Effect of impactor area on collision rate estimates Page: 5 of 6
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area on those rates. This note uses a combination of analytic and numerical calculations to bound
the effect of impactor area on the rate of catastrophic collisions. The analytic discussion indicates
the types of approximations implicit in both treatments. A change of variables shows that the
ratio of the full and approximate rates is independent of the mass of the target objects and varies
only with the distribution exponent c and the mass-area scaling exponent s. A numerical
integration shows that the variation with s is negligible, that with c is about 10%, and that the
overall error is on the order of 30-40%, which is sufficiently small and varies so little for
parameters of interest that it could be neglected or inserted as a correction.
References
1. G. Canavan and O. Judd," Analytic Estimates of Space Debris Growth Rates," Los Alamos
National Laboratory report LA-UR-95-3588, November 1995.
2. G. Cleghorn, Orbital Debris (Washington, National Research Council, 1995).Fig. 4-1
3. D. Kessler, "Collisional Cascading: The Limits of Population Growth in Low Earth Orbit,"
Adv. Space Res, Vol. 11, 1991, p. (12)63.
4. D. Kessler and B. Cour-Palais, "Collision Frequency of Artificial Satellites: The Creation of a
Debris Belt," Journal of Geophysical Research, Vol. 83, 1 June 1978, p. 2639.3
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Canavan, G. H. Effect of impactor area on collision rate estimates, report, August 1, 1996; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc675589/m1/5/: accessed April 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.