth asteroids through the end of the twentieth century. With the commissioning of the Keck II 10-m telescope and NASA's participation in the project, there is the potential for pre-mission physical measurements at visible and near-infrared wavelengths of specific NEOs of high scientific interest. A dedicated 2-m-class telescope would permit most discovered NEOs to become accessible for physical characterization.

Perhaps the greatest progress and potential for direct physical measurements of NEOs will occur through radar observations that complement spectral studies.4 Of the 37 near-Earth objects detected as of 1997 by radar, 4 were first observed before 1980, 20 were first observed during the 1980s, and 13 were first observed during the 1990s. The Goldstone antenna of NASA's Deep Space Network is responsible for the sole detections of nine NEOs and the most informative observations of three others. Images with several tens of meters of resolution have been obtained for three objects—(1620) Geographos, (4179) Toutatis, and (6489) Golevka—and shape models have been constructed for those objects and (4769) Castalia.5 At least 100 of the currently known NEOs are expected to be detectable by the Arecibo telescope during its first decade of operation following the completion of a major upgrade in 1997. Given current NEO population estimates, a thorough survey could reveal a sufficient number of close Earth approaches to allow Arecibo to construct 1000-pixel images of about one object per month. Thus, radar offers tremendous potential for achieving detailed shape models for a large number of NEOs.

Understanding the Mineralogical and Chemical Compositions of Asteroids

Visible and near-infrared reflectance spectroscopy provides the most sensitive and broadly applied remote sensing techniques for characterizing the major mineral phases present within asteroids.6 At visible and near-



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