4. Model diameters
Precise knowledge of the geometric albedo is needed if diameter calculation is to be attempted for individual asteroids. However, if the main goal is to examine the diameter distribution for a set of asteroids, it is possible to make use of the albedo distribution of the numbered asteroids. Previous results (Zellner and Bowell 1977, Ishida et al. 1984 and Gradie and Tedesco 1982) show a decreasing albedo-trend with increasing heliocentric distance. We have made an independent investigation based on geometric albedos from the IRAS Minor Planet Survey (Tedesco et al. 1992; hereafter IRAS). We have calculated the fraction (probability) for high () and low (p= ) albedo asteroids as a function of the semimajor axis (L95). The results are given in equation 8 where and are the low and high albedo fractions.
1) The probability for the asteroid to have low () geometric albedo is calculated using relation (8).
2) A random value, evenly distributed in the interval decides albedo class. If the random number is lower than the probability calculated in step 1, the low albedo class is chosen; if the random number is higher, the high albedo class is chosen.
3) The geometric albedo is randomly chosen from the corresponding normally distributed albedo function with mean value and standard deviation given in Table 6 (L95). The values in Table 6 are based on geometric albedos from IRAS.
Table 6. Mean values and standard deviations for the two geometric albedo distributions.
The above approach can produce erroneous albedos for individual asteroids, but the distribution for a large set of asteroids is reasonably correct. Given the geometric albedo and absolute magnitude, the formula
was used to calculate a model-diameter d in kilometers (Bowell and Lumme 1979). The above diameter calculation was done for all UESAC and PLS asteroids with a determined orbit. Fig. 3 shows the cumulative number per equal (0.1) log d interval for UESAC'92, UESAC'93 and PLS asteroids. The linear parts of the curves can be represented by expressions of the form:
The expressions are based on points in the interval .
© European Southern Observatory (ESO) 1997
Online publication: July 8, 1998