STATISTICS OF CLOSE APPROACHES BETWEEN ASTEROIDS AND PLANETS - PROJECT SPACEGUARD

Within Project SPACEGUARD, numerical integration for ≅200,000 years of a large number of orbits of planet-crossing asteroids has been used to generate a data base of close approaches to the major planets. These data are used to test the possibility of predicting-for a specific asteroid and for an entire population-the number of close approaches within a given distance, by using statistical theories such as the ones by Kessler (1981, Icarus 48, 39-48) and Wetherill (1967, J. Geophys. Res. 72, 2429-2444). The fundamental assumption of the statistical theories is the absence of mean motion resonance locking between the asteroid and the target planet. The orbits belonging to the class Toro-as defined in Milani et al. (1989b, Icarus 78, 212-269)-violate this assumption and indeed the numbers of close approaches in the data base are very diferent from the statistical predictions. For the other dynamical classes the statistical theories give very good predictions whenever the assumption on the relative orbital geometry are fulfilled; both Kessler theory and Wetherill theory have difficulties in predicting accurately close approaches between orbits which are either almost coplanar or almost tangent. We propose a modified version of Kessler theory which can cope with these singular cases and give very stable and reliable predictions of the number of close approaches at large to moderate distances. Even the use of the instantaneous orbital elements allows a fairly accurate computation of the total number of close approaches for an entire population; therefore, an accurate computation of the orbits is not necessary. However, these results cannot be extrapolated in an accurate way to predict the frequency of very close approaches, including physical collisions. By means of correlation analysis we have also tested the assumption-used in Monte Carlo studies-that the orbital elements of a planet-crossing orbit change only because of the close approaches; this is essentially true for the semi-major axis of such an orbit, provided it is not in resonance, either with the target planet (Toro class) or with Jupiter (Alinda class). The qualitative dynamical classification proposed in Milani et al. (1989b) is confirmed as a useful tool, although some specific attributions to a class have to be corrected on the basis of objective tests of the definitions of the classes. © 1990.