We critically review the data on the sizes, shapes, albedos, and colors of cometary nuclei. Reliable sizes have been determined for 65 ecliptic comets (ECs) and 13 nearly isotropic comets (NICs). The effective radii fall in the range 0.2-15 km for the ECs and 1.6-37 km for the NICs. We note that several nuclei recently measured by the Hubble Space Telescope are subkilometer in radius, and that only 5 of the 65 well-measured EC nuclei have effective radii larger than 5 km. We estimate that the cumulative size distribution (CSD) of the ECs obeys a single power law with an exponent qS = 1.9 ± 0.3 down to a radius of ~1.6 km. Below this value there is an apparent deficiency of nuclei, possibly owing to observational bias and/or mass loss. When augmented by 21 near-Earth objects (NEOs) that are thought to be extinct ECs, the CSD flattens to qS = 1.6 ± 0.2. The cumulative size distribution of NICs remains ill-defined because of the limited statistical basis compared to ECs. The axial ratios a/b of the measured nuclei of ECs have a median value of ~1.5 and rarely exceed a value of 2, although it must be noted that the observed a/b values are often lower limits because of uncertainties in the aspect angle. The range of rotational periods extends from 5 to 70 h. The lower limit is significantly larger than that of main-belt asteroids and NEOs (~2.2 h, excluding the monolithic fast rotators), and this has implications for the bulk density of cometary nuclei. By combining rotation and shape data when available, we find a lower limit of 0.6 g cm-3 for the nucleus bulk density to ensure stability against centrifugal disruption. Cometary nuclei are very dark objects with globally averaged albedos falling within a very restricted range: 0.02-0.06, and possibly even narrower. (B-V), (V-R), and (R-I) color indices indicate that, on average, the color of cometary nuclei is redder than the color of the Sun. There is, however, a large diversity of colors, ranging from slightly blue to very red. While two comets have well-characterized phase functions with a slope of 0.04 mag deg-1, there is evidence for steeper (2P/Encke, 48P/Johnson) and shallower (28P/Neujmin 1) functions, so that the observed range is 0.025-0.06 mag deg-1. The study of the physical properties of cometary nuclei is still in its infancy, with many unresolved issues, but significant progress is expected in the near future from current and new facilities, both groundbased and spaceborne.
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